CHAPTER 41 OF BULFINCH'S METHOLOGY, THE AGE OF FABLE BULFINCH'S METHOLOGY, THE AGE OF FABLE, by Thomas Bulfinch CHAPTER 41 THE DRUITS, IONA The druids were the priests or ministers of religion among the ancient Celtic nations in Gaul, Britain, and Germany. Our information respecting them is borrowed from notices in the Greek and Roman writers, compared with the remains of Welsh and Gaelic poetry still extant. The druids combined the functions of the priest, the magistrate, the scholar, and the physician. They stood to the people of the Celtic tribes in a relation closely analogous to that in which the Brahmins of India, the Magi of Persia, and the priests of the Egyptians stood to the people, respectively, by whom they were revered. The druids taught the existence of one God to whom they gave a name, Beyal, which Celtic antiquaries tell us means the life of everything, or the source of all beings, and which seems to have affinity with the Phoenician Beyal. What renders this affinity more striking is that the druids as well as the Phoenicians identified this their supreme deity with the sun. Fire was regarded as a symbol of the divinity. The Latin writers assert that the druids also worshipped numerous inferior gods. They used no images to represent the object of their worship, nor did they meet in temples or buildings of any kind for the performance of their sacred rites. A circle of stones, each stone generally of vast size, enclosing an area of from twenty feet to thirty yards in diameter, constituted their sacred place. The most celebrated of those now remaining is Stonehenge, on Salisbury Plain, England. These sacred circles are generally situated near some stream or under the shadow of a grove or wide-spreading oak. In the center of the circle stood the Cromlec, or altar, which was a large stone placed in the manner of a table upon other stones set up on end. The druids also had their high places, which were large stones or piles of stones on the summits of hills. These were called cairns, and were used in the worship of the deity under the symbol of the sun. That the druids offered sacrifices to their deity there can be no doubt, but there is some uncertainty as to what they offered, and of the ceremonies connected with their religious services we know almost nothing. The classical Roman writers affirm that they offered on great occasions human sacrifices, as for success in war, or for the relief of dangerous diseases. Caesar has given a detailed account of the manner in which this was done. They have images of immense size, the limbs of which are framed with twisted twigs, and filled with living persons. These being set on fire, those within are encompassed by the flames. Many attempts have been made by Celtic writers to shake the testimony of the Roman historians to this fact, but without success. The druids observed two festivals each year. The former took place in the beginning of May, and was called Beltane, or Fire of God. On this occasion a large fire was kindled on some elevated spot, in honour of the sun, whose returning beneficence they thus welcomed after the gloom and desolation of winter. Of this custom a trace remains in the name given to Whitsunday, in parts of Scotland to this day. Sir Walter Scott uses the word in the boat song in The Lady of the Lake. Ours is no sapling chanced sown by the fountain, blooming at Beltane in winter to fade. The other great festival of the druids was called Sawan, or Fire of Peace, and was held at Hollow Eve, 1st of November, which still retains this designation in the Highlands of Scotland. On this occasion the druids assembled, in solemn conclave, in the most central part of the district, to discharge the judicial functions of their order. All questions, whether public or private, all crimes against person or property, were at this time brought before them for adjudication. With these judicial acts were combined certain superstitious usages, especially the kindling of the sacred fire from which all the fires in the district, which had been beforehand scrupulously extinguished, might be relighted. This usage of kindling fires on Hollow Eve lingered in the British Islands long after the establishment of Christianity. Besides these two great festivals, the druids were in the habit of observing the full moon, and especially the sixth day of the moon. On the latter they sought the mistletoe which grew on their favourite oaks, and to which, as well as to the oak itself, they ascribed a peculiar virtue and sacredness. The discovery of it was an occasion of rejoicing and solemn worship. They call it, says Pliny, by a word in their language which means, heal all, and having made a solemn preparation for feasting and sacrifice under the tree. They drive thither two milk-white bulls, whose horns are then for the first time bound. The priest, then, robed in white, ascends the tree, and cuts off the mistletoe with a golden sickle. It is caught in a white mantle after which they proceed to slay the victims, at the same time praying that God would render his gift prosperous to those to whom he had given it. They drink the water in which it has been infused, and think it a remedy for all diseases. The mistletoe is a parasitic plant, and it is not always nor often found on the oak, so that when it is found it is the more precious. The druids were the teachers of morality, as well as of religion. Of their ethical teaching a valuable specimen is preserved in the triads of the Welsh bards, and from this we may gather that their views of moral rectitude were on the whole just, and that they held and inculcated many very noble and valuable principles of conduct. They were also the men of science and learning of their age and people. Whether they were acquainted with letters or not has been disputed, though the probability is strong that they were, to some extent. But it is certain that they committed none of their doctrine, their history, or their poetry to writing. Their teaching was oral, and their literature, if such a word may be used in such a case, was preserved solely by tradition. But the Roman writers admit that they paid much attention to the order and laws of nature, and investigated and taught to the youth under their charge many things concerning the stars, and their motions, the size of the world and the lands, and concerning the might and power of the immortal gods. Their history consisted in traditional tales in which the heroic deeds of their forefathers were celebrated. These were apparently inverse, and thus constituted part of the poetry as well as the history of the druids. In the poems of Ocean we have, if not the actual productions of druidical times, what may be considered faithful representations of the songs of the Bards. The Bards were an essential part of the druidical hierarchy. One author, Pennant, says, the Bards were supposed to be endowed with powers equal to inspiration. They were the oral historians of all past transactions, public and private. They were also accomplished genealogists, etc. Pennant gives a minute account of the Eisteddfads, or sessions of the Bards and minstrels, which were held in Wales for many centuries long after the druidical priesthood in its other departments became extinct. At these meetings none but Bards of Merritt were suffered to rehearse their pieces, and minstrels of skill to perform. Judges were appointed to decide on their respective abilities, and suitable degrees were conferred. In the earlier period the judges were appointed by the Welsh princes, and after the conquest of Wales, by commission from the kings of England. Yet the tradition is that Edward I, in revenge for the influence of the Bards in animating the resistance of the people to his sway, persecuted them with great cruelty. This tradition has furnished the poet Gray with the subject of his celebrated ode, the Bard. There are still occasional meetings of the lovers of Welsh poetry and music held under the ancient name. Among Mrs. Hemons' poems is one written for an Eisteddfad, or meeting of Welsh Bards, held in London May 22nd, 1822. It begins with a description of the ancient meeting, of which the following lines are apart. Mids the eternal cliffs whose strength defied the crusted Roman in his hour of pride, and where the druids ancient Cromlech frowned, and the oaks breathed mysterious murmurs round, there thronged the inspired of yore on plain and height, in the sun's face beneath the eye of light, and bearing unto heaven each noble head stood in the circle where none else might tread. The druidical system was at its height at the time of the Roman invasion under Julius Caesar. Against the druids as their chief enemies, these conquerors of the world directed their unsparing fury. The druids, harassed at all points on the mainland, retreated to Anglesey and Iona, where for a season they found shelter, and continued their now dishonored rites. The druids retained their predominance in Iona, and over the adjacent islands and mainland, until they were supplanted, and their superstitions overturned by the arrival of St. Colombo, the apostle of the Highlands, by whom the inhabitants of that district were first led to profess Christianity. Iona One of the smallest of the British Isles, situated near a rugged and barren coast, surrounded by dangerous seas and possessing no sources of internal wealth, Iona has obtained an imperishable place in history as the seat of civilization and religion at a time when the darkness of heathenism hung over almost the whole of northern Europe. Iona, or Icon Kill, is situated at the extremity of the island of Maul, from which it is separated by a strait of half a mile in breadth, its distance from the Scottish mainland being thirty-six miles. Colombo was a native of Ireland, and connected by birth with the princes of the land. Ireland was at that time a land of gospel light, while the western and northern parts of Scotland were still immersed in the darkness of heathenism. Colombo with twelve friends landed on the island of Iona in the year of our Lord five sixty-three, having made the passage in a wicker boat covered with hides. The druids who occupied the island endeavored to prevent his settling there, and the savage nations of the adjoining shores incommodated him with their hostility, on several occasions endangering his life by their attacks. Yet by his perseverance and zeal he surmounted all opposition, procuring from the king a gift of the island, and establishing a monastery there, of which he was the abbot. He was unwirried in his labours to disseminate a knowledge of the scriptures throughout the highlands and islands of Scotland, and such was the reverence paid him that though not a bishop, but merely a presbyter and monk, the entire province with its bishops was subject to him and his successors. The Pictish monarch was so impressed with a sense of his wisdom and worth that he held him in the highest honour, and the neighbouring chiefs and princes sought his council, and availed themselves of his judgment in settling their disputes. When Columba landed on Iona he was attended by twelve followers whom he had formed into a religious body of which he was the head. To these, as occasion required, others were from time to time added so that the original number was always kept up. Their institution was called a monastery, and the superior an abbot, but the system had little in common with the monastic institutions of later times. The name by which those who submitted to the rule were known was that of Kaldes, probably from the Latin, Cultore's Dei, worshippers of God. They were a body of religious persons associated together for the purpose of aiding each other in the common work of preaching the gospel and teaching youth, as well as maintaining themselves in the fervour of devotion by united exercises of worship. On entering the order certain vows were taken by the members, but they were not those which were usually imposed by monastic orders, for of these which are three, celibacy, poverty, and obedience. The Kaldes were bound to none except the third. To poverty they did not bind themselves, on the contrary they seemed to have laboured diligently to procure for themselves and those dependent on them the comforts of life. Marriage was also allowed then, and most of them seemed to have entered that state. True, their wives were not permitted to reside with them at the institution, but they had a residence assigned to them in an adjacent locality. Near Iona there is an island which still bears the name of Island Namban, women's island, where their husbands seemed to have resided with them, except when duty required their presence in the school or the sanctuary. Campbell, in his poem of Ray Ulura, alludes to the married monks of Iona. The pure Kaldes were Albin's earliest priests of God, ere yet an island of her seas, by foot of Saxon Monk was trod. Long ere her churchmen by bigotry were barred from Holy Wedlock's tie, to as then that E. famed afar, in Iona preached the word with power, and Ray Ulura, beauty star, was the partner of his bower. In one of his Irish melodies Moor gives the legend of St. Sinanus and the lady who sought shelter on the island, but was repulsed. Oh hasten leave this sacred isle on Holy Bark ere morning smile, for on thy deck though dark it be, a female form I see, and I have sworn this sainted sod shall ne'er by women's foot be trod. In these respects and in others the Kaldes departed from the established rules of the Romish church, and consequently were deemed heretical. The consequence was that as the power of the latter advanced that of the Kaldes was enfeebled. It was not however until the thirteenth century that the communities of the Kaldes were suppressed and the members dispersed. They still continued to labour as individuals, and resisted the inroads of papal usurpation as best they might, till the light of the Reformation dawned on the world. Iona, from its position in the western seas, was exposed to the assaults of the Norwegian and Danish rovers by whom those seas were infested, and by them it was repeatedly pillaged, its dwellings burnt, and its peaceful inhabitants put to the sword. These unfavourable circumstances led to its gradual decline, which was expedited by the subversion of the Kaldes throughout Scotland. Under the reign of Popery the island became the seat of a nunnery, the ruins of which are still seen. At the Reformation the nuns were allowed to remain, living in community when the abbey was dismantled. Iona is now chiefly resorted to by travellers, on account of the numerous ecclesiastical and sepulchral remains that are found upon it. The principal of these is the cathedral or abbey church, and the chapel of the nunnery. Besides these remains of ecclesiastical antiquity there are some of an earlier date, and pointing to the existence on the island of forms of worship and belief different from those of Christianity. These are the circular cairns which are found in various parts, and which seem to have been of druidical origin. It is in reference to these remains of ancient religion that Johnson exclaims, that man is little to be envied whose patriotism would not gain force upon the plains of Marathon, for whose piety would not grow warmer amid the ruins of Iona. In the Lord of the Isles Scott beautifully contrasts the church on Iona with the cave of Stapha opposite. Nature herself it seemed would raise a minister to her maker's praise, nor for a meaner use ascend her columns or her arches bend. Nor of a theme less solemn tells that mighty surge that ebbs and swells, and still between each awful pause from the high vault an answer draws, in varied tone prolonged and high, that mocks the organ's melody. Nor doth its entrance front in vain to old Iona's holy feign, that nature's voice might seem to say, well hast thou done, frail child of clay, thy humble powers that stately shrine tasked high and hard, but witness mine. End of Bullfinch's mythology, the age of the fabled by Thomas Spoolfinch.


Everyone, it's your girl, Kenzie here from Leighton Sports Cards, and I am ripping here from the National. We've got 21-22 Panini Frizz and Basketball Hobby, pre-box break number 21, Random Teams. Again, here's a look at the random results. You can always find these at leightonsportscards.com underneath the results tab, and the link is also in chat for you. All right, here we go. Where's the blue one right now? Oh no, that one's yours. I took my yellow one. I didn't need one. It's mine. Let's get out of there. 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Good evening, aspirants. Welcome to the Hindu Daily News Analysis for the date 11th of January, 2023, brought to you by Shankar Ice Academy. Displayed here are the articles which we are going to discuss today. Interested aspirants can go through it. With this, let's start with our first news article for the day. Now, take a look at this editorial. This article talks about the recently concluded Kasi Tamil Sangam. Since this editorial is written by our Union Minister, it becomes important for our examination. Now, let us try to decode some important points given in this article through our discussion. Before that, the syllabus relevant for this article is highlighted here. Interested aspirants can go through it. Now, let's see in brief about the Kasi Tamil Sangam. See, it was a month-long program which was held in Varanasi, Uttar Pradesh in the months of November and December last year. This program was an initiative by Government of India as part of the Asadika Amrit Magotsav and to uphold the spirit of Ek Bharat Shrestha Bharat. The objective of the program was to celebrate, reaffirm and rediscover the old links between Tamil Nadu and Kasi. I hope you all remember about Asadika Amrit Magotsav. See, it was an initiative of the Government of India to celebrate and commemorate 75 years of Indian independence. On the other hand, Ek Bharat Shrestha Bharat aims to enhance interaction and promote mutual understanding between peoples of different states and union territories through the concept of state-wise pairings. The states carry out activities to promote a sustained and structured cultural connect in the areas of language learning, culture, traditions and music, tourism and cuisine, sports and sharing of best practices, etc. With this basic understanding about Amrit Ka Asadika Magotsav and Ek Bharat Shrestha Bharat, let us see some important features of this event. Here note that Kasi Tamil Changamam celebrated many aspects of the historical and civilizational connection between India's North and South. Now, let us see some features of cultural connectivity between Kasi and Tamil Nadu. See, Kasi is the cultural capital of India, whereas Tamil Nadu and Tamil culture is the centre of India's antiquity and pride. Know that Kasi is one of the world's oldest living cities, while Tamil is one of the oldest languages spoken presently in the world. So, this Kasi Tamil Changamam tried to connect both these old traditions together. Here note that both Kasi and Tamil Nadu have rich, old traditions of arts, music, craftsmanship, philosophy, spirituality and literature. During ancient times, for devotees who could not visit Kasi, the Pandyas had built the Kasi Vishwanadhar Temple. Today, this temple is located in the district of Tenkasi, which is present in the state of Tamil Nadu. Even today, the relevance of Kasi Athra comes up during the traditional Tamil marriage processions. The Kedareswara Temple at Kedargat is the oldest temple which was renovated in the Dravidian style by Kumara Guru Bharat, who was a Tamil poet. See, this Kumara Guru Bharat founded the Kumaraswami Muth, which continues to look after the temple. Here note that the first elaborate record of a Tamil saint's arrival at Kasi after Adi Shankara is the one of Kumara Guru Bharat. He is known to have sought land from the Mughal prince Dara Shikho and established the Kumaraswami Muth in the 1600s. This Muth still exists and manages the Kedareswara Temple at Kedargat. See, this is an perfect example of cultural connectivity which existed in the medieval times between Tamil Nadu and Kasi. A Tamil poet who went to live in Kasi established a Muth which looked after the Kedarswara Temple. Now, coming to one another great poet of Tamil Nadu. Sri Subramanya Bharati was born in Tamil Nadu, lived in Kasi for many years. By living there, he learned the Hindi languages and appreciated the cultural link which was present between Tamil Nadu and the northern parts of India. Sri is one of the most famous Tamil poets who is frequently quoted in Tamil literature even today. What we have seen till now are some of the cultural connectivity that prevailed between Tamil Nadu and Kasi in the last years. Now, moving on. See, actually the broader objective of the event is to bring two knowledge and cultural traditions of that of the north and south of India closer and create an understanding of our shared heritage and deepen the people-to-people bond between the regions. To make that possible, the event was organized by the Ministry of Education in collaboration with various other union ministries. Here, note one important fact. Aigbaras Trastha Bharat is an initiative which is overseen by the Ministry of Education. So, in prilams, if a question is asked, what is the nodal ministry for Aigbaras Trastha Bharat, the correct answer will be Ministry of Education. Now, coming back. The Sangamam created a unique platform to rediscover and integrate our heritage and ancient knowledge with modern thought, philosophy, technology and craftsmanship. For example, we know that Varanasi is well known for Banaras silk series and the district of Kanjiburam which is present in Tamil Nadu is also well known for its silk series. So, by connecting both these places, its viewers can transform the traditional accumulated knowledge between them. By this way, we can promote innovation in the silk saree industry. This is what the Sangamam tried to do. Here, note that multiple departments of the union government participated in the event. By doing so, the participants who participated in the Kasi Tamil Sangamam got exposed to modern practices of branding, quality control, marketing, product consistency, use of modern machinery and value addition. So, from this, we can say that this initiative was not only to connect both different parts of India but also to act as an initiative which promotes innovation and entrepreneurship among the people who participated in it. Here, note that the government even organized a textile scorn claim during the Sangamam. Why specifically textile sector? See, it is because of its great job creating potential. The technical textiles portion in the sector as possibility to grow more. Here, the term technical textile products include functional textiles that are used in vehicles, protective clothing, bulletproof vests and construction. So, the textile scorn claim which was organized during the Tamil Kasi Sangamam included a specific area for technical textiles. Other than this, the article also talks about Mr Modi's 5F formula. Here, the 5F formula encompasses form to fiber, fiber to factory, factory to fashion, fashion to foreign. Here, the idea was to create a complete textile manufacturing ecosystem in India. Since no other competing nation will have a complete textile ecosystem like us, this integrated vision will aid in the economic growth of the textile sector in our country. The latest initiative launched by the government in regard to textile sector is the PM Mitra initiative. This initiative creates a wider textile ecosystem in India which manufactures good quality textiles for the world market. Now, coming to the other schemes discussed in the article. One important scheme the article talks about is one district, one product scheme. See, the scheme aims to realize our PM's vision of fostering balanced regional development across all districts of the country. Basically, the idea is to select, brand and promote one product from each district of our country. Here, note that our Prime Minister is currently acting as a brand ambassador for these products and often gives them to world leaders when he is visiting their countries. So, the article says that the one district, one product scheme will take India products to the world market. The other important initiatives mentioned in the article are open network for digital commerce and the government e-marketplace. See, both these initiatives are brought by the union ministries to give a real boost to the marketing of traditional products, which are made in India. Make note of both these initiatives. We will discuss about them sometime later. Now, moving on. See, the Kasi Tamil Sangamam was in line with the National Education Policy 2020. Here, note that National Education Policy 2020 focuses on integrating the wealth of Indian knowledge system with modern systems of knowledge. I am quoting National Education Policy 2020 here because, the Kasi Tamil Sangamam aimed to provide an opportunity for people from all walks of life, including scholars, students, philosophers, traders, artisans, etc., from the two regions to come together, share their knowledge, culture and best practices and learn from each other's experiences. With this, we have come to the end of this discussion. Before ending our discussion, let us see the educational partners for this Kasi Tamil Sangamam. Here, note that IIT Madras and Banaras Hindu University acted as the two implementing agencies for the program. The Sangamam ended on December 16th and about 2 lakh people visited the campus of Banaras Hindu University between the one month period of Kasi Tamil Sangamam. From this discussion, we can conclude that Kasi Tamil Sangamam has really ignited a new cultural zeal in India and wetted the country's appetite for more. Through this discussion, we discussed about all the aspects of Kasi Tamil Sangamam in detail. With these points in mind, now let's move on to the next news article discussion. Take a look at this news article. According to the news article, the central government has deputated the Central Reserve Police Force to give arms training to village defense committees in the region of Jammu. Recently, there were terror attacks in Jammu and Kashmir that resulted in the death of seven civilians. So, the union government is re-establishing these village defense committees and renamed them as village defense guards. See, these village defense guards are going to act as a deterrent against the terrorist attacks. This is about the news article given here. In this context, let us see about this village defense guards. If you had noticed carefully, I used the word re-establish instead of the word establish. This is because the village defense committees are making a comeback after three decades. The village defense committees were first set up in the year 1995. They were set up by the government with the view that they will act as a force multiplier against militant attacks. The village defense committees have now been renamed as village defense guards. The newly formed village defense guards will function under the direction of the SP or SSP of the district concerned. Now, coming to the question, how are the village defense committees different from the village defense guards? See, for the most part, both are same. Here note that both village defense guard and village defense committee is a group of civilians who are provided with guns and ammunition to tackle militants in case of attack until the arrival of the security force. The only major difference between the two is in terms of renumeration. Under the new scheme, the persons leading the village defense guard will be paid Rs. 4500 per month by the government, while others will get Rs. 4000 each. In the village defense committees, only the special police officer leading them were provided a renumeration of Rs. 1500 monthly. The other members of the village defense committees were only volunteers. We saw that in the village defense guards, the civilians are provided with arms and training. Why do you think the government has decided to arm up its civilians? How did this idea first come up? See, during the 1965 and 1971 Indo-Pakwas, the government armed the ex-servicemen and youth along the border villages of Jammu and Kashmir to curb the infiltration of Pakistani spies. This particular scheme saw some success, with locals guarding their areas even at night. The success of this prompted the government to set up village defense committees in the year 1995. These committees were also quite successful. Since the committees had members from the local community, they were well versed in the local topography. Due to this fact, they played a significant role in combating militancy particular in areas where there were poor road connectivity. They were one of the most feared armed groups among militants. They primarily operated in areas where the armed forces found it difficult to arrive on time due to difficult terrain. But later, there were demands from certain quarters of the population to disband the village defense committees. This is due to the rise in allegations of crime including abduction and rape by the members of the village defense committees. The committees also faced allegations of human rights violation. So, over a period of time, the numbers of village defense committees members had dropped significantly. And after some time, they ceased to exist due to the lack of government support. But right now, due to increasing cases of targeted killing in Jammu and Kashmir, the government has felt the need to arm the civilians. So, they have renamed the village defense committees as village defense guards and deputed the central reserve police force to provide the necessary training. The CRPF has been asked to train civilians only in Rajauri and Poonch districts. I am sure more opinion pieces would be written about this move of the government in the coming days. Until then, I am just asking for your opinion. Do you think it is a right move to arm civilians to act as deterrents against terrorists? Post your opinion in the comment section. With this, let's move on to the next news article discussion. Look at this news article given here. This article states that the National Human Rights Commission has issued notices to the collector of Kalahandi in Odisha. See, an incident happened in Odisha where a pregnant woman went into labor. So, the ambulance was contacted. But unfortunately, the ambulance could not reach the remote village due to poor road connectivity. So, the family members had to carry the woman by a cot across Indraavadi river on a country boat. In this regard, the National Human Rights Commission directed the collector to submit a report within four weeks. This is all about the article given here. Taking this as an opportunity, we will revise about National Human Rights Commission in Prilam's point of view. See, National Human Rights Commission of India was established on 12th October 1993. See, it was established under the Protection of Human Rights Act. So, it is a statutory body and not a constitutional body. See, it is equated in New Delhi. Here, know that in 1993, the United Nations General Assembly in Paris adopted a resolution regarding the principles of human rights. These principles came to be known as Paris Principles. NHRC was established in India in conformity with these Paris principles only. Basically, NHRC works for the promotion and protection of human rights. This is about a beef bragground about NHRC. Now, coming to the members present in it. Currently, the NHRC is a multi-member body consisting of a chairman and five members. Chairman should be a retired Chief Justice of India or a Judge of the Supreme Court. Regarding the other five members, one member should be a retired or serving Judge of the Supreme Court of India and one member should be a retired or serving Chief Justice of a High Court. And other members should be amongst persons having knowledge or practical experience in human rights issues. Important fact to be noted here is that, out of these three members, at least one person should be a woman. In addition to this, the chairpersons of various national commissions like that of what I provided here are also deemed to be members of NHRC. So, in total, the commission has one chairman, five full-time members and seven deemed members. The chairperson and members are appointed by the president by warrant under his hand and seal. Before appointing these persons, president has to get the recommendations of a committee of six members. Now, let's learn about this particular appointment committee of NHRC. Here note that, Prime Minister acts as the chairperson of this committee. It also includes the Speaker of the House of the People or Lok Sabha, Home Minister, Leader of Opposition in Lok Sabha, Leader of Opposition in Rajasabha and Deputy Chairman of the Rajasabha. This is all about the appointment committee of NHRC. Now, let's learn about the term of the NHRC chairman and its members. Chairperson or members of NHRC holds office for a term of three years or until the age of 70. They are also eligible for reappointment. But here note that, chairperson or member of NHRC are not eligible for further employment under Indian government or any state government. This is all about the term of the members of NHRC. With this, we have come to the end of this discussion. Through this discussion, we have revised some basic points about NHRC. With these learned points, now let's move on to the next news article discussion. Now, have a look at this data point provided here. This column visualizes the data about the status of same-sex marriage in the present world. So, now let's see the reason why suddenly this data point has appeared in the news today. See, last Sunday, thousands of members and supporters of LGBTQ plus community came to the streets of New Delhi. They agitated for the equal marriage rights to be provided to them. This agitation was due to the fact that Supreme Court recently transferred the petitions to itself which are pending in various psychotes. The transferred petitions were related to providing legal recognition of same-sex marriages in India. The Supreme Court's move has renewed the vigor among the members of the LGBTQ plus community to obtain legal status for their marriages. This is why this data point about same-sex marriage is given today in the Hindu. In this context, let's learn about the points provided in the article. First of all, let's have an idea about the legal status of LGBTQ plus community in India. See, section 377 of the IPC dealt with the cases of homosexuality in India. This section stated that whoever voluntarily has carnal intercourse against the order of nature with any man, woman or animal shall be punished.  And they were even considered as offenses under this section. In the year 2018, the Supreme Court in the famous Nauta Singh Joker case decriminalized homosexuality by striking out some of the parts of section 377 which criminalized homosexuality. It held that the criminalization of sexual relationship between adults of the same sex were unconstitutional.  And both these sexual streams are still considered to be offenses under section 377 of the IPC. So, if a question is asked in the prelims saying that section 377 of IPC was completely done away by the judgment of Nauta Singh Joker case, the statement is wrong. Only some parts of the section which deal with homosexuality was declared unconstitutional, while the other provisions of the same section are still in force. Despite the 2018 ruling, members of LGBTQ community in India are complaining about the lack of acceptance and discrimination in the society. Here know that Supreme Court has only decriminalized homosexuality, but neither the Supreme Court nor the government provided any legal status or rights such as marriage rights to the LGBTQ plus community. This is why several petitions asking for the providing legal rights for marriages between the LGBTQ community members were filed in many high courts around India. So, to answer this question only Supreme Court clubbed all these petitions and took it upon itself to answer the question of whether marriages among LGBTQ plus community members can be given legal status or not. With this basic understanding about LGBTQs legal status in India, we will analyze the data points provided in the article. Now, look at this chart. This chart shows us the number of people in countries where same sex marriage is legal and those in nations where the same sex marriage is not legal. The data says that currently more than 6.77 billion people around the world are living in countries where same sex marriage is not legal and only 1.21 billion are living in nations where it is legal. From this we can infer that worldwide most of the nations have not yet provided legal status for marriages among LGBTQ community members. Here know one important fact, the Netherlands was the first country to make same sex marriages legal in the year 2000. Now, look at this another chart. This chart shows us the legality of same sex marriages in countries where homosexuality is legal as of 2022. See, only 32 countries have legalized same sex marriage, whereas in 91 countries it is currently illegal. Now, look at this map. This map depicts the geographical spread of same sex marriage recognition as of 2022. See, most of the countries in Europe, Oceania, North and South America have legalized same sex marriage or at least given restricted rights to such couples. But very few nations in Asia and Africa have legalized same sex marriage. Notably, in many of these African and Asian nations, homosexuality has been decriminalized in recent decades. India is one among the examples of this particular case. However, legal status has not been given to same sex marriages in these countries. Now, look at this chart. This is about a survey which was conducted by the Pew Research Center. The survey was conducted across 34 countries between May 13 and October 2 of the year 2019. The survey says that only 37% of respondents from India said that homosexuality should be accepted by society. In 23 of the 34 countries where the survey has taken place, a higher population of respondents said that it should be accepted. In the case of India, over 25% of respondents refused to answer the question or said that they didn't know the answer. This shows the reluctance to offer an opinion on this particular subject. The people in India are still considering the topic of LGBTQ as a taboo and are not willing to discuss this particular topic in public. This is what the Pew Research data says also. With this, we have come to the end of this discussion. Through this discussion, we saw about the legality of homosexual marriages in India and we also compared the different countries with respect to providing legal status for same sex marriages. And finally, we saw about the Pew Research Center's research of common people's idea on homosexuality in India. With these learned points, now let's move on to the next news article. Now, have a look at this news article. The news article is about a study on Blackbuck in India conducted by a team from IASC. Before seeing about the study and its findings, let us first see some important points about Blackbuck's. See, Blackbuck is an antelope found mainly in India and Nepal. In earlier times, the distribution of this animal extended all over India except for the western coast. But presently, its distribution is restricted to Rajasthan, Gujarat, Madhya Pradesh, Tamil Nadu and other parts of Peninsular India. Now, let us see about its physical characteristics. Blackbuck is covered with dark brown or black fur. The chest, belly, eyes and chin are covered in white fur. The fur of the male Blackbuck's are darker than the female ones and the male Blackbuck's also have a prominent spiralling horns. You can see the spiralling horns from this image. The females also have horns but they are not ringed or spiraled. In addition to this, the females are much smaller than their male counterparts. Next important thing about the Blackbuck is that they basically have a strong eyesight and they are also fast runners. Using both these abilities, they escape from their predators easily. Now, coming to its habitat. Being a herbivorous animal, the Blackbuck's live in open grasslands. They also live in dry shrub areas, thinly forested areas also. They are generally seen in the area where there are good sources of water all the year round. They prefer to live in thinly forested areas because only in the thinly forested areas they can run away from their predators. Here note one important fact, they cannot handle low temperatures. So, we cannot find the Blackbuck's in colder regions like the foothills of Himalayas. Now, let us see a few points about its social structure and lifestyle. Blackbuck's are social animals meaning they live in groups. The Blackbuck's live in herds which include 5 to 15 individuals. The herd of Blackbuck's is a haram by its structure. It consists of an adult male and numerous females with their young. In the cold season, the Blackbuck's are diurnal while during the hot season they spend most of their day resting in shady areas being active only in early morning and late afternoon. The Blackbuck's are by nature very cautious and shy animals. Having seen the social structure, let us see the conservation status of these species. See, earlier the Blackbuck was listed as vulnerable but due to consistent conservation efforts, the population of the Blackbuck in the wild has increased. So, in the year 2017 the Blackbuck was reclassified as least concerned. In the case of wildlife protection act 1972, they are placed under schedule 1 and in sites they are placed in appendix 3. One additional information is that Blackbuck is the state animal of three states in India. The states are Andhra Pradesh, Haryana and Punjab. Now, coming to the news article. The news article says that the Blackbuck's are mainly seen in three broad clusters across India. They are found in the northern, southern and eastern regions. These clusters are far from one another and in between these clusters there is a dense human settlement. Due to this, the Blackbuck's find it difficult to move from one cluster to another. The IISC study is about the impact of this separation of the Blackbuck genetic diversity in India. The team from IISC collected gene samples from all three clusters and found that all the three clusters earlier had a single ancestor. In due course of time, the ancestral Blackbuck population first split into two groups, the northern and southern cluster. The eastern cluster later emerged from the southern cluster. Another interesting finding from the study is that while female Blackbuck stay in the same population cluster, the male Blackbuck moves from one cluster to another. This is hiding in the genetic diversity in the Blackbuck population in India. The findings conclude that the Indian Blackbuck has managed to survive in a human-dominated landscape. Maybe this is also one of the reasons why Blackbuck is listed in Least Concern in the IUCN Red List. This is all with respect to the Blackbuck's in India. With this, we have come to the end of this discussion. Through this discussion, we learned about the new study conducted by the IISC regarding the Blackbuck's and we also saw some information about the species of Blackbuck's which have been inhabiting the regions of western India and peninsular India. With this, let's move on to the next news article discussion. See this article here. This article is regarding Section 6A of the Citizenship Act 1955. Know that Section 6A deals with special provisions as to the citizenship of persons covered by the Assam Accord. This provision was introduced in the year 1985 following the signing of the Assam Accord between the Government of India and the agitating groups in the state of Assam. Share note that this special provision was earlier challenged in the Supreme Court. The petitioner argued that the special provision was in violation of Article 6 of the Indian Constitution. The then three-judge bench of the Supreme Court had referred the case to a larger constitutional bench. So, yesterday, accordingly, the constitution bench led by the Chief Justice of India said it will first decide whether the provision is constitutionally valid before proceeding to other issues raised in the petition. This is the crux of the article given here. So, through this discussion, we will try to learn about Section 6A of the Citizenship Act 1955, then the reason for its enactment and finally we will see about the key provisions of the Section 6A of the Citizenship Act 1955. The syllabus for this discussion is highlighted here. Interested aspirants can go through it. Now, let's start with Section 6A of the Citizenship Act 1955. As I said earlier, Section 6A of the Citizenship Act contains provisions with respect to citizenship of persons covered by the Assam Accord. This particular section was added to the Citizenship Act through an amendment made in the year 1985. Now, we will briefly see about the Assam Accord and why it was signed. The Assam Accord was a memorandum of settlement signed between the Government of India, Government of Assam and the leaders of Assam movement. See, it was a tripartite agreement which was signed on 15 August 1985. This accord led to the conclusion of a six-year agitation that was launched by the All Assam Students Union in the year 1975. Now, coming to the reason for the agitation by the Students Union. As we all know, British India was partitioned into India and Pakistan in the year 1947. The now-Bangladesh was known as East Pakistan earlier. It was under the administrative control of the Pakistan government which had been running in the capital of West Pakistan Islamabad. Due to cultural differences and the discriminatory practices followed by the West Pakistan people in the East Pakistan revolted against the West Pakistan. This is the backstory why Bangladesh Liberation War happened in the year 1971. Due to the war, many people from Bangladesh migrated to the bordering states of India. The native Assam students opined that these illegal migrants were taking over college seats and employment in their home state. So, they organized an agitation which demanded for identification and deportation of illegal migrants in Assam. Between the years 1979 and 1985, Assam witnessed huge political instability, collapse of state government and President's rule. Also, the elections were totally boycotted by the people. So, to cope up with the situation and to pay heed to the demand of the Assam students, the then Prime Minister of India Rajiv Gandhi signed the Assam Accord in the year 1985. According to the Accord, Ministry of Home Affairs was made the nodal ministry for the implementation of the provisions of the Accord. This is the beef background about why the Assam Accord was signed in the year 1985. Now, we will see about the key provisions of the section 6A of the Citizenship Act 1955. First, let's take subsection 2. It says that all persons of Indian origin who came to Assam prior to 1966 from Bangladesh and who have been ordinarily resident in Assam shall be deemed to be citizens of India. Note that this subsection 2 also includes the persons whose name appeared on the electoral rolls used in the 1967 elections. Now, talking about subsection 3. It says that every person of Indian origin who came to Assam on or after 1966 but before 25th March 1971 shall be detected to be a foreigner. They are detected in accordance with the provisions of the Foreigners Act 1946 and Foreigners Tribunal Order 1964. Subsection 3 further says the detected persons shall be deleted from the electoral rolls and they will be required to register themselves before the registration officers of the respective districts. This is all about subsection 3. Now, coming to subsection 4. It says that a person registered under subsection 3 shall have the same rights and obligations as a citizen of India but they will be not entitled to be included in any electoral roll for a period of 10 years. Finally, subsection 5 says that a person registered under subsection 3 shall be deemed to be a citizen of India for all purposes after the expiry of 10 years following the date of deduction. This means that they shall be included in any electoral roll on the expiry of a period of 10 years. Let me simplify and say what I have said till now. See, subsection 2 of section 6A of the Citizenship Act 1955 deals with those persons who have entered into Assam before 1st of January 1966. According to the subsection 2, these persons will be granted citizenship right. This is about subsection 2 of section 6A of the Citizenship Act. Now, coming to the subsection 3, 4. See, according to these subsections, those persons who have entered into Assam between the years 1966 and 1971 shall not be granted citizenship right for a period of 10 years. For these 10 years, they will be not entitled to vote also. After the expiry of this 10-year period, they can register with the district registration officer to gain the electoral rights and also the citizenship rights of India. This is all about the key provisions of the section 6A of the Citizenship Act 1955. Now, coming to the news article. As I said earlier, section 6A was earlier challenged in the Supreme Court. The petitioner argued that section 6A is violative of right to equality provided under article 14. This argument was based on the fact that section 6A only focuses on Assam and it left out other border states in regularizing illegal migrants. Here also note that section 6A is violative of article 6 of the Indian Constitution because article 6 only recognizes people who migrated to India prior to 1948 as its citizens. But section 6A of Citizenship Act recognizes illegal migrants who entered the state of Assam from East Pakistan till 1966 as India's citizen. So, this section 6A runs contrary to the article 6 of the Indian Constitution. This is why the petitioner has challenged the section 6A of the Citizenship Act 1955. With this, we have come to the end of this discussion. Through this discussion, we saw about section 6A of the Citizenship Act 1955 and why the section 6A was included in the year 1985. See, it was included because of the Assam Accord which was signed in the same year. It was included in the Citizenship Act 1955 to implement the provisions of the Assam Accord which was signed in the year 1985. And finally, we saw some of the provisions of the section 6A of the Citizenship Act. With this, let's move on to the next news article. Take a look at these two articles. The first article is from yesterday's newspaper. The article says that the direct trade general of civil aviation has issued a so-cost notice to Air India. This is because Air India has failed to report to DGCA about the incident involving unruly passengers. The second news article is from today's newspaper. The article says that DGCA issued a so-cost notice to go first airline. This is because the airline took off without boarding 50 passengers who are waiting in the shuttle bus. So, from this, we can say that both these articles are related to DGCA and so-cost notices. So, let us briefly first see about what is meant by a so-cost notice. Here, so-cost notice is a legal document. It is mainly given to a party dispute. The so-cost notice outlines the details of the alleged offence committed by the party in the dispute. After receiving the notice, the party in dispute must explain itself. In the cases that we just saw, the DGCA issued so-cost notice to Air India and go-first airlines. This is because both Air India and go-first airlines are the party in dispute. So, Air India and go-first airline must explain themselves to the DGCA. This is all about the term so-cost notice. Now, coming back, see the news here is not per se relevant for our examination. But since the Directorate-General of Civil Aviation is in the news, we can expect a prelims question from this. So, in this discussion, let us see about the Directorate-General of Civil Aviation. Here note that Directorate-General of Civil Aviation is an attached office of the Ministry of Civil Aviation. See, it is the regulatory body governing the safety aspects of civil aviation in India. The DGCA headquarters is located in New Delhi, while regional officers of it are located in various parts of India. The administration of the DGCA vests with the Directorate-General. Now, you may have a question. Is the DGCA a statutory body or not? See, according to Aircraft Act 1934, which was amended in the year 2020, DGCA is a statutory body. Schexen IVA of Aircraft Amendment Act 2020 talks about the creation of DGCA by the central government for the regulation of civil aviation in India. So, DGCA is a statutory body. Here note one important point. Only the civil aviation present in India is regulated by this body, while the military aviation is regulated by the Indian Air Force. Now, with this basic information, let us see some functions of DGCA. See, DGCA regulates the registration of civil aircrafts in India. It formulates the standards for civil aircrafts. It also provides airworthiness certificates to civil aircraft that meets its standards. Here also note that DGCA issues license to pilots, aircraft maintenance engineers, air traffic controllers and freight engineers. It also conducts various exams to check their skills. DGCA regulates air traffic to from within over India by both India-based airlines and foreign airlines. DGCA also coordinates all regulatory functions with the International Civil Aviation Organization. What is this ICAO? To know about International Civil Aviation Organization, we must first know about Chicago Convention of 1944. In December 1944, the Convention on International Civil Aviation was signed at Chicago. This convention only is called as Chicago Convention. The convention entered into force on 4th April 1947. Based on the provisions of the Convention, the International Civil Aviation Organization came into being on 4th April 1947 itself. Here note that ICAO became a specialized agency of the United Nations linked to the Economic and Social Council. This is all about ICAO. In India, the DGCA coordinates all regulatory functions with the International Civil Aviation Organization. It regulates aircraft noise and engine emissions in accordance with ICAO. DGCA also gives advice to the central government on questions related to civil aviation. Finally, the DGCA promotes indigenous design and manufacture of aircraft and aircraft components. These are all the major functions of DGCA. So, from this, we can say that DGCA performs a regulatory function of regulating the civil aviation industry in India. So, the so-called notices issued to the two airlines which we saw earlier was in accordance with the functions of DGCA. With this, we have come to the end of this discussion. In this discussion, we covered the DGCA in Prillim's perspective. With these learned points in mind, now let's move on to the next part of our Hindu Daily News Analysis. Today, I have taken five different questions for our discussion. Four will be discussed by me and one will be the quiz question for you. Now, coming to the first question. See, this is a two-statement question and it is regarding the scheme Smile. Now, let me read out the question first. With reference to the support for marginalized individuals for livelihood and enterprise scheme, consider the following statements. Statement one. It is being implemented by the Ministry of Social Justice and Empowerment. See, the statement is correct. Now, coming to the second statement. It aims to provide rehabilitation to the transgender community and the people engaged in the act of begging. See, this statement is also correct. Now, let's see in brief about this scheme. See, the Smile scheme was launched in the year 2021. The nodal agency as we saw in the first statement with respect to this scheme is Ministry of Social Justice and Empowerment. It is a comprehensive rehabilitation scheme through the transgender community and the people engaged in the act of begging. The scheme provides for the use of existing shelter homes available with these states and union territory governments and urban local bodies for rehabilitation of search persons. In case of non-availability of existing shelter homes, new dedicated shelter homes are to be set up by the implementing agency. So, as I said already, both these statements are correct. So, the correct answer for this question is option C, both one and two. Now, moving on to the second question. See, this is a three-statement question. Let me read out the question first. Consider the following statements about Village Defence Committees. Coming to the first statement. The Village Defence Committees are established in Jammu and Kashmir and Northeastern states to curb militancy. See, as we saw in our discussion, this statement is wrong. It is a particular initiative which is limited to the union territory of Jammu and Kashmir. So, statement one is wrong. Now, coming to the second statement. The Village Defence Committee has been composed of members containing only ex-servicemen and retired police officers. See, this statement is also wrong. The committee consists of members of not only ex-servicemen and retired police officers but also common civilians. So, statement two is wrong. Now, coming to the third statement. The Village Defence Committee are provided with advanced self-loading assault rifles. See, this statement is incorrect. The members of the Village Defence Committees are only provided with basic manually loading rifles. So, statement three is also incorrect. The question asks for the incorrect statements. So, the correct answer for this question is option D, 1, 2 and 3. Now, moving on to the third question. This is also a three-statement question. Let me read out the question first. Consider the following statements about Gindi National Park. First statement. With an area of just 2.70 square kilometer, Gindi National Park is the smallest in India. See, this statement is wrong. South Button Island National Park in the Andaman and Nicobar Islands is the smallest national park in India. Now, coming to the second statement. It contains Tropical Dry Evergreen Forest. See, statement two is correct. Gindi National Park is one of the last place in India with Tropical Dry Evergreen Forest. Now, coming to the third statement. It has significant blackback population. See, this statement is correct. This is why I have framed this question for today's discussion. The Gindi National Park is home to many fauna include blackbugs. The question asks for the correct statement. So, the correct answer for this question is option B, 2 and 3 only. Now, moving on to the fourth question. It is a three-statement question. Let me read out the question first. Consider the following statements about Bureau of Civil Aviation Security. It is mentioned in Section 4B of Aviation Amendment Act 2020. See, this statement is correct. Bureau of Civil Aviation Security was formed as an body through the Aviation Amendment Act 2020. And it was formed according to the provisions present in Section 4B of the Amendment Act. So, statement one is correct. Now, coming to the second statement. It is headed by the Director General of Bureau of Civil Aviation Security. See, this statement is correct. Now, coming to the third statement. It is responsible for carrying out the regulatory and oversight functions in respect to matters relating to Civil Aviation Security. See, this statement is correct. I have provided here the Section 4B of Aviation Amendment Act 2020. Interested aspirants can pause the video and go through it. See, DGCA is currently in news frequently. So, UPSC might ask this lesser known body in the prelims examination. So, make a note of this Bureau of Civil Aviation Security. It is a potential prelims question. Since all the three statements given here are correct, the correct answer for this question is option D, 1, 2 and 3. Displayed here is the quiz question for you to solve. Interested aspirants can post the correct answer in the comment section. Displayed here is the main question for you to write. Interested aspirants can write the answer and post it in the comment section. With this, we have come to the end of our discussion. If you have liked our video, please hit the like button, do comment and share it with your friends. Thank you for watching.


Hi everyone, my name is Alice Pellemarie and I'm going to present you a joint work with Damien Stélie on the hardness of NTRU. So let me start with a bit of context. So if you're not familiar with NTRU, let me just recap a few information on it. So NTRU is an algorithmic problem that is based on lattices. It's supposed to be post-quantum, meaning that we don't know how to break it even if you have a quantum computer. It uses structure lattices, which means that it's quite efficient. And it's been used a lot already in many different cryptographic constructions. So as an example, you can cite three of the submissions that made it to the round three of the NIST post-quantum standardization process and that are using NTRU, so two encryption schemes and one signature scheme. And it's also one of the characteristics of NTRU that it's quite old for lattice-based cryptographic assumptions, so it's been already studied quite a lot, like it's been around for more than 20 years. And there is one aspect of NTRU which has not been studied so much so far and which is the topic of our article. It's the relations between the hardness of different variants of NTRU and between NTRU and other algorithmic problems. So this is what we call a reduction here on my picture. Narrow means a reduction, so it means here, for instance, this was the state of the art before our article. And it says that you can reduce decision NTRU to search NTRU, which means in other words that if you can solve search NTRU, then you can solve decision NTRU. So it's not a very surprising reduction, it's quite immediate because so I'm going to define more formally what is search and decision NTRU, but the idea of search NTRU is to recover some secret information, whereas the problem asked by decision NTRU is just to distinguish if something is an NTRU instance or uniform. So if you can recover the secret information related to NTRU, then you can say, oh, it's an NTRU instance, but if you don't get any secret, then you say it's going to be uniform. So if you can solve search, usually you can solve decision variants of the problems. So this was the only reduction that was known related to NTRU. And what we do in this work is we prove a bunch of other reductions. So let me comment a bit on this picture. So this is what we prove. We introduce two search variants of NTRU, I'm going to define them, but we realize that there are two quite natural ways of defining the search variant of NTRU. And for the moment, we don't know if both search variants are equivalent. So we have one search variant, here's the first one, which we can prove is equivalent to the decision N variant of NTRU. And we have the second search variant, which we can prove is at least as hard as some worst case problem on ideal lattices. So ideal lattices are just lattices with some extra structure. And so, yeah, so the picture is not completely complete yet because what we really would like for crypto is to have some guarantees of the harness of the decision and NTRU problem because this is the one that we usually use to construct a product with primitive. And so we would like to have a guarantee of its harness based on some worst case problems and ideal lattices, for instance, and you can see that for the moment, we don't have a reduction from a worst case lattice problem to decision NTRU. But this is already a beginning. OK, so now let me go into more details about this result. And I'm going to start first by defining NTRU and the three variants of NTRU I've told you about, like the decision variant and the two search variant. So first of all, I'm going to use number shields and ring of integers. So I'm going to fix for this talk a cyclotomic number field of power of two. But you can take any any nice number field. I mean, the reductions I'm going to show you the parameters are going to depend on some quantities of the number fields. But if the discriminant is not too big and if you know a good basis of the ring of integer, everything is going to be the same. And if you are not familiar with number field and ring of integers, you can just imagine for most of the talk that K is just the field of rational number and R is just the ring of integer numbers and RQ is just Z mod QZ. So I'm going to say once this is important that we are in the field and not just over the rational and over the integers. But for most of the talk, it's not important. So let me start by defining what is an NTRU instance. So an NTRU instance essentially is an element that lives in R modulo Q. And which can be written as, so I'm going to write it H.  So I'm going to parameterize my NTRU instance by two parameters Q, which is a modulus, and gamma, which measures how small F and G are. So this smallness measurement is going to take this form. So I'm going to assume that the Euclidean norm of F and G. So when F and G are polynomials, you just take the Euclidean norm of the vector of the coefficients of the polynomial. And so I'm going to assume, I mean in a gamma Q instance, these quantities are going to be bounded by square root Q over gamma. So the larger gamma, the smaller F and G. And gamma, I'm going to call it the gap because we're going to see later on that if you take H uniform mod Q, you expect to be able to be, sorry, you expect to be able to write it as F over G with F and G of the order of square root Q. So if you take gamma is one here, essentially every H is an NTRU instance. But when you increase gamma, then the number of gamma NTRU instances decreases because you impose stronger and stronger conditions on the size of F and G. And F and G is a small F and G that can be used to write H. I'm going to call that an NTRU trapdoor, a trapdoor for H. So some remark that is important here is that F and G are not unique. You can have multiple ways of writing H as F over G and F prime over G. But they are semi-unique in the sense that the span of the vector FG is unique. So say differently, if I have two trapdoors FG and F prime G prime, then F prime is alpha F and G prime is alpha G for some alpha in the field. Or another way to write it again is F over G is equal to F prime over G prime. And here I am performing the division over the field K, not modulo Q. So this is some quantity that is unique and which I'm going to call HK. So it's kind of a lift of H over the rationales. Okay, so now that I've defined NTRU instances, I can define the different variants of NTRU problem. So the decision variant is what you would expect for a decision variant of a problem.  So that's very natural and I'm not going to spend too much time. The search problem is a bit more tricky. So probably the most natural variant of the search problem you would want to define if you are asked to define the search variant of NTRU would be this variant which we call NTRU vector problem, which is I give you some H, which is an NTRU instance. So H can be written as F over G mod Q for some small F and G and I ask you to recover a trapdoor. So recover another, not necessarily the same, but another pair of FG, such that F and G are small and H is F over G. So that's a natural search variant. And yes, I'm going to comment on the name NTRU vector in a few seconds, but let me just define the other variant, which I also believe makes a lot of sense. So the problem of the NTRU vector variant is that, so as I've said, you are just asked to recover one trapdoor, but it's not unique what you have to recover. So you could also say, okay, maybe I don't really care about recovering F and G small. I just care about recovering the lift of H in K, like F divided by G in K, what I called HK on the previous slide. And the good point of this variant, which I'm going to call NTRU module, is that the solution of this program is unique. So there is a unique HK. So say differently, just to be sure we're on the same page, I just want not necessarily to recover a small trapdoor, but any multiple of this trapdoor, so alpha F, alpha G for any alpha, which can be very large. I'm happy with that. Anything in the span of the vector FG. So that's all for the two search entry problems and the decision and entry problem. And I just wanted to comment a bit on, so I've told you at the beginning that NTRU is a lattice problem, but from the definition, it might not be so clear. So let me just introduce you the lattice, which is behind the entry problems. So this is a module lattice of front two. So if you are not familiar with module lattices, just take R equals Z and then this is just going to be a lattice of dimension two over the integers. Otherwise it's a lattice of dimension two over some ring R. So this is a basis of the lattice of the lambda H, so which is a lattice associated to some elements H in the field, in the ring R. And so what's the property of this lattice is that you can also define it as the pair of all vectors, so GF and not FG, but it's okay, such that G times H is F modulo Q. So if G is invertible, this is exactly H is equal to F over G mod two. So this lattice contains all ways to write H as F over G, but not this is a really small, so not everything in the lattice is a trapdoor. Trapdoor is a small F and G in the lattice essentially.  If you sample H uniformly at random mod Q, then you would expect from instance using the Gaussian and heuristic that the shortest vector of this lattice B H is roughly squared Q up to some squared in factor. On the other hand, if you take H to be an entry instance, then you will have a short vector in this lattice because you know that H can be written that you get a vector GF in this lattice with G and F smaller than the square root Q over gamma. So that should probably be a square root two times square root Q over gamma here because it's a vector with two coordinates. Anyway, so you get a very, I mean, a much shorter vector in the lattice than what you would expect if H was uniform. And so this is what we call a unique SVP instance because you get something, some lambda one much smaller than expected, especially if gamma is large, it's going to be much smaller. And so if I rephrase my different entry problems in terms of this lattice, so the decision and entry problem has to distinguish whether the lattice has a unique short vector or not. So it has to guess the value of lambda one of the shortest vector of the lattice. If you look at the entry vector variant of the problem, the question is, can we find a short vector in the lattice lambda H? So which is why we called it entry vector. And if you look at the entry module variant, we don't want to recover a short vector, but we want to recover the dimension one subspace stand by a short vector because we know that all the short vector are going to be on the same line and we want to recover this line. So if you have a ring, this line is called a rank one module and this is why we call this bias an entry module problem. So essentially we want to find the direction in which the lattice lambda H is dense. Okay, so this concludes the definition of the three variants of entry. And so now I would like to discuss a bit about what we know about entry, what we knew and what we know thanks to the result group pro. So let me discuss a bit about reductions that were known about entry. So we have a few reductions that were known on entry, which I didn't show on the first picture because they couldn't really be shown on this one. So we know that if you sample F and G from some Gaussian distribution, but a large one. So it's not the regime in which we are interested in this work because in this work, we assume that F and G are smaller than square root Q. Here we take them from a distribution which is slightly larger than square root Q. Then you can prove at least for cyclotomic fields that F over G is indistinguishable from uniform on your Q. So this means that the decisional variant of entry is probably hard if F and G are sufficiently large, which is again, not the regime in which we are interested here because we want a regime where F and G are smaller than square root Q. And so entry instances are sparse among all the elements of Q. You also have another reduction which shows that decisional entry cannot be harder than ring a WA. So it's not very interesting for entry because it's an upper bound on the harness of entry but it's something already. And we have also attacks. So that's essentially all we knew for the reductions on entry. Let's just say a few words about attacks on entry because that's also important. Maybe if we cannot prove reduction that's because we have attacks. So I'm only going to consider polynomial time attacks here. So because entry is a lattice problem you can of course run any lattice reduction algorithm. So in polynomial time you would run LLL in order to break it. So this will break entry, the decisional variant of entry and the module variant of entry. If the gap is large enough, so for LLL is going to be if the gap is larger than two to the N. But in the case of entry we also have some attacks that are specific to entry and not to all module lattice problems or all lattice problems which reaches which breaks decisional variant of entry and entry module for some regime of parameters that are different from the ones of LLL. So you have a condition here which is maybe a bit complicated but one example to keep in mind is if the modulus is two to the square root N and the gap is roughly the same as the square root Q. So meaning that F and G are very small, let's say constant size and the modulus is two to the square root N then you can break decisional entry and entry module and it's not, I mean if you would use just LLL you wouldn't break it for these parameters. Okay, so this is essentially all we know about attacks and reductions from entry. And so this is what we prove with a bit more details. So I put the real names of entry problems now so we prove that decisional entry variant is equivalent to the entry module variant. The entry module variant is no harder than the entry vector variant and the entry vector variant is at least as hard as worst case ideology. So in this picture I put in black the immediate errors. So we have already seen that if you can solve some search variant, you can solve decisional variant and if you can find a short vector you can find the span of this short vector. So this arrow is a bit maybe less obvious but it's still very easy to prove. So it means that if you can solve entry module and you can solve ideal SVP so you can find short vectors in ideal lattices then you can solve entry vector problem. And in red you have the two interesting arrows that require some work and that are maybe more interesting in terms of security guarantees. So which shows that decisional entry is at least as hard as the module variant of entry and that entry vector is at least as hard as some worst case ideal problem, ideal lattice problem. So something I want to emphasize also in this picture is that especially the red arrows they require some very specific distribution and entry instances and some specific range of parameters. So not all the arrows may compose like sometimes you get incompatible conditions to compose the arrows. And so if you want to know how the gap degrades along the reduction so you can pause on this slide but essentially for all the trigger reductions we have no loss and for the red reductions the interesting one we have a small loss so you can look at it. Okay, so I wanted to try to plot all we know about entry on one slide. So it's a complicated slide and I'm not sure it's very useful but still it's there. So let me show you, you can pause also if you want to have a look. So on this slide on the x-axis you have the modulus q and on the y-axis you have the size of fng. So it's not the gap that I'm plotting but the size of the upper bound on fng and the scale is log log. So you go from polynomial to two to the n and in between you have two to the square root n because you can be interested in various parameter ranges for intro. So in gray you have the area where the size of fng is larger than q then you have low entry instances with fng larger than q. So in purple you have the area where you can prove that decision and entry is unconditionally hard. So if you have fng of this side and Gaussian then it's indistinguishable from uniform. In red you have the area where you have the subfield attack or Kirchner-Fuck attack or LLL attacks. So all the attacks on entry. So the red area is where you should not choose your parameters. You have polynomial time attacks and so all reductions they can be positioned here. So the equivalence between decision and true and intro modules is there is few restrictions on it.  And the restriction between, I mean there is a reduction between from ideal SAP to intro vector problem is restricted to the size of fng being sufficiently large. So you have two areas here. So in blue it's something that works for all number fields at least with small discriminants. And in polynomial time, classical time and in light blue you need a quantum, it is a quantum reduction and it's only for cyclotomic fields. Okay, so let me move on to the techniques of the two interesting reductions and I'm going to start from the reduction from ideal SAP to intro vector. So this reduction is a one to one reduction. So we start with an ideal and we're going to transform it into an intro instance such that any solution to the intro instance gives us a small vector in the ideal. So for simplicity here, I'm going to assume my ideal is principal and it's just the set of all multiples of some generator Z, which I know. So all integral multiple of Z. And I have some element G in I which is small in my ideal. So here is the place where the intuition, if you imagine that the ring R is the ring of integer Z, it might be misleading because then Z is going to be the shortest element of the ideal and it's trivially solved. But in the general case where R is a ring of integer of a number field, then the shortest vector G is usually going to be an integral multiple of Z. And this is the multiple we would like to find. So how do we transform that into an intro instance? Well, we just do a bit of manipulation. We multiply this equation by Q over Z to get like G times Q over Z is a multiple of Q. And now if I call H this Q over Z, I get G times H is zero mod Q. So the problem here, if I do that, it looks like an intro, but H is a rationale. It's an element of the field. It's Q over Z and in intro, we want H to be something in the ring R. So we just add a line and we round Q over Z. So we get G times Q over Z, the rounding part, is equal to what's left, which is minus G times the fractional part of Q over Z, modulo Q. And now I just take H to be this rounding of Q over Z, F to be minus G times the rational part of Q over Z, and I get that G H is F mod Q. G is small because it's a short vector of I, and F is also of the order of the same size as G, because this fractional part is something that is comprised between zero minus one-elf and one-half, let's say, over the integer. So it's small. So F and G are both small and we get an intro instance. So what I've done so far is if I'm given a principle ideal, I am able to construct an intro instance, such that if G is a small element of the ideal, then there exists a trapdoor FG for the intro instance H. So it's not completely sufficient yet, but you can prove that the converse is true for this intro instance, that is any trapdoor F prime G prime for H will have G prime, which is an element of I. And since it's a trapdoor, G prime is also small, and so this gives you a small element in the ideal, and so you can solve ideal SAP by solving intro for the input H. Okay, so just to conclude on this reduction, so I've presented it to you just in the case of principle ideals, but you can extend it, as I said, to any non-principle ideal. The idea is that you can always write a non-principle ideal as the intersection of a principle ideal for which you know a generator and the ring of integers. And so if you write it like this, then you can just do everything that I've said with this element Z and it's going to work. And another extension of the reduction is that, so the reduction I've presented to you was one to one. If you have an ideal lattice, you can transform it into an intro instance, but what we would like to have is worst case to average case, meaning if you can solve for some average case distribution of an intro, the intro problem, then you can solve ideal SAP for all ideal lattices. And so we can achieve that by using a previous work which showed a worst case to average case reduction for ideal lattices. And then we use the one to one reduction that I've just showed you to reduce that to average case intro. So this was the idea of the first reduction. Let me now move on to the second reduction from decision and intro to intro module. So this reduction is not going to be one to one. So I'm going to phrase the problem a bit differently. So my objective is given some intro instance H to recover edge case. If you remember intro module, we want to recover F over G with a division performed over the rationale and we're given as input F over G module XU. And to do so, so this is a reduction. So we can assume that we have an oracle that solves decision and intro. And here, in order to give you the intuition, I'm going to assume that I have what I'm going to call a perfect oracle. So it's an oracle such that if I give it H which is F over G, it's going to say yes, if there exists F and G smaller than some bound B. So I don't know B but there is some bound B such that if H can be written as F over G then the oracle is going to say yes. And if H cannot be written as F over G with F and G smaller than B then the oracle is going to say no. So it's perfect in the sense that there is really some bound B that says yes or no and it's not some continuous degradation of the success probability. So what can I do if I have such an oracle? Well, the idea is going to be pick any X and Y you want integer and compute X time H plus Y. So if I write it as a fraction it's X F plus Y G divided by G mod Q and now I can query the oracle on this new H prime. And the oracle is going to say yes if X F plus Y G is smaller than B but it's going to say no with very high probability if X F plus Y G is larger than B. So by querying the oracle on H prime I can learn whether X F plus Y G is smaller than B or not. And the important properties here is that I can do that for any X and Y of my choice. And in particular I can choose X and Y such that they only modify one coordinate of F and G at a time. So I can separate the coordinates of F and G and recover them one by one. So I can rephrase my problem in a simpler way by saying I have just F and G that are one dimensional real numbers. I have some bound B which I don't know. And what I can do is I can choose X and Y as I want and I can learn whether X F plus Y G is larger than B or not. And I want to recover F over G. And well, it's just a remark that I cannot hope to recover F and G. I can only hope to recover F over G because if you see my problem, if you scale everything by alpha, so if you scale F, G and B by alpha which are all unknown to the attacker then the behavior of the oracle is going to be the same. So I cannot hope to distinguish to recover F and G exactly. But I can hope to recover F over G and it's actually not complicated to recover F and G here. So the idea is to going to increase so fix for instance some X zero and increase Y zero until the oracle changes from yes to no. And when it changes its answer, we know that we have found some equation X zero F plus Y zero G is equal to B. We do that twice, we get two equations and then we can just solve for F over G. So that's really an easy algorithm. So this again is a simplified version of the algorithm. There are more technical details to handle and in particular the main technicalities here is that the oracle is not going to be perfect but it's going, the only thing you can assume on the oracle is that when it's distributed as in true it says yes and when it's distributed as uniform it says no but everything in between we don't know what happens. And so in order to deal with that we don't do the proof and the algorithm as I've showed to you by hand but we use a framework that was introduced by Piker, Triguff and Stefan Davidov it's to prove the hardness of ring LWUE which is called the oracle hidden center framework problem. Sorry. And essentially the only thing you need to show thanks to their framework is that the probability of success has some nice condition like being deep sheets and things like that and then you can call the framework and it's going to give you an algorithm to find the solution F over G. So let me conclude now. So here is a summary of the reductions we prove. There is a bunch of open questions related to what we have proven so far. So one open question is regarding the distributions. I mentioned that we don't use the same distributions for all the reductions so it would be nice to have one distribution that works for all the reductions. Another open question is whether we can prove the hardness of decision and entry based on some worst case ideal SVP problem. And for this, a natural idea would be whether we could prove that worst case ideal SVP reduces to n from module instead of n through vector. So far we don't know how to do that. And finally the last open problem is whether we could replace this worst case problem on ideal lattices by some worst case problem on module lattices for modules of length two or more because for the moment they are believed to be maybe a bit safer than ideal lattices. So that's all for me. Thank you for watching this video.