Welcome to my presentation Beyond Birthday Bound Secure Freshly Geeing Application to Authenticated Encryption. Many cryptographic schemes that we use nowadays are based on a block cipher. Difficult examples are counter mode encryption, CBC encryption, OCP authenticated encryption schemes. But these schemes they often evaluate a secret key repeatedly. So they use the secret key many times during the lifetime of the key. And to show you this let's look at a typical construction which is a TETA-CB authenticated encryption scheme. And the TETA-CB authenticated encryption scheme is the generalization of OCP-1, OCP-2, OCP-3. It is based on a 3-core block cipher. And this 3-core block cipher is used as evaluated many times, always for the same key. And then you have some tweak which is different for every evaluation. You've got associated data and message checksum that get processed to obtain the tag. And you've got the messages that get encrypted independently to get the cipher texts. And for now it's not important how TETA-CB works exactly and why it's secure. What's important is that the same key is used for every tweak of a block cipher evaluation. And while in a black box setting this might not be a problem, if you consider this evaluation in a fragile environment one might be able to obtain leakage from the key. And if the key is used many, many times you get repeated evaluation of the key and hence repeated leakage of the key. And one must make sure that this is not a problem. One must protect the key against this kind of leakage. And one way of protection is implementation protection. The idea is that you take a very simple, very lightweight scheme which you put protection on top. And protection on top would for instance be masking or hiding. And while the scheme is very efficient this makes the countermeasure typically design-specific and sometimes rather expensive. Alternatively you can invest a bit more in the mode, you get a more solid mode, but then you don't need to put protection on the side. So you get protection by design. Sometimes it's less efficient. In fact the older solutions, many block cipher solutions were less efficient. Nowadays we have seen some quite efficient solutions, mostly permutation-based solutions. But there is also a method in the middle that combines the best of both approaches. So this approach uses leakage resilience where it's needed and it uses implementation protected where that one is needed. And this approach is known as re-keying. And it can be seen as a method in the middle. So as I said it uses leakage resilience where that one is needed and implementation protection where implementation protection is needed. It's also known as a leveled implementation. And more detailed, the idea of parallel fresh re-keying is that you mix cars use of the key material. And the key material, the evaluations of the key are strongly protected. So this means a strong protection is only needed for cryptographically light building blocks. In detail, a re-keying scheme is typically put on top of a block cipher where you have the message that goes into the cipher text. And now instead of putting the key to the block cipher, you put a sub-key to the block cipher which is derived from the key and the re-gear. So the re-keying function, the core re-keying function typically needs strong protection against for instance DPA because the key is evaluated repeatedly. But this function turns out that this function does not need to be cryptographically strong. The core must be cryptographically strong because it deals with the message but it only needs lighter protection against for instance SBA. Because it does not use the key but only a sub-key which is used once or twice. And the idea of parallel fresh re-keying was formalized by Abdallah and Bilhara in 2000. Abdallah and Bilhara looked at the construction that's here on the right. So you have the message, it goes to the cipher text and the sub-key is derived from a PRF evaluated on the key and the re-gear. It took a couple of years before follow-up work came and this is a work by Mathwaad et al. in 2010. They looked at minimalized sub-key, minimalized re-keying. So instead of a random function you take a universal hash function. So notably it really resembles the idea of Abdallah and Bilhara although Mathwaad et al. didn't notice this connection. For years later the Brownig et al. mounted a key recovery attack on the scheme in the birthday bout and they presented two remedies which I called DKM plus one and DKM plus two named after the authors. DKM plus two is particularly interesting. It's this construction that uses a tweakable block cipher and it puts the re-kear on top. So instead of a normal block cipher it uses a tweakable block cipher and the re-kear goes into the re-keying function but also into the tweakable block cipher. But if you think about re-keying in a broader sense and if you think about tweakable block ciphers in a broader sense you might conclude that they somehow share ideas. So intuitively a re-keying function is really comparable to a tweakable block cipher. The interface is the same and the goal is the same. They both do block encryption and can be used to do block encryption. So the idea of re-keying reminds a bit of tweakable block ciphers. There's one subtle difference and this difference is that in a re-keying scheme a tweak change or a re-kear change results in a different key to the underlying block cipher. In tweakable block ciphers this is originally not the case. But there have been schemes where this is the case and this is known as tweak-re-keyable tweakable block ciphers. So in a tweak-re-keyable tweakable block cipher one takes a normal block cipher and one builds a tweakable block cipher on top of that that changes the key to the block cipher if the tweak also changes. So this term already dates back to a couple of years to around 2015-2017. But it turns out actually that although the field of re-keying was not that developed the field of tweakable block ciphers and also in particular the field of tweak-re-keyable tweakable block ciphers has a vast literature. Already in 2009 Minimatsu presented a tweak-re-keyable tweakable block cipher of all my letters. And the scheme might remind you of an earlier scheme namely the one of Abdallah and Belaghe. It's really a comparable scheme but the design goal is different. Abdallah and Belaghe tried to find a random function and Minimatsu targeted an invertible primitive. Notably, from this perspective, the scheme of Medvedal can be seen to be a closer match to the one of Minimatsu than the one of Abdallah and Belaghe even though they didn't draw this parallel. In 2015 I introduced two Beyond Birthday Pound Secure tweak-re-keyable tweakable block ciphers. The idea is that the key and the tweak they get added to get the sub-key which in general of course for leakage is not a very good idea. But in the black box setting this is fine and the key and the tweak also get mingled to get the masking to the input and the output value of the block cipher. One at all patched one, a small gap in the MEN2 construction and also generalized this construction to 32 schemes which I will not depict. And Naito presented a tweak-re-keyable scheme that targeted authenticated encryption. And eventually Jadal introduced XHX which is a generalized construction where you have a block cipher and you have a universal hash function. There is an agent input of the key and the tweak that generates three sub-keys, one that goes into the block cipher and two that go into the mask. And what we see basically is that the knowledge on tweak-re-keyable tweakable block ciphers is quite solid. So tweak-re-keyable tweakable block ciphers have received quite some attention, but re-keying solutions not so much. And this leads to an interesting question, can we use this knowledge on tweak-re-keyable tweakable block ciphers to improve our solutions in re-keying? And this is the question that I analyzed in this work and I presented three solutions based on tweak-re-keyable tweakable block ciphers. The first one I called R1, it is a derivative of MEN1 although it's not the same. And so it takes the block cipher and then the sub-key is derived using a universal hash function U and then U gets also multiplied with the re-gear R. And it has a restriction that the kappa, the key size to the block size must be equal to the re-gear size must be equal to the block size, but in this case it gets 2N over 3-bit security. The second construction is R2, it's not based on MEN2 but rather on one at all construction number 12, which shows better suited for this. It also takes kappa is equal to rho is equal to N and it is not identical to this construction, but it's rather different to suit the re-keying purpose, but still I managed to prove N-bit security of this construction. And finally we take R3, which is an adaptation or basically a simplification of xhx. Recall that xhx uses a universal hash function that generates three sub-keys and now it only generates two sub-keys U and a V that goes into the masking. And this one achieves N-bit security if the key size is equal to the block size. And finally it also covers permutation-based constructions if kappa equals 0, then you get birthday bound security. In the paper I give a full justification of why I selected these three schemes as inspiration and also I give a proof of these constructions. I will not go into details for the proof, but rather I will consider more, focus more on the applications in this presentation. But before doing so, let me first make a comparison. For simplicity taking kappa is equal to rho is equal to N, fd0 is a random function till the e is equal to block cipher and e a block cipher. And for the sake of counting, assume that the universal hash function is as expensive as 1 and the finite field multiplication. And then these are the numbers so I split the cost into the sub-key cost which needs strong, for instance, DPA protection and the core cost which needs weak, for instance, SBA protection. Note that here the universal hash of R2 costs 2 because it uses a universal hash function that generates two sub-keys. And now if you compare, for instance, if you compare, for instance, R2 with DKM1. R2 and DKM1 is equally expensive so the sub-key function is equally expensive, the core is equally expensive, the key size equally expensive, also the state is equally high, but it achieves optimal security. If you compare R3 to DKM2, you see that it's a bit different. So DKM2 uses a dedicated 3-key block cipher in the core whereas R3 uses normal block cipher, conventional block cipher, but it also needs additional sub-key generation and then gets a larger key. Not necessarily, but if you take finite field multiplication it gets a 2M bit key because security is the same. So basically what we see is that it's a trade-off between what primitive can you use, what primitive do you want to use and which scheme is more suited. And the cool thing of these solutions is that they are not just re-keying schemes on their own so you don't need to put them on top of a block cipher. You can actually use them as 3-core block cipher, noting that a re-keying scheme and a 3-core block cipher scheme is basically the same. And this is particularly interesting in light of the fact that the 3-cable block cipher is a very popular primitive for mode design. To give you an example in the CSR competition that ended a couple of years ago, 18 out of 57 schemes were based on a 3-core block cipher. Also many MAC functions like ZMAG are based on a 3-core block cipher. And here I depicted this typical example to set a CB and let me quickly recap it from the first slide. So we have a key that goes into all 3-core block cipher calls. We get messages that get processed independently. We've got associated data and a checksum that will be processed to get a tag. It's a very popular and very widely used design, although not necessarily in this shape. For example, OCB-3 or also OCB-2, but most notably OCB-3, is Tata-CB instantiated with the XEX 3-core block cipher. XEX is a 3-core block cipher on top of a normal block cipher. Deoxys-1 for example uses Tata-CB but then instantiates it with a dedicated Deoxys-BC 3-core block cipher. But one can just as well instantiate the scheme with a re-gear. And this brings me to a typical example, Tata-CB-R3. And Tata-CB-R3 is just Tata-CB instantiated with the R-key re-gear. This means that the tweaks that were input to the 3-core block ciphers now serve as a re-gear to the scheme. And this gives some nice features. So it achieves ended security and it makes a normal amount of lightly protected block cipher calls and makes strongly protected universal hash function calls. And by design it is easier to protect against side channel attacks. And the reason for this is that R3 is. And it's particularly interesting to see what happens if you take a scheme with a permutation. So the subkey in the key size to the block cipher is 0. But then you get birthday about security but it's based on a random permutation. If you compare now for instance to OCB 3, OCB 3 only gets birthday about security. However, this is security in the standard model. And it turns out that it is impossible to prove optimal security in the standard model if you base it on a 3-core block cipher. So it only gets end of 2-bit security but in the standard model. On the downside it makes strongly protected block cipher calls. So you need to strongly protect the block ciphers. The block cipher evaluation. If you compare it to DTE which is Digest, Tag and Crypt by Bertie et al. I would like to mention that it is hard to compare it because they have a different goal. They target nonce misuse resistance. It's a different approach and this also leads to a different type of scheme. But it's still interesting to kind of count the cost. And here we look at the scheme where the hash function of DTE is based on a block cipher. So it's for instance smuggled down guard based on Divismire. Then you get a normal amount of unprotected calls. You also need lightly protected calls and strongly protected calls. So you have a different goal, different primitives that need to be protected. And this also gives a different setting. Not particularly the DTA is sequential whereas TTCB is parallel. To conclude what we have observed is that two different fields basically consider the same problem. And you can use solutions from one of them to obtain solutions for the other direction. A bit more on the Riekeing approach. I already mentioned for simplicity let's look at multiplication for the finite field multiplication for the universal hash. But it has been shown that multiplication is not strong enough. One can mount side channel attacks on this multiplication. So it's interesting to see what other solutions can we take for the subkey generation. It's interesting to note that ISAP is submission to the NIST lightweight competition uses a sponge for Riekeing. And this appears to be a very solid approach. This concludes my presentation so thank you for your attention.


Hey, this is Brett with Summit Auto in Fond du Lac, Wisconsin. You're new and used Jeep and Jeep Wrangler headquarters today. I thought I'd check out this brand new 2021 Jeep Wrangler Sport. This vehicle has a 3.6-liter Pentastar V6 motor, which pumps out 285 horsepower. It's combined with the 8-speed automatic transmission. It's going to get you 24 miles per gallon on the highway, 20 city for a combined total of 21 miles per gallon. Hydro blue, pearl coat is the color. We shoot all of our videos in 1080p, 60 frames per second. So if you have HD capabilities on your computer, tablet, or a smartphone device, turn them on right now, because it is definitely your best way to check out the looks, styling, and options of this particular Jeep before seeing it in person. And if you'd like to check out our entire inventory in the upper right-hand part of your screen is a link to our website. Click that and check us out there. This is a 25S package. And it's got a couple add-ons on it. It comes with the 17-inch painted alloy rims. And it has Michelin 245 75R17 tires. And these are kind of an all-terrain tread pattern on there. So this one has the side steps, which are in addition. I do like the blacked-out Jeep logo and the Wrangler Sport logo on there. Comes with the normal halogen headlamps, the plastic front bumpers. Get the tow hooks on there. Notice you do get the little Jeep logo on your headlight. Get the running lights and the fenders, little Easter eggs here. You get the sandals on that plastic shroud.  You also get the T50 indicator on there so you know which torque's wrench to take your doors off with. We're going to take a look at the original window sticker. I'm not going to go through everything on it, but just some of the more important points. Feel free to pause this at any second. Make sure that this one has all the options you're looking for. 3.6-liter V6 with the e-torque, 8-speed automatic transmission. Everything on your left there is your standard equipment. Your optional equipment are the HydroBlue ProCo, which is $245 option. Customer-preferred 25S package is $3,200, which gives you the silver rims, the deep tint sunscreen windows, heated power mirrors, and the power windows. You also get remote keyless entry, automatic headlamps, the leather-wrapped steering wheel, speed-sensitive power locks, and then the sun visors with illuminated vanity mirrors. This one also has the technology group, which is a $995 option. Gives you Apple CarPlay and Android Auto, as well as the 7-inch LCD or TFT color display. You connect four with the 7-inch display, air conditioning with automatic temperature control. This one also has six months of Sirius XM free, trailer-toe and heavy-duty electrical group is $795, which gives you the auxiliary switches, the 700 amp maintenance-free battery, class two receiver hitch, and seven and four pin wiring.   Three-year 36 bumper-to-bumper warranty and five-year 60 powertrain warranty. Your miles per gallon are right there, 24 highway, 20 city, and average of 21. Safety ratings not too bad, four-star front, and then a three-star rollover, not rated for the other ones. I do like hydro blue on the Wranglers. You don't see very many two-doors in the hydro blue color. So that's one of the reasons I really wanted to do a video on this one. You do get the trailer-toe group, which gives you the receiver hitch, four-pin and seven-pin wiring, those LED tail lamps, and the reverse parking sensors on there as well. Back storage area, you get the case for the front hardtop pieces, and you do get a little bit of storage area underneath here as well as spots for your door hinge and roof and windshield bolts.  You just set it down, pull that strap, and it'll lock right into place. So pretty nice system there to get these hardtop pieces off. There's three bolts on the side, one on the top of each side, so a total of eight bolts. There's two quick disconnects with spots to put them. You can see all the bars are color matched, so when you do have that top off, it matches the rest of the vehicle. And then you do get the JL badge back here, which gives you the two-door four-door wheelbase and overall length, as well as water-forting right there. I like the new rear gates. They shut a lot smoother. Then the old ones on the JKs, four-wheel disc brakes, kind of get an idea of that hardtop there.  You do get the blind spot monitoring and heated mirrors in the mirrors.  They do have side airbags now, factory floor mats. To get to that second row, you can see that front seat slides up pretty far. Does have latch child safety system back there.  Like I said on the window sticker, does have the auto headlamps, the tilt and telescopic steering wheel, power mirrors, power locks. And as we hop inside here, we'll turn the instrument cluster on so you can see the radio and everything you get the Jeep animation right there. Brighten it up a little bit. You do get a digital speedometer compass display. You can put time, miles per gallon, all that good stuff on there. It's all configurable. You get that leather-wrapped steering wheel, cruise controls on the right, Bluetooth and information center controls on the left and audio controls on the back of the steering wheel. That technology group gives you the seven inch TFT radio that you connect for. So it gives you AMFM and Sirius XM radio capabilities. You can do your climate controls here as well. Notice you do have the dual climate control, which is nice. You can do media and stuff here. And then you can also do your apps. You have the backup camera, which is an HD backup camera. You can see just how crystal clear that is. And those grid lines are dynamic, meaning that they're gonna turn as you turn that steering wheel, which is nice when you're hooking up to a boat camper or trailer. And notice that that center line lines right up with your receiver hitch so you can get hooked up to whatever you're towing the first time, every time without a lot of help. You can actually turn that camera off. And then it does have the Android Auto and Apple CarPlay on here as well, where you can project your cell phone to the screen through those systems. So if you have a navigation system on your cell phone, such as Waze or Google Maps, you can project it to the screen. And it's like you just, just like you have nav on your screen there. So even though this radio doesn't come with nav, you can add it through Android Auto and Apple CarPlay. It's a really neat system. We actually did a demo on Android Auto if you wanna check that out in the upper right-hand part of your screen.  Power windows, you have a media center here, USB, USB-C and an aux jack, and then here are your four upfitter switches, part of that trailer tow group. Four by four shifter right there, your eight-speed automatic transmission, you get the little Jeep logo on the top, and here's your keyless entry, has the flipper key on it, and it's a real chunky key fob. You're always gonna know which key you have in your pocket, and I do like the flipper key pretty neat. You get that kind of mineral gray painted dash on the sports. Seems like all the different trim levels, they put something different on the dash. Like the Saharas are leather, the Rubikons are red, some of them are gray. You get the LED lights up there, and the quick disconnects on those front hard top pieces are almost identical to the ones on the JK. The only thing different is they don't have the screw-ins right here that the JK is dead, so they come off a little bit easier than the JKs. Anyways, we'll do one more final walk around with the lights on and everything, so you can see those LED tail lamps. And I would personally like to thank you for checking out the video today, and hopefully from this HD video, you will have gotten a really good look at this 2021 Jeep Wrangler Sport in Hydro Blue Proco. I really like it. And to see more pictures of this Jeep or one of our other 450 new and used cars, trucks, SUVs, minivans, Wranglers, you name it, we got it, go to our website right there, www.summitauto.com, full pictures and descriptions of every single vehicle from two locations, all at summitauto.com, and if you'd like to check out more HD videos, you can go to youtube.com slash summit auto. Remember to like, subscribe, and share on this video and all the videos that you see there. In fact, in a second, you will see a link to subscribe to our YouTube channel on your left, a link to more Jeep Wrangler videos like this one on your right. If you have not been to our website on the bottom, a link to our inventory on our website, click those, check us out, and we're super excited to be offering Wranglers just like this 2021 Jeep Wrangler Sport in hydro blue pro code. Thanks again for checking out the video.


Until recently, Americans have thought of Alaska as an area of arctic winds and sub-zero cold. But this picture is only partly true, for the face of our 49th state is as varied as it is large. Steep mountains fall away to river valleys and sweeping plains. And though much of Alaska is rocky and barren, there are also nearly a million acres of fertile plains, which during the almost endless sunlight of summer produce healthy crops. Modern Alaska is also an area of urban centers. The largest cities anchorage where new homes, hotels and businesses are rising rapidly to keep pace with the needs of a growing population. Many of Alaska's original citizens, the Eskimos, live as they have for centuries, earning their livelihood by fishing and trapping. The Eskimos maintain many of their past traditions. And yet skills of the 20th century come easily. The state's excellent vocational schools have played an important part in this transition. It is almost 70 years since the great Alaskan gold rush, but gold is still being mined in some parts of the state. One of Alaska's biggest gold mines has turned out to be the sea. The fishing industry brings 70 million dollars into the state each year, and her canneries provide two-thirds of all the canned salmon sold in the world. The King Crab, another important export, is also caught and processed along the Alaskan coast. Today the gas and oil industry is rapidly becoming the state's most important. Alaska has come a long way since its discovery in 1741 by Vitus Bering, a Danish sea captain in the service of the Russian Tsar. Russian fur traders and trappers followed, building scattered settlements along the coast. Traces of the Russian period still remain. By the middle of the 19th century, the Russians were anxious to be rid of the vast, distant land. And on March 30th, 1867, Secretary of State William Seward purchased the territory for seven and a quarter million dollars, or about two cents an acre. Even so, many Americans called it Seward's Folly, and suggested that he might now want to purchase Iceland and Greenland. They were not far off. Seward said that Alaska, Greenland and Iceland were all important to America's defense. He was the first to recognize the strategic importance of the polar region. In mid-October, with a Marine Honor Guard participating in the ceremonies at Sitka, General Lovell Rousseau accepted the territory for the United States. General Jefferson Columbus Davis became commander of the military district. For the next ten years, the Army had the responsibility of governing the land in the absence of civilian rule. With almost no communications and transportation facilities, such semblance of government as there was was exercised by the commanding general of the troops at Sitka. New garrisons were built and some exploration carried out, but Washington showed little interest in Alaska. Finally, in 1877, the Army troops were withdrawn. For the next few years, the Coast Guard patrolling the shores of the Northern land, and then the Navy took on the responsibility for control and administration. The successive commanders of the vessels stationed at Sitka were, for all practical purposes, the government of Alaska. Finally, in 1884, Congress passed a bill which placed a civil government over Alaska. Years passed with little happening to change the pattern of living in the remote region. The Army sponsored various expeditions to explore the interior, and men came back with much information concerning the geography and life of areas where few explorers had ever penetrated. During this period, marine shipboard detachments helped keep law and order in the new territory. In 1896, with a discovery of gold in the Yukon and other parts of Alaska, the nation's attitude toward the territory changed dramatically. From throughout the world, adventurers traveled north to strike it rich. Complete towns were built almost overnight. The Alaskan gold rush enriched folklore with new and colorful names and legends that still perpetuate the magic of the far north. Once again, the Army was called north to help in law enforcement and to provide relief and medical aid in emergencies. When a great storm destroyed large areas of Gnome in 1900, Army troops were essential in maintaining order, saving property, providing relief. Although interest in the territory waned with the passing of the gold rush, the Army signal corps under the leadership of such men as General Greeley and Lieutenant Mitchell pressed forward with an ambitious plan for establishing a communication system which brought the distant populated sections of the country together and linked it with the continental United States. Cable ships put to sea to complete the link with the United States. With the establishment of the complete system in 1904, one of the greatest barriers to the development of the territory was removed. In the early 1930s, destitute farmers from the northern United States arrived under a government sponsored resettlement program. Some became permanent residents, but Alaska remained primarily a forgotten neglected area. World War II changed that. Japanese troops occupied Attu and Kiska in the Aleutian Islands, the first enemy occupation of American soil since 1814. A year later, the United States struck back. At last, we understood the importance of Alaska. Seward had proved himself not only a shrewd statesman, but a firesighted strategic planner. America would never turn its back on its northern territory again. World War II brought great improvements in airfields and service, a key means of travel in this vast region. It also brought radio range stations, an increase in mapping and coastal charting, and Alaska's first road system linking it with the states. There was also an enormous increase in housing, schools, utilities and other projects. And most important of all, 300,000 young men of the Army, Air Force and Navy came to Alaska, many of whom would return to live permanently in the territory after the war. We came out of the war with a grim appreciation of Alaska's importance to us, an importance dramatically heightened by the polar concept of modern war. For Alaska lies astride the shortest route between Soviet Siberia's missile and bomber bases and the industrial heartland of the United States. It is the United States area closest to Russian territory, only 56 miles across the Bering Sea from the Siberian Peninsula. The 49th state is a vital factor in our overall polar defense. The Alaska Air Command has the exclusive responsibility for due line, our distant early warning system. Alaska is the western anchor of this system, which provides early warning of any attack against North America. Every plane, both friendly and unknown, is spotted and its course plotted. Because of Alaska's strategic location, it is playing a growing role as a midpoint maintenance and refueling center along the polar circle air routes. The Navy in Alaska maintains surveillance over 2,800,000 square miles of navigable water in the area. Marine detachments are stationed at naval bases on ADAC and Kodiak. And at Fort Greeley, the Army maintains the Northern Warfare Training Center to provide combat-ready cold climate forces. During the winter, the troops learn to cope with extreme cold weather. Their schooling includes classroom work and long-range patrols. Although carried out chiefly for training purposes, these patrols frequently prove to be the most reliable and often the only source of information concerning the remote regions of the state. Marching in the sub-treasing cold, maintaining combat effectiveness, setting up tents, providing food and operating equipment, these are all situations which only can be learned through experience. During the summer, the students learn not only to survive in the wilderness, but also the precise sure methods of movement on sheer rock. They must learn to put their faith and place their lives in the ropes, which are essential to troop movement in this kind of country. The Alaskan Scouts, part of the Alaskan National Guard, are an effective operating force in the Northern region. Scouts comprised of Eskimos and Indians have the ability to function in extremely cold areas. The Alaskan Scouts are well suited for their mission of reconnaissance, surveillance and patrol. However, Alaska is primarily an air theater. The Alaskan Air Command is the largest component of our armed forces in the state. It is the hub of Alaska's defense against air attacks. At regular intervals, simulated attacks are made to test the response and fighting readiness of Air Force interceptor squadrons from Elmendorf and other bases, including Air Force and Army search and rescue efforts in Alaska's vast inland region. The Rescue Coordination Center at Elmendorf keeps busy the year round. In-flight laboratories furnish vital data for both military and civilian air activity, and weather conditions are recorded by complex technical equipment. Near Anchorage, the Army, Navy and Air Force share this building. The Unified Service Headquarters of the Alaskan Command, ALCOM. ALCOM is one of seven unified commands reporting directly to the Joint Chiefs of Staff. It directs the efforts of all contributing to the nation's defense in Alaska. 650 miles to the southeast in the state capital of Juneau is the headquarters of the Coast Guard, an organization which has been serving in Alaska since the 1860s. Today, the Coast Guard performs a variety of functions essential to a region with almost 35,000 miles of coastline. It is, for example, responsible for maintaining thousands of navigational buoys. These markers, ranging widely in size, are set along the coastline and shipping lanes. The service also maintains lighthouses, which must be supplied throughout the year. It is often a difficult business, especially when the shoreline necessitates hauling supplies directly from launches onto rocks high above. The Coast Guard also provides search and rescue operations for all shipping in the area. Through coordination of ships and planes, the distress boat is quickly located and towed to safety. Among the many patrols carried out by the Coast Guard is an annual trip all the way to the Arctic Circle and back. During the long months of the voyage, the Coast Guard performs a variety of functions, including providing medical and dental care to the Eskimos in isolated villages. The mission of the Coast Guard in Alaska continues in the same spirit and tradition that has marked the involvement of all the services in the life of the land. This was never better illustrated than in the days and weeks that followed Good Friday, 1964. Two crewmen aboard a ship at Valdez recorded the incredible scene. 5.36 p.m., the worst earthquake in North American history, struck the state of Alaska. The quake brought enormous destruction. In anchorage, buildings and streets collapsed. Seward was in flames. Kodiak flooded. The tidal wave following the quake left a mass of beached ships, overturned railway cars and all the other after effects of a major disaster. The Army, Air Force, Navy and Marines rose to the challenge in the devastated area. They moved swiftly, saving lives and attacking the pressing needs of recovery and rescue work. Military personnel worked with civil defense officials in setting up a command headquarters. Troops were rushed by truck convoy and planes to the area's hardest hit. The homeless were taken to military bases. During the days that followed, field kitchens and hospitals were set up to cope with the emergency. In the anchorage area alone, over 1,000 troops took part in security and travel control. For many months, the armed forces continued the massive job of cleaning up. The Corps of Engineers helped to clear the debris, repair the key railroad and dock facilities and in the city of Valdez to plan its rebuilding on a new site. Within a few months, Alaska not only had recovered from the earthquake but was well on its way toward building for the future. William Seward's dream has become a reality. On its centennial anniversary, Alaska is a prosperous and booming state. The military has played an essential role in the development and growth of Alaska. And the Armed Forces military report takes pride in saluting this, the 49th of our United States. Today, America's fighting men still man the northern ramparts, carrying on and keeping bright the heritage of Alaska.


Hello everybody! This video will show you how to take ownership of a file or folder and get access to view and edit them. If you refuse access to a file or folder when you are trying to open or edit them in Windows, it means you don't have the right to access or edit such objects. In Windows, the user who is the owner of a file or folder will automatically gain the right to modify, access, read and edit writes for an object. This type of user will always have the right to access a file or folder. When creating a file or folder, the user account which you use to enter the system is automatically assigned owner's rights. However, you may need to change the current owner's rights so that they belong to you or to another user. It can be caused by deleting a user account, having several users work with one computer at the same time, or by using a hard disk from another computer. In the owner of inaccessible files and folders will be the best solution to such problems. To do it, right-click on the file or folder and select Properties in the menu. Go to the tab Security and click on Advanced. In the Advanced Security Settings window that opens, click on Change in the line Owner. In the next window, User or Group, specify the name of the user account in the field, enter the object name to select, and click Check Names. If you gave the correct name, it should change to show the past to full user name, with the name of the computer before it. After that, click OK. Returning to the Advanced Security Settings window, you will see that your user account is now shown as the object owner. If this object is a folder, under the owner line you will also see an option, replace owner on subcontainers and objects. Make sure that the box is checked and click Apply. Confirm your action in the User account control window by clicking Yes. OK. After that, try opening the folder which refused access at first. As you can see, it is now open for the current user as this user has become its owner. All the actions that we have described work all right if they are done with the account having administrator's rights. If you need to get access to the folder from an account which has no administrator rights, changing the owner of files and folders will not give you full access. In this case, add your user to permissions of this folder. To do it, go to the Properties of such folder, then to Security tab, and click on Advanced. In the Advanced Security Settings window that opens, click on Add. Click on the link. Select a principle and in the field enter the object name to select, specify the name of your account and click on Check Names. After that, select the necessary options in the field Basic Permissions and click OK. Apply. OK. OK. After that, try opening the folder which refused access at first. As you can see, now it is open for the current user. That is all for now. Thanks for watching. Leave your comments. If you like this video, click the Like button below and subscribe to our channel to see more.


Hello and welcome to the session. My name is Mansi and I'm going to help you with the following question. The question says find the derivative of 5xq plus 3x minus 1 into x minus 1. Let us start with a solution to this question. First of all let fx be equal to fxq plus 3x minus 1 multiplied by x minus 1. Let us open the bracket first of all. We have 5xq into x is 5 into x raised to power 4, 5xq into minus 1 is minus 5xq plus 3x into x is 3x square plus 3x into minus 1 is minus 3x, minus 1 into x is minus x, minus 1 into minus 1 is plus 1. This is same as 5 into x raised to power 4 minus 5xq plus 3x square, now minus 3x minus x is minus 4x plus 1. Now we find out f dash x that will be equal to 5 into 4 into x raised to power 4 minus 1, minus 5 into 3 into x raised to power 3 minus 1 plus 3 into 2 into x raised to power 2 minus 1 minus 4 into x raised to power 1 minus 1 plus 0. This happens because we see f dash x will be derivative of each term of fx added or subtracted. So for the first term we have 5x4 is 5 into 4 into x raise to power 4 minus 1 because d by dx of x raise to power n is equal to n into x raise to power n minus 1. In the first case n is 4 in the second n is 3 in the third n is 2 in the fourth n is 1 and since the last term is a constant so derivative of a constant is 0 so we get a 0 in the end. We have 5 4's are 20 x raise to power 3 minus 15 x square plus 6x minus 4. So our answer to this question is 20 x cube minus 15 x square plus 6x minus 4. I hope that you understood the question and enjoyed the session. Have a good day.


Welcome friends to another session on certs and in this session we are going to understand what are compound certs So you would have encountered certs like 2 root 2 Minus 3 root 5 now. This is not a single cert. This is a combination of two certs separated by a Negative sign so hence how do we define compound certs? So compound certs are expressions expressions Compound certs are what expressions and they are consisting of consisting of consisting of two or two or more Serds, okay, two or more Serds So it could be root 2 minus 2 3 root 5 plus 7 like that. Okay, right and then they must be connected They must be connected by connected by either plus or minus Signs, okay, so these are this is how we define a compound search. So let us say let us take some examples So examples would be we have already shown you one so three root five Plus five root three is another example. See they may be of the same order. They may not be of the same order Okay, so let us say third root of five Minus two times Seventh root of six. This is also a compound. So all our compound search mind you three root five into Five root three is not a compound. So it is not a compound. So why because it can be reducing reduced to a Not a compound So let me write this and I'm saying this could be reduced to a single sir, how you can Multiply three times five. So this can be written as three times five and root five times root three, isn't it? So which is nothing but 15 times root of five into three, which is nothing but 15 15 Okay, so hence this is when there is a multiplication or division sign then we don't consider them to be a compound search So what are compound search expressions? Obviously Consisting of two or more certs. So hence don't think that okay only two certs should be there So there is three root three minus four root two plus six root seven. This is these are all Compound certs, okay, and you have to just take care that they must be separate by plus or minus signs then you will get Compound certs now We are interested in operations of compound certs. So for example, I'm interested in multiplying two compound certs So let us say example multiply Multiply let us say root two plus root seven and With multiply this with let us say root two Minus root seven if you see both are compound certs, right now how to multiply so we will we will use all the basics of algebra To you to multiply, right?  So similarly what we can write here is as root two Squire minus root seven Squired so which is nothing but two minus seven, which is equal to negative five. So we use rules of algebra To operate on compound certs, let's take another example find the find the square of the question is find the square of Root seven plus root five This is a question.  So hence hit this will be root seven square plus two root seven Times root five plus root five Squired which is nothing but seven plus two root thirty five because you can multiply the numbers under the same route and This is nothing but five. So hence it is twelve plus two Thirty five. This is how we operate on compound shirts. Let's take another example where there is a Variable instead of a constant. So let us say I have to square square root of 3a plus x Plus root of 3a minus x Okay, so we have to square this ugly-looking term. Don't worry. You'll be able to do it very simply So 3a plus x plus 3a Minus x whole square, you have to write, isn't it?   So if you see this is a Square, this is 2. This is a this is B and finally I have to write this as root of 3a minus x squared Okay, so what will you get you will get? 3a plus x then Plus Two times since the roots are same so I can take both the quantities inside 3a plus x 3a minus x plus This becomes 3a minus x Right because the roots will go because there were square terms Now if you see closely this x and this minus x will just disappear and 3a plus 3a will become 6a So 6a plus Two times Under root now this if you see inside the under root there is a plus B a minus B form So I can write this as 3a Square minus x squared is it look closely. This is nothing, but if you see I'm writing it separately so that you can understand 3a plus x 3a minus x Let us say this is a If you see this one is a here and this one is B here Isn't it so it is like a plus B into a minus B so and hence it is nothing but a square minus B square, right? So what is our final thing? So this is 6a plus 2 3a square is nothing but 9a square minus x square So this is what the final answer would be so what is the learning learning is compound serves what are compound serves two serves or more serves separated by plus and minus sign and then we use the common algebraic laws and Principles to do operations on compound serves