So the classical ciphers last week we we mentioned Caesar cipher and That led to a brute force attack. We're a brute force attack involves Not using our brains, but just trying every possible key and it works in the Caesar cipher because there are only 26 possible keys so we can try them all and This brute force attack is successful because if we take the cipher text and Decrypt using every possible key Then we'll be able to detect of all those possible Plane text which are produced so we decrypt a cipher text with a key to get a plain text value We'll get 26 possible plain text values only one of them will make sense All the others the other 25 will look like just random arrangements of English letters And that generally holds that when we decrypt something if we use the correct key We'll get plain text that we can recognize It will have some structure that we can recognize if we decrypt some cipher text using an incorrect key and By incorrect key. I mean a key that is different from what it was Used for encryption. So if we decrypt with an incorrect key, we'll get plain text, which is Random-looking it doesn't have a structure and we'll be we'll assume as the attacker we can recognize that Because we get plain text, which doesn't make sense. We use the wrong key Okay, so as we try different keys if the plain text doesn't make sense assume That's the wrong key try the next key until you decrypt the cipher text with a key that results in plain text that makes sense And it turns out in practice in most or if not all applications that that's true that Decrypting with the wrong key gives us random or Recognizably wrong results decrypting with the correct key gives something we can recognize is correct We then went on to So that introduced the concept of a brute-force attack We mentioned a different cipher where basically we have the 26 English characters and allow the the person encrypting to choose an arrangement that each of the input plain text characters will map to one of the 26 Possible English characters for example a when it's encrypted will become D in the ciphertext B will become Z and Z will become Q as one possible encryption mode but we can The people encrypting and decrypting choose that arrangement and they must let each other know what that arrangement is and We saw that in that case the number of arrangements possible Is 26 factorial in effect there are 26 factorial possible keys because From the attackers perspective, we don't know this arrangement The encryptor chooses it we need to find that arrangement that produces the correct Plaintext as the attacker and then since there are 26 factorial possible arrangements Then from a brute-force attack the attacker would need to try 26 factorial possible keys and Then we saw if we jump back we flicked between a few of these slides some of the concepts versus some of the examples If you look at the bottom line here, and it's a bit confusing someone asked me a question This 26 factorial is really this last line as a special case. It's in the wrong column 26 factorial is the key space the key space is the number of keys The key length only is only relevant for the binary keys So the first six rows in this table will return to them later means key length is 32 bits or 256 bits 26 factorial doesn't mean the key length It's the key space. So those two should be really in the same column 26 factorial is approximately 2 to the power of 88 26 factorial If we need to try all of those keys if we have a computer that can try keys at a speed of 10 to the power of 15 keys per second so What's that 1 million billion keys per second? Then it would take 10,000 years to do a brute-force attack So this shows that it's quite easy to defend against the brute-force attack brute-force attacks In theory easy try all keys But in practice we can make a system secure against a brute-force attack by just making the key large enough Make sure the key space is a size such that even with the fastest computers today And even with millions of those fastest computers Someone still won't be able to find the key because there's not enough time And we'll see that with practical keys today that the key length is such that brute-force attacks are not possible back to Some of our classical ciphers so the mono alphabetic cipher this substitution cipher brute-force attack not possible But it turns out it's very easy to break using what we say crypt analysis and We exploit the fact that the plain text has some structure in it In particular the language English language and the same with any other language has some letters that occur frequently more frequently frequently than others Some diagrams that occur more frequently Frequently than others so diagrams are pairs of letters and Trigrams and words even So what we do is we look at the cipher text look at the how the algorithm works and Try and work from the given the cipher text and back to the plain text and in the same time discovering the key It's quite hard to show in the lecture such an attack but one of your homework tasks from last week was to do some reading and If you skip forward a few pages, I give you the printout of the the web page where I give an example This is the example I'll browse through it, but it's easy to see Which page I think in the printouts Page 21 in your printouts Called classical ciphers and frequency analysis examples It's easy for you to read on paper than on the on the screen But it just steps through some simple examples of attacks on different ciphers starting with a Caesar cipher and a brute force attack so it starts with This dvvk zdc is some cipher text the attacker knows the cipher text They know Caesar cipher was used a brute force attack Really involves looping through all 26 possible keys and you'll see it on yours that all right I use just use some software to decrypt just a script to decrypt and I tried all 26 possible keys And we see one of them makes sense. Where is it 17? Meet in lobby at 10. Okay, so all the others don't make sense So this is a brute force attack on Caesar cipher The next thing is and again you should read through it in more depth than what we can cover today is the fact that Some text some large piece of text a book or a set of books will contain Some letters occurring more frequently than others So in this example, I use some software to count the letters in an example book So I downloaded a book from a website in text format and this program crypto count letters of that book Percent sort just counts the letters and sorts them from the the the largest percent Down So returns that the letter e Occurs 12 percent of the time in the text The letter t 9% and so on and if only shows the first 10 or so 10 or 15 You can find for the rest as well Just showing that in a large text with a lot of words. You'll probably find that the letter e Was usually the most frequent letter in English t and a are up there as well Of course in different texts, especially as they're shorter those frequencies will change But if you cover a large set of texts, you'll see some pattern there q x and Say and you are quite maybe q and x especially are quite infrequent down the bottom Same with any other language in tie in other languages. There's some structure Some characters occur more often than others also, we can count the diagrams and We see that th occurs most often h e i n e r and Other diagrams pairs of letters, which are not shown are much more infrequent and Trigrams is the triples t h e a n d i n g you I think you see in in words and in phrases Those triples occur more frequently than others Just going back to letters If every letter occurred at the same frequency, what percent should we have? How much what percent of ease should we have? if every letter was Equally distributed across the text what percent of ease and or teas would we have? One divided by 26 so we have 26 letters if they're equally distributed then would have one divided by 26 as a fraction Which is about three point eight five percent so if The letter a occurred the same at the same frequency as z and q and r Then that are all occur about three point eight five percent So that all have about the same value, but of course in this case in practice some are more frequent than others That's in the plain text and the example here Another cipher text again using Caesar cipher and against hard to see on the screen, but a longer Cipher text here not just a few words, but a several sentences. I think it was Again, we could do a brute force attack So that's possible on the Caesar cipher, but we can do some form of frequency analysis. So What we do is we take that ciphertext at the top and Here I count the letters of the cipher text and I see J occurs most frequently at 13 percent Y is nine percent s is nine percent and so on From that we can almost work out What the key is using the Caesar cipher? What is it? How do we work it out? How do we work out the key in the cipher text? The most frequent character is J In the original plain text we'd expect the most frequent character to be E Because in large plain text we know from the statistics of the most frequent character is E Not always in short plain text, but it's a good guess to say okay If the most frequent letter in the cipher text is J Most likely that corresponds to E in the plain text So we find in the Caesar cipher. What would shift us from E to J? What is it? I Think it's sit here a key of five J is the most common letter in the cipher text We expect the most common letter in the plain text to be E That means if we need to map using the Caesar cipher E to J. It's a shift of five positions so a key of five and We actually try it with a key of five that is so by guessing the key of five just from that analysis We decrypt immediately. So this is not brute force. We don't try all keys We deduce the key try it and it turns out that yes, it does produce some some text that makes sense Okay, so this is crypt analysis It's not a brute force attack Instead of trying 26 keys We've cut it down to trying just one key plus a little bit of analysis of the frequency of letters It works quite well with a Caesar cipher The reason it works is because Just going back to the Caesar cipher The Caesar cipher always maps one letter of plain text to the same letter in cipher text So if there is a plain text message which has 12% ease in it Then the cipher text if we use this form of the Caesar cipher if the plain text had 12% ease Then the cipher text must have 12% h's Okay, if we use this example Caesar cipher a key of three So therefore if we count the letters in the cipher text and we get about 12% of the letter h Then we guess all right h maps to e and that gives us a key of three So Caesar cipher is both insecure with respect to brute force attack and insecure with respect to crypt analysis The next example on that web page again. I highly recommend you reading through it because it's hard to see on the screen Remember a mono alphabetic cipher Takes 10,000 years for the fastest computer to break in in brute force attack so brute force is not possible but a Crypt analysis turns out we can do in a 10 or 15 minutes by hand Okay, and this goes through the steps of doing such analysis So again, we start with some cipher text The attacker has some cipher text is listed there We know that it's the mono alphabetic cipher, but we don't know what mapping what arrangement of letters were used We need to find that out So what we do Given the cipher text count the frequency of letters And we count them when we find out t is the most frequent Zed is next and oh What's your guess now? Maybe t in cipher text maps to e in plain text because we see t is the most frequent letter in the cipher text We expect e to be the most frequent letter in the plain text. So in terms of the mapping e When it was encrypted could have become t It's not always true But usually one of those top frequent letters e t a and n map to one of the frequent letters in the cipher text So we do a little bit of trial and error Take the cipher text replace all the letter t's with a letter e and Then do that for the others that is maybe zed in the cipher text maps to If we go what? T so the top the top four or five in Expected plain text e t a oh I What we get in the cipher text Here is t z o lg. So we could try those mappings and Then look at the cipher text and start replacing the letter t with e Replace the letter z with t and see if we start to see some words appear in the cipher text from decrypting to get the plain text Sometimes it works quickly that is t does map to e sometimes we we find it doesn't make sense We need to try something else But with a computer that you can do that quite easily we can also do it with diagrams What was the most frequent expected diagram? remind me Th, okay, we measure in the cipher text we get o f Maybe you pairs of letters in the cipher text o f Correspond to th so try and replace them and see if we start to build up words in the cipher text And that's what we do here. We It's hard to see but this is the cipher text But I've replaced some letters with uppercase letters Which are the corresponding plain text if I map according to our frequency statistics that is the letter here of Which was I think t in cipher text I've written it as e in plain text Doesn't give us much clue as to what the message means yet That was just replacing t with e but we do it with the other letters And we keep trying We map t to z Or what was input as it becomes t and I go through you can go through a few steps try some others and Then you may start see if you know what you're looking for at least some patterns thi Int they are common things we'd expect to see in English text te I Nte something n e t What's that? Internet Okay, so if you have some context that well you can guess what the message may be about you can start to detect words So that suggests Maybe the letter K Maps to R and we can try that and replace all the K's with ours and and keep going through a few iterations and we see Something this something something and so on you see the word internet there Return and try some of the more frequent letters and if you keep going it doesn't take long a few more steps And you get to hear this course something Introduce okay to the Secure it Okay, so you basically have it now because you're starting to see words and because you've got Most letters in a word you can start to work out quite quickly what the remaining letters are and the next couple of steps you you've almost completed and You get to the end so some our original plain text All right on pen and paper. It takes a few steps It takes more than 10 or 15 minutes But with a computer it's almost instantaneous because a computer can do that quite well as well it looks for It tries different mappings and it looks for common words So if we do a mapping and we get words which are in the dictionary, then it's most likely the correct mapping if we get words that are We get sequences of letters which are not words and it's likely an incorrect mapping so we can program a computer to do that for us So a mono-alphabetic cipher brute force impossible crypt analysis easy trivial really a game Have a look read through that one in more depth As homework mono-alphabetic is not secure Despite brute force attack not being possible the problem with it is that The frequency of the plain text so the fact that he is the most frequent character in the plain text Maps directly to the cipher text so if there's one Character is the most frequent in the plain text then there'll be one character in the cipher text which is the most frequent So we just need to find out which one and then we can start trial for the other frequent characters So the cipher text when we encrypt our plain text Contains the frequency statistics which are present in this plain text and that's bad So there are ways to improve it Encrypt multiple letters of plain text at a time So instead of take one letter letter a and map it to a queue for example take a pair of letters th encrypts to zf or Take a triple of letters and map it to another triple of letters that starts to spread out the statistics in the cipher text or To as we'll see in another approach use multiple alphabets So instead of a mono alphabetic cipher a poly alphabetic cipher, so we'll see both of them in the next few examples This just gives another viewpoint of the most frequent letters. I think this was taken from many legal texts so Hundreds of thousands of words of text and they count the letters We'll come back to this one to compare some of these ciphers later So let's look at a cipher that doesn't operate on a each letter at a time Like the last two we saw it operates on a pair of letters and that can help to spread the statistics in the cipher text so that One letter which is frequent in the plain text doesn't map to one letter which has the same frequency in the Ciphertext it's called the play for a cipher. Let's go through it. There's two steps We do some initialization where we create a matrix. So again, we use English letters. How many English letters are we? How many do we have? 26 we create a five by five matrix gives us 25 characters. So we need a special case We've only got space for 25 letters. Which one are we going to remove in this? so we need to agree on which one will remove and Typically or the original version of play fair said let's treat i and j is the same letter Because often in plain text you'll be able to recognize that Okay, by the context of the word whether that letter is supposed to be an i or a j So this is part of the algorithm saying in our plain text if we see the letter j Let's just change it to i and we'll see it still works quite well So what we do is we write down a five by five matrix and we choose a key word in this case not a number Not a single character, but a word and we write that word row by row and Then so if our word is four letters long It's the first four columns on the first row then the remaining 21 entries in our matrix are the alphabet and We make sure that we do not repeat any letters Let's try and you'll see that's not so hard. So just the initialization step first so the The two people communicating they must have a keyword. So that's the secret that they share They both must know that keyword. No one else knows that keyword. So we start What have we got the keyword in this case? And maybe it's on the election notes. I can't remember but Thailand So that's our secret that the two users choose the attacker doesn't know that So what we do is you write that and a five by five matrix T H I THA I L and We make sure we don't repeat any letters So we've already got an a the next letter is an a but we've already written it in the matrix So we skip this next a and go to n D So there's our keyword written in the matrix Don't repeat letters and the rest of that five by five matrix We fill out with the rest of the alphabet in order. We've already got a so we go through a b All right, we need to make sure we skip the letters that we've already got in there So we don't do d again. I've got h so we go to K We've got J Here's our special case I and J think of them as the same letter So we that we don't write a J here Because we can only fit 25 letters in our matrix. Okay? This is the way the algorithm works. We we're going to use the matrix to encrypt in a moment so we need to Really remove one letter and the decision one decision is to say, okay, let's remove the letter Or let's join the letter I and J So if we'll see later if we want to encrypt the word Which has an I in it then we Will use the I in the matrix if we want to encrypt the word which has the J in it We think of it as the letter I in the matrix and when we decrypt The user will be able to recognize whether the letter that we get in the plain text is supposed to be an I or a J Because there are not many words where it would be confusing whether the letter is I or J If you replace a word which has an I with a J that word won't make sense If you replace a word which has a J with an I that word will most likely not make sense So you'll be able to use the context of that word to distinguish which one is which We'll see in some examples Let's fill in the matrix. What do we get to oh? almost there V So there's our what we call our play fair matrix play fair is it's named after some guy who I Think it was some general that they named it after That's the initialization Now when we want to encrypt something we use this matrix to encrypt so The person who's encrypting can create the matrix and when someone wants to decrypt they create the same matrix Okay, so the person who decrypts knows the key word is Thailand they create the matrix in exactly the same manner so as a simple example we'll Start with the plain text of The word hello We want to encrypt hello and get some ciphertext just to show you how the algorithm works The play fair cipher operates on pairs of letters That is we look at a pair of letters of the plain text at a time How many letters in our plain text in this case? Five we don't have an even number if we're going to have a pair of letters at a time We actually needed an even number of letters So we need some special cases in this algorithm to say if our plain text has an odd number of letters add some padding To make it an even number of letters and a common way to add padding is to add a letter on the end Such that someone will still understand the message Maybe add the letter X on the end and you get hello X as the plain text Still someone who receives that will most likely understand that it means hello And when you have much longer plain text It's not a problem if you add one letter at the end because someone will still be able to read the entire message But the algorithm works on pairs of letters, so we must make sure the plain text has an Even number of letters But there's another special case which we'll see in a moment, but let's let's show the general case what we do is we take a pair of letters at a time and Our first pair is he so the first pair is he We look up those letters in the matrix and we find the positions of h and e and To encrypt that pair of letters we Find so for h we find the letter which is on the same row and As h and the same column as its partner So the same row as h and the same column as e is the letter L so it's going to Encrypt and I'll write it as uppercase here because often we Write ciphertext is uppercase just to make it clear. This is ciphertext. This is plain text H e Maps the LD so look at the pair of letters of plain text and The one on the same row as ours and The same column as our partner Becomes the output ciphertext the same row as H or the first letter H and the same column as the second letter the output is L Then for the second letter output the same row as e and the same column as h outputs D So that's the first We encrypt pair of letters at a time. So we encrypted the first pair try the next pair What happens? What is the next pair of plain text letters? LL That rule doesn't work Okay, because the same row as L and the same column as L is L And we'd encrypt LL to LL which is not very good encryption not to change the plain text So in fact, we have another special case if we have a pair of letters which are the same separate them and We separate them by introducing some padding So in this case the first pair was he the second pair would be LL We recognize well, we can't do that. So let's introduce some padding here Let's introduce another letter a special letter. Let's say X So become he L x L o And that's nice because it also gives us our even number of letters. So we've got three pairs So that's needed if we have in a pair of the same two letters because If we used our rule on the same two letters, we'd get the same output ciphertext so in fact To encrypt. Hello. The next step we do is We take LX So we had LL we introduced the X there and encrypt that What does it become? All right L? X same row as L is a and same column and as X so it becomes Cypher text a and The same row as X the same column as L. We get Z and the last one. What have we got? Lo What do we get? Here we need a special case Lo is the next pair the last pair of plain text letters When and we look at the matrix and we see L and O are on the same on the same column In that case just move down Wrap around if necessary so Lo What's down from L E? What's down from O? You becomes EU If our two input plain text letters are on the same row move to the right If they're on the same column move down if not find on the same Row as our letter and the same Column as our partner letter Le then it will become what? EO so le we think of if we have le L becomes e e becomes O if we're encrypting Q you Q would become R you would become P it wraps around U Z Z L Wrap around on the columns and on the rows and we have our we have our Ciphertext so that's our ciphertext we send to our friend our friend receives LD AZ EU our friend knows the keyword is Thailand and creates the same matrix and Applies almost the same rules to decrypt The same rules except when we're on the same row on Or column instead of moving down from what? EU To decrypt will move up EU will become LO When we decrypt We need to get the original plain text back which was he LX LO in these simple ciphers Oh, usually we're not go through the decryption But you should try them Decryption is easy to test if you decrypt and get the original plain text back It's correct if you don't get the original plain text. You've made a mistake Especially in your quizzes or in the exam It very easy to test if you've got it zero marks or full marks Just encrypt it and decrypt it and if you get the same answer you are okay With these ciphers at least What's important in this cypher what's different from the others is it's operating on a pair of letters at a time and We'll just write it again our plain text We needed this X to make it to separate yell So think of the plain text like this, but we know it means hello because there's no word hell X LO so we can guess X is a special character and We got cypher text LD AZ EU Look at the mapping from one letter of plain text to one letter of cypher text Look at the elves The first time we encrypt the L the output is a The second time we encrypt the L we get an output of E That's important and that's an important characteristic of this cypher And then it makes it harder to do that frequency analysis of letters L occurs. I'm not sure if it's it's on one of the slides. Let's go back L occurs about 4% of the time in plain text With a mono-alphabetic cypher Caesar cypher L would map to the same letter each time and that same letter would occur about 4% of the time in the cypher text but in the play fair cypher Even though L may occur 4% of the time in the plain text All right, here's it's quite short so we can't look at percentages But in a long plain text if L occurs 4% of the time The letter we get out from encrypting L Doesn't necessarily occur 4% of the time because L maps to multiple different letters And that makes it better to withstand Someone doing an attack that looks at the frequency of letters because now we really spread out the frequency of letters One letter doesn't always map to the same letter. It maps to different letters and the same concepts can be applied by Applying applying our encryption across different lengths of characters two three and so on It works better when our plain text is much longer So that's the strength of the play fair cypher but We still have the frequency of diagrams diagrams or pairs of letters So if later we have HE we have a very long plain text later. There's a HE here It will still become LD If later we have an LO we'll get ciphertext EU So diagrams still map to the same ciphertext, but single letters do not and an attacker can use the fact that some diagrams occur more frequently than others TH EN IN and so on and again can break the play fair cypher With a little bit more effort than the mono alphabetic, but nothing that a computer cannot do so it's better because it doesn't map One letter of plain text always to the same letter of ciphertext But it still has limitations because pairs of letters always map to the same output We did that It's better than mono alphabetic, but for computers once you look at diagrams trigrams expected words It's very easy to break still So what we need for a strong cipher is to make sure the ciphertext contains no statistics That make it easy for the attacker to work out the original plain text and that's what we're moving towards now We saw with the mono alphabetic cipher With the mono alphabetic cipher and I'll jump back to it. We map one letter Always to the same ciphertext letter a always maps to D in this example y always to F so if our plain text has 12% ease our ciphertext will have 12% s's in this case and that's bad from The strength of the cipher. It's easy for the attacker to use that frequency of letters what we want is that The letter e even though it occurs 12% on the plain text Then it doesn't map to the the same letter each time and in fact That it distributes the letters amongst those 26 so sometimes e maps to a sometimes it maps to be sometimes through to z So that there's an even distribution of the letters in the ciphertext Ideally the ciphertext should have Letters no letter occurring more frequently than any other letter and That would be a perfect sofa and the way to achieve that is to Allow a cipher to map to multiple different letters called a polyalphabetic cipher and we'll go through two examples Vision air cipher and the one-time pad and there's another one in the textbook where there are others But we'll just go through to demonstrate this the vision air cipher think of it as 26 different Caesar ciphers remember the Caesar cipher says take a letter Take the key and shift that letter by the key number of positions to the right to get the ciphertext Well, we've got 26 different keys we can use So what the vision air cipher does is we have instead of one key we have One key letter for each input plain text letter We actually have a key word so the example here if the plain text is internet technologies The key word in this example sir and on What we do is we repeat the key words such that we generate a key which is the same length as the plain text So I repeat it if we don't we don't have to complete the key word. So if we had And here in the plain text with the key would be si r So we just repeat it until we fill out such that the key is Just the key word repeated But the key is the length of the plain text Then to encrypt we take the plain text letter I and we apply the Caesar cipher where the key is s and If you take the Caesar cipher input plain text I key of s you can check you get a is output Then the next letter and is the plain text letter in the Caesar cipher the key in the Caesar cipher is I We get V on output and we keep encrypting users in the Caesar cipher But instead of using a Caesar cipher with the same key for every letter We change the key according to the key word Everyone can decrypt Caesar cipher a vision air cipher Common quiz question quiz questions are usually not encrypt but decrypt Because they are harder a you need to know the algorithm and be Sometimes Sometimes they're harder, but you can well they're easier for you because you can check the answer Okay, if you decrypt Ciphertext and you get Random letters in the quiz the most likely you've done it wrong If you decrypt the ciphertext in the quiz and you get a word that you understand the most likely you've done it correct but In this case to decrypt we again use the Caesar cipher if we have the letter a as cipher text We know the key is s we use the Caesar cipher with a key of s and Do the shift back to the left by s positions s is what? 19 or 20 The the point of this in terms of security is that if we look at our plain text letters Look at the letter t. It occurs three times in this short plain text t here and there's two t's together and Look at the letters in the cipher text that it maps to The third letter t i and t becomes k The next t becomes h this this T becomes k again So we've changed the letters in the cipher text except here. We've got a k again And we'll see that that's a flaw in in this cipher Let's try other letters e there are four instances of e e becomes m L R and V So even though e is the most frequent letter normally in plain text using the vision air cipher It will not map to any one letter in the cipher text Meaning it's hard to work out. What is the mapping from the cipher text letters back to the plain text letters? So it's all about making sure this cipher text doesn't contain the statistics of the language It doesn't contain one letter that occurs 12 percent of the time and this starts to achieve it If we especially have a much longer plain text, we'll see that occur. We could count the letter the number of a's How many a should we get? What percent of a should we get in the cipher text? one in 26 ideally 3.85 percent and the number of B's in the cipher text should be one in 26 if it works well Okay, so that's what we want that the cipher text appears random There's no distribution of letters one doesn't occur more frequently than the other and this is starting to achieve it It's almost perfect The problem with this especially when we have large plain text Which is usually the case when we're communicating. We don't always just send small messages We usually send a sequence of messages or some long messages The problem is that we need to repeat the keyword and It can turn out as we repeat the keyword multiple times We do start to get some letters in the plain text mapping to the same letter in the cipher text and that's bad we'd like The plain text letter to always map to a different letter in the cipher text But the repeating keyword doesn't allow that especially for long plain text. So this is a much better cipher than what we've seen With the mono alphabetic cipher and even the play fair cipher, but it's still possible to break And we will not go through an example. There's some you can get software that will do it for you quite easily And you can do it manually, but you need to look for the fact that There's a keyword of a particular length that starts to repeat and Therefore you'll start to get repetitions in the output cipher text related to how long the input keyword is So it is quite easy to break using a computer The weakness is that we use a structured keyword Why did we use a keyword to make it easy for the two users to exchange a key? I just read no know the keyword and I tell my friend and it's easy to remember and to write down a Better way is do not use a keyword, but use to use a random sequence of letters and That's the next cipher the one-time pad Almost the same in this example But instead of using a keyword and then repeating that keyword choose a random sequence of letters Which are? Which is the same length as the plain text if our plain text is a thousand letters long choose a key Which is a thousand letters long? Such that those letters are chosen randomly if we do that then we get a perfect cipher The one-time pad is the only known scheme that we consider unbreakable And we'll talk more about what unbreakable means After this and when we return to some other slides, but there's no way to break it if we do it correct even a brute force Will not defeat it even if we have all the computers and all the time in in the universe We cannot break it So we'll see some reasons why later, but first how does it work? Well, we won't go through an example because it's the same as Same as this But instead of using the keyword just choose random characters here But make sure they are random okay, so you need to to Correctly choose random characters. You can't maybe just pick them from your head You need a computer to to correctly choose those random characters if you do Even if there's repetitions of letters in the plain text We will successfully spread out the frequency of letters in the cipher text for a long plain text The number of a's in the cipher text. It'll be 3.85 percent B's the same frequency 3.85 Zeds 3.85 percent that is one out of 26 of the letters will be each of those letters so what we've gone through is five different Classical ciphers to try and demonstrate some of the key concepts used in encryption even in real ciphers today The point is Try and get the cipher text which has no structure Even though the plain text has some structure get the cipher text to be appear to appear random questions It's gone through those ciphers quickly a lot of new concepts some questions You should be able to encrypt with each of those five ciphers Caesar mono alphabetic play fair vision air one-time pad and Similarly decrypt Caesar cipher. Okay, you can encrypt decrypt with Caesar cipher Yes, okay What about play fair that one made sense? All right, you may need to practice a little bit before you remember the steps But once you practice the ciphers once or twice, I think you'll work it out Vision air everyone can encrypt with vision air cipher If you can do Caesar cipher you can do vision air because it's the same It's just that we Change the key each letter. Let's try it Just to confirm just do the first one or two letters here. I and T as I are what do we do? We have plain text and we have the key s bring up the The numbering of letters so it's easy to do quickly Hard to see but we see that I is eight S is 18 So Caesar cipher. What do we get? encrypt I is 8s is 18 eyes the 8th letter s is the 18th Caesar cipher add them together and then mod by 26 8 plus 18 is 26 mod by 26 we get zero or a It's just the Caesar cipher and N Is in fact the 13th or letter 13? Just do this one I Is 8 so this is this I is the second letter in our keyword and We get what 21? Mod 26 is 21 and the 21st is V Okay, and you can keep going so it's the Caesar cipher The cipher text a V and if you keep going K M and so on so you can do the Caesar cipher Mono alphabetic we It's hard to do in practice because you need to write down all 26 letters, but it's not so hard Play fair you need to practice a little bit Vision air well if you can do Caesar cipher you can do vision air just remember. It's the keyword repeats and one time pad Exactly the same as vision air, but the keyword is no longer a repeating word. It's just a random set of characters so Exactly the same procedure Any questions before we summarize on the concepts that we've learned? Right, let's look at these these trade-offs and the security so We arrived at the one-time pad it is Very simple in fact. There are different implementations the implementation We see of using the Caesar cipher is what we use on English characters, but for a computer when you're operating on binary You can just use an exclusive or it turns out that if you take your binary plain text you exclusive or with a Random sequence of bits of the same length of the plain text you'll get the same effect as well You'll get the one-time pad. You'll get a perfect ciphertext as output So it's actually very easy to implement in hardware Xor is very fast in hardware We call it unbreakable and we'll see we're on one of our earlier slides that will define unbreakable as meaning Unconditionally secure or unconditional security Under no conditions Can we break it? We cannot use the frequency analysis to try and work back We cannot look at diagrams and trigrams because there is no No diagrams or trigrams that occur more frequently than any others and there are no letters that occur more frequently than any others in the ciphertext So there's no way to take advantage of that structure in the plain text Can we do a brute force attack though? Even I give you all the computers in the world and I give you all the time in in forever, okay As much time as you want Let's say you have an infinite a computer with infinite processing capability So it can instantly try all possible values will it work Right you you can try all possible keys. So assume you can try all possible keys and There are many many keys possible. So we need enough time, but assuming you could try all possible keys Still you would not find the plain text and the reason why is because what you'll do is you take your ciphertext decrypt and You get some potential plain text You'd recrypt with one key then you take the same plain cipher text decrypt with a second key Get the second set of potential plain text and you do it with all the possible keys. That's brute force So you'll get many possible plain text values and Then we said you need to choose the one which makes sense Okay, it's say the English words Well, it turns out that there are so many keys such that if you try all the keys Many of the possible plain text values will make sense There won't be just one that is a English phrase or an English Sequence of English words, there'll be many that make sense and Then the attacker has no way to determine which one is the true message because if you get many Say English words or English Sentences that make sense How do you know which one's the true one and there's no way to know other than guessing and in practice There'll be many such that a guess gives almost a zero chance of guessing So even if you had a brute force attack you had enough time to do a brute force attack You still wouldn't get the plain text and that's what we mean by unconditional security a brute force attack doesn't help This is an example of that concept, but just With two keys so This was the cipher text The attacker knew the cipher text the attacker did a brute force attack. They try many possible keys Two keys they tried of all of them. I only list two they tried this key To make it a little bit easier to read we introduced a 27th character space Okay, but the same concept So we take this cipher text we decrypt with this key this random sequence of letters And we get this possible plain text mr. Mustard with a candle stick in the hole Then we we keep trying if we tried all possible keys then another key this random sequence of characters We get miss scarlet with a knife in the library as a possible plain text It's the role of the attacker now to consider these plain text values and say which one was the original plain text Anyone know What can you do? The only thing you can do is guess in this case if there are only two that made sense then guessing gives you a 50% chance But in practice because there are so many keys you'll get many like in billions and billions of plain text that makes sense and the chance of guessing When you choose from billions and billions is one divided by billions and billions which is almost zero So the attacker has no way to find the true plain text Even if they do a brute force attack And it's the only known cipher that has that characteristic under conditional security for this to work Let's say I I had the original plain text I had it was mr. Mustard with a candle stick in the hole and I encrypted I chose this key To send my cipher text to you so you can decrypt. I must somehow get the key to you That's a challenge Now consider if my plain text was maybe 10 gigabytes My key must be the exact same length 10 10 gigabytes So to get a 10 gigabyte message to you first I must somehow get a 10 gigabyte key to you And we must do that manually write it down on a piece of paper Encoder on a CD or a multiple DVDs on a USB drive That's very hard to distribute keys of such a size So the problem with the one-time pad is if you want to encrypt large messages you need a very large key and Distributing large keys is hard That's the first problem The other problem the key must be random It turns out creating random sequences Many long random sequences is not easy even for computers so It's hard to generate many many different random sequences such that we can have a key That is truly random so the one-time pad is Perfect in terms of security But has two practical limitations It's hard to create Random keys especially many different random keys, and it's hard to distribute random keys or long keys Hence, it's not used much It was said to be used by the Russians during the Cold War to to send short messages to each other Because with short messages, it's possible because you only need a shorter key But once you want to encrypt data streams of data or large data files it becomes impractical So we've arrived at the perfect cypher But because it's not practical we need other ways to make cyphers secure. They may not be perfect but they need to be both practical and Secure enough so later we'll talk about what do we mean by secure enough All of these cyphers are what we call substitution cyphers replace one letter with another letter in the alphabet Transposition is simply rearranging letters a quick one or two examples rail fence transposition Let's try it. We take the plain text and we write it across rows So on the slide we had our plain text and I'll write that plain text The key is the depth. It makes sense when we go through the example. We're going to write it across three rows so Three rows row one two three Internet technologies and applications we'll get their technologies someone tell me when I make a mistake and applications Now all we do to encrypt or to obtain the cypher text is read row by row I'll write it in lower case. It's easier read the first row and Then read the second row and then the third row and add a space, but let's try it a transposition cypher So the key is the depth or the number of rows If I had a four rows or a key of four then I'd write INTE across those four rows and then come back to the first row So we write our plain text in rows and then read row by row to obtain the cypher text That's it. It's a transposition cypher. It rearranges the letters Each letter in the plain text exists in the cypher text. We haven't substituted any In the plain text there is no letter Q in the cypher text, there's no letter Q In the plain text E occurs four times In the cypher text it occurs four times. So we're just rearranging in this case Again, very easy to break given cypher text Basically, if you start to try different depths Then you can again look at possible or expected words and see if you if you try a depth of If this is the cypher text given to you you'd maybe try a depth of two and Write it using a depth of two and see if you'd make words If not, you'll soon discover you can't make words with a depth of two You try a depth of three if that doesn't work four or five and so on and It's not so hard to automate breaking such a cypher. This is an example of a transposition cypher Rows columns a different transposition and it's slightly better We write we have a key which indicates a number of num at number of columns Plain text and key So this one the key was a depth of three and the next example that key is there's a three one five Six to four. They're in fact the numbers one to six Just mixed up We'll see the significance what we do is we write our plain text in columns So we had security The number of columns is determined by the key the key has numbers one to six. So we'll write it in six columns security and Cryptography We'll pad this out so that we have an equal number of Entries in each row. Let's just add an X at the end just to fill it out So it's actually security and cryptography X We need to have the same or each row filled out to get the cypher text. We read The columns but according to the ordering So we'll read the columns like st r r But we don't read this column first. We read the column which is number one E y y a So the cypher text Write it below e y y a this column Then r do y The sec the the key tells us which column to read then s t r r icg x x C a p p and UN th There's our cypher text Just a different transposition cypher Write our plain text in Across a set of columns and then to get the cypher text read the columns as as indicated by the key the key is in must be If we want six columns one to six rearranged if we can have a different length key it can be seven five three That's up to whoever chooses the key again The plain text letters appear in the cypher text frequency analysis We haven't changed the frequency of letters if there were 12% of ease in the plain text there are 12% of ease in the cypher text So that doesn't help the transposition doesn't change the frequency statistics But it turns out applying transpositions combined with substitutions Can be used to build very secure cypher's and we'll see that in the next lecture will return and see that two concepts one is that This one's easy to break. It's not so hard to break if you have just the cypher text but if you apply that same encryption again on e y y r do y that is write that in a sequence of columns and Rearrange Then it will be harder to break Multiple operations multiple applications of the same simple cypher makes us cypher secure and Combinations of transpositions and substitutions can make a cypher secure. So we'll get to that next lecture. So Make sure you can do the seven Classical cypher's that we've gone through today and last week We'll continue next lecture


Remember, women's strike two weeks ago, if we stop working, world stops moving was the motto. As a matter of fact, it is obvious these days to everyone. There is a discussion here about necessary work and who does it every day. Who is doing all the work, the women, the migrants, who does care work, nursing, teaching or selling food to staff in the supermarket, working in agriculture, catching up the vegetables from the fields. What about the international care change these days? The women at the cash box and the supermarket here nearby, they put a writing on the wall. Dear customer, we work for you every day and we'll continue doing it. Some of us are mothers facing problems in a special way, so show respect, be patient. I heard the story of a cashier, she said, first time I feel and I know being system-relevant. Nurses are posting on social media, thank you for your hand clapping and chocolate, it's great, it would be better you join us in our labelled struggles. So you see, somehow an increasing workers' pride and I hope so much labor unions will keep pushing, not agreeing and compromises for keeping peace in these hard times. What about democracy these days? A nurse in Berlin and her comrades brought up a petition, including we need security equipment right now. But also we want to be part of an emergency council, we must be involved in decision making. Time is up to end the economisation of health sector, abolish DIG's team right now. The petition went up to over 100,000 supporters within two days. So it is right, we all don't feel comfortable in willing to give up fundamental rights these days and we have to be careful, for example now they discuss to collect our moving data by tracking our mobile phones. Though most of the new rules seem to be necessary, willing in is really hard and frightening too. But on the other hand, like a glim of hope for myself, there is self-empowerment too growing from the ground. And what a crazy world we are living in. Politicians on TV are talking about public control over pharmaceutical industries and private hospitals, state control over companies, even about converting automotive industries towards producing medical stuff. It's crazy. What I tried to say, there are a lot of discussions about democracy and social rights on a new and maybe deeper level. So there is a wide open window in my opinion of opportunities to push our issues right now. It can close very soon. Really, I hope that we all left in socialist movement are able and have the power to right of the wave.


This paper provides a comprehensive overview of hydrogen storage technologies for mobility applications. It discusses the advantages and disadvantages of various storage methods such as compressed hydrogen, metal hydrides and liquid hydrogen. Compressed hydrogen is currently the most widely used method due to its ability to store large amounts of hydrogen in a small volume, but it has several drawbacks such as the need for complex thermal management systems and the potential for explosion if not handled properly. Metal hydrides and liquid hydrogen offer more efficient storage options, but they require higher operating pressures and temperatures, which can be difficult to manage. Despite their drawbacks, both of these methods offer promising solutions for hydrogen storage in the near future. This article was authored by A.T.N. Revard, Michelle Trudeau and Kareem Zagib.


Now, Roma Wines, present. Suspense. Tonight, Actors Blood, written and told to us by Ben Hect and starring Frederick March. Suspense is presented for your enjoyment by Roma Wines. That's R-O-M-A, Roma Wines. Those excellent California wines that can add so much pleasantness to the way you live. To your happiness and entertaining guests. To your enjoyment of everyday meals. Yes, right now, a glass full would be very pleasant, as Roma Wines bring you... Suspense. This is the Man in Black, here for the Roma Wine Company of Fresno, California. To raise the curtain on a presentation unique in these weekly half-hours of suspense. Tonight from Hollywood, Roma Wines bring you a star of the first magnitude, Mr. Frederick March. And in person, one of America's foremost tellers of tales, Mr. Ben Hect of Broadway and Hollywood. Who will appear as actor and narrator in a suspense play dealing with the mysterious death and the twisted passions and loyalties of the world behind the footlights. And so with Actors Blood and with the performance of Frederick March, supported by Ben Hect, from whom we will hear the narrative in the author's own words. We again hope to keep you in suspense. Do you remember Maurice Tillio? Probably not. Only students of the theatre are people old enough to have applauded the heyday of Mrs. Leslie Carter and John Drew. And the theatrical dialogues of the Divine Sarah would be likely to remember. During the years I knew him, I saw him in harness but three times. Once in revival, once at a benefit. And the third time was the occasion of the anecdote I've set out to relate. By that time, his only claim to fame was the fact that he was the father of Marsha Tillio. On a summer night in 1927, Marsha made a final exit worthy of the Tillio tradition. For weeks after it happened, old Tillio went around like the ancient mariner, holding with his baleful eye in his mournful song, whoever crossed upon his path. But after a while, he too seemed to drop out of sight in the wake of his glamorous daughter and, like her, was forgotten. Then late one night, as I was getting ready for bed, the bells in my apartment rang. Ben, I come with a message from the dead. Indeed. Well, come on in and tell me about it. Ben, do you believe in ghosts? I've got nothing against them. Good. I have just come from a miserable modern dress caricature of that greatest of the Bard's plays, Macbeth. You will scarcely credit what these upstarts have done to Shakespeare's masterpiece. They haven't ordered the text, have they? You recall the fourth scene of the third act. Oh, yes. The scene in which Banquo's ghost appears. Just so. In the folio edition of the play, the stage directions clearly read, the ghost of Banquo enters and sits in Macbeth's place. The foul production which I have just witnessed, the ghost does no such thing. It is an empty chair to which Macbeth shrieks his guilty line. Thou canst not say I did it. Never shake thy gory locks at me. An invisible ghost, eh? That's not so illogical. But what drama is there in it? How can we feel Macbeth's terror if it's an empty stool at which he shouts? I've ought to quit my sight. Let the earth hide thee. Thy bones are mirrorless. Thy blood is cold. Thou hast no speculation in those eyes which thou dost glare with. The way you read those lines, sir, I have no trouble seeing this ghost. Thank you. Now listen. I am going to produce that scene in modern dress.   Look, Maurice, I am very fond of you.  Like Hamlet, I am but mad north-northwest. The empty place at the table would be purely symbolic, I assure you. And no apparitions will appear, not to you and me, yet any rake. I cannot guarantee what my daughter's murderer will see there. Marsha's murderer will be there? He will all be there. All who loved her, all who hated her. And woe to the hand that shed this costly blood. But if you know who the murderer is, why don't you tell the police? Ah, police. My daughter, sir, would not have wanted so crude and sordid an epilogue to her life story. Like her father before her and my parents before me, she had actors' blood in her veins. She shall be avenged, my friend. But it will be no affair of handcuffs and policemen. I'll not go whining on Marsha's behalf among the cigar butts and cuspidors in some precinct station. No, no. Her murderer shall be unmasked at a mighty banquet. On Friday next at 8.30, curtain time, my friend. I'll see you there. Yes, yes, I'll be there. With Ben Hecht in person as the narrator of his own story and with Frederick Marsha's star, you have heard the prologue to Actors' Blood, tonight's tale of suspense. And now, in this brief intermission, let us picture a scene beneath a radiant Caribbean moon at the fashionable Hotel Nacional de Cuba in Havana. An American dinner guest has just raised his glass in a toast to Havana, its traditions, its beauty, the superb dinner, and wine. His Cuban host replies, true, the traditions, the scenery, and the food you enjoy, they are Cuban. But the wine of which you speak so highly, that is of your country. It is the famed Roma wine made in your own California. Yes, it may surprise you that California produces Roma wines of such uniformly superb quality that they are imported by many foreign countries. But millions of Americans do know and enjoy the excellence of Roma wines daily with meals and when entertaining. These millions have made Roma America's largest selling wines. They know too that Roma wines are amazingly inexpensive. Only pennies a glass are wines of such distinguished character. That's because here in America, you pay no high import duty, no expensive shipping charges for Roma, wines that combine age-old wine-making skill with modern testing and quality control. So, ask for R-O-M-A, Roma wines made in California for enjoyment throughout the world. And now it is with pleasure that we bring back to our sound stage Ben Hecht, narrator and author of Actors Blood, starring Frederick March, tonight's tale of... Suspense. It rained on that Friday night, thunder rolled in the sky, and the streets were full of that picnic-like confusion which storm brings to the city. Waiting under the hotel awning for a taxi, I turned over in my mind a strange invitation that had brought me out into this wild and stormy night. I was rather thrilled at the prospect of old Tilleyu's dinner, for his intention was plain to assemble a company of suspects in the murder of his daughter, Marsha, and he was obviously going to climax the evening by some formal accusation of guilt. I knew pretty well who the suspects were, and I suppose I was one of them. Alfred O'Shea would be there, of course. Alfred O'Shea. The man who had written Marsha Tilleyu's first successful play and their last. Broadway had its own private joke about the title of the last. It was called Forgotten Lady. It was after the final curtain of the last performance of Forgotten Lady that Alfred O'Shea chose to tell her. Marsha told the story of the time as a joke on herself. Hello, Marsha. Oh, why, darling, you waited for me in my dressing room. Like old times, I'm touched. Really touched.  You know why I'm here. I do. All right, I'll say it again. I'll say it for the last time. I want a divorce. I want to marry Reena Kratznoff. I want to marry Reena Kratznoff. Oh, it's such a bad line and from such a great playwright. No, dear Alfred. Not for her. It would be too belittling a successor. Can't you see, darling, after all we've been to each other? It's why it's like Pygmalion wanting to trade in his beautiful galatier for a wooden Indian. And it's no dice, huh? No dice, Alfred. No divorce. Not as long as I live. Now be a darling and help me out of this dress. Okay, Marsha, you just make your own bargain. You can come out from behind that screen now, Father. How did you know I was there? You're asthma, darling. I'm glad you're here. Even if you are a perfectly fiendish old eavesdropper. Here, you can unhook me since that swine refused to... I warned you against marrying that jack-o'-n-apes of a playwright, Marsha. Oh, Father, you're saying I told you so. What I really wanted was to weep on your shoulder. Ouch! I'm sorry, sorry. Look here, Marsha. What are you going to do about this career of yours? Now, darling, please don't go into that old routine about my being the last scion of the royal family of the American theater. I'm nothing but a combination of your name and a playwright who specializes in shallow, brittle female leads that enable me to get applause by simply acting myself. Marsha, Marsha. I won't allow you to speak this way about yourself. You're a great artist. Oh. You've taken your place in the great tradition of the stage beside the immortal figures of Rachelle, Sidon's, Bernhardt and Majesta. Marsha, let O'Shay go. He was never worthy of you. Play Juliet next season. Show them, show them you don't need a fashionable playwright and tailor-made parts to succeed. Show them you have actors' blood. Actors' blood, actors' blood! I'm sick of hearing about it. Just because you and Mother thought it was cute to stick me out there behind the footlights at the age of five, because you never had any real life. You didn't see any reason why your daughter should have. I'm supposed to have actors' blood. All right, all right, all right. I'm only thinking of you, Marsha. Only of you. But that O'Shay is a hot-headed Irishman. He came very near to threatening your life when you refused to do as he asked. Good. I wish he would kill me.  Yes, O'Shay was a suspect. He would be at Old Tiliu's dinner. He would be seated across the table from the empty chair. And would he see a bank-closed ghost of Marsha Tiliu? But O'Shay would be in a goodly company of suspects. Fritz von Klauber would be there, for sure. Fritz von Klauber. Not a man I should have liked to have as an enemy that... abnormally sensitive to insult, von Klauber was possessed also of an impenetrable Prussian stupidity. His first American production was a play called Jubilee for Spring, and Marsha Tiliu starred in it. It was the most sensational flop for the Broadway season. After the first night performance in the 21 Club, Marsha held her own private autopsy on von Klauber's dead turkey. You see, darlings, Mr. von Klauber, my esteemed producer loves his turkey farm so much, he sometimes forgets he's on Broadway. Terrific, Marsha. How about that for my collar? Sure, Walter. Anything at all. It's all yours. von Klauber. He's over there at the next table. He's heard every word. Good. Let him hear. He's going to hear for me in the morning anyway when I start looking for a new producer.  Go ahead. Drag me in public. I could kill you for this. Do you hear me?  You could, darling. Well, if my beloved husband doesn't do me in as he keeps threatening to do, perhaps I'll ask you to oblige. I may yet be spared the nuisance of doing the job myself. Marsha, I forbid you to talk like this. Sorry, Father. Must be the actor's blood cropping up again. Yes, von Klauber would surely be present to Tiliu's ghostly dinner. As I got into the taxi and gave the driver Tiliu's address, my mind was still turning upon the terrible question, who killed Marsha Tiliu? Third on my list of suspects was a character named Maury Stein. Maury Stein. A one-time racing tout and small-time gangster, Maury turned his brilliant if slightly frightening talent to flesh peddling. That is to say, he was a theatrical agent. Marsha did two shows under his management. Both of them flops. It wasn't her fault. There was no belittlement of the name Tiliu. It was still an electric sign but growing ghostly, slipping still aglow into the side streets of fame. Maury Stein was Marsha Tiliu's last substitute for love. Will you stop staring at that door? Let's get out of here. Oh, relax. This is a charming room. I like it here. Look, Chick, I said let's get out of here. Understand? Perfectly. I understand that Mrs. Maury Stein become walking in that door. Perhaps she'll put two and two together about us. That'd make you sad, wouldn't it? Because you've signed over all your unscrupulously earned money to your good wife. Oh, just in case questions should be asked, you know. And if she gets any ideas, she may cut you off without a dime. And then you...  You know, I've half a mind to... Did you hear what I said?  Give her so much as to pick up your coat. We're gone.  Sister, nobody talks to Maury Stein like that and gets away with it, see? Nobody. There was to be one more opening night in Marcia Tilleyu's career. And ironically enough, the three men she had caused to fear most of all her enemies were doing the honors. O'Shea had written it, Van Klauber was the producer, and Maury Stein had put up the money. I arrived backstage at the Broadhurst at 8.20 to find the three of them in hysterics. Ten minutes to curtain time and no Marcia. I found Old Tilleyu sitting in her dressing room, nursing a sprained ankle, and very upset. And then I'm worried. For the first time, I'm really worried about Marcia. What's the matter? I don't know. We've been calling her hotels since six o'clock. She refuses to answer the phone. Ben, go over there. You're the only one she'll listen to. No Tilleyu has ever missed a performance and Marcia of all people must not be the first. It's those villains out there who've done this. Spreading insidious poison like Iago. Tearing at her heart with her fangs until she's afraid to go on. Go Ben, try to reason with her. Okay, Pop. I'll do my best to bring her back. I trotted the three blocks to Marcia's hotel. The clerk of the desk met me with a dead pan. Well, Mr. Hack, Miss Tilleyu hasn't come down yet. No key in her box. I took the elevator up. I turned left and walked down the corridor and knocked down the door. No answer. I tried enough. The door opened. And then it all added up. Yes, it added up to a gaudy room in Shambles. Mirror smashed. Perfume bottle shattered. The portrait of Marcia is purette cut to ribbons. And finally it added up to Marcia herself. Cold and white and terribly beautiful. Lying there on the bed with three round bullet holes in a neat triangle just over the heart. There was no mistaking it. Marcia Tilleyu was dead, murdered. That was the sum total of the addition I was doing in my head as I rode in a taxi the 20 blocks from my hotel to old Tilleyu's house on West 84th Street. Maybe I added it up wrong, but I felt sure I hadn't. I was even more certain when I saw old Tilleyu standing there at the head of the table to greet the guests he had assembled with the promise of revealing the identity of Marcia's murder. Promptly at 8.30 he made his entrance. He had brought a stranger into the room with him. Thank you all of you for waiting so patiently. I trust you found your mutual company not too tiresome. I should like to introduce my guest of honor. May I present Mr. Carl Schuttler of the district attorney's office. Now if you will all be seated, the place cards are plainly marked. Please, please do not disarrange them. Thank you, gentlemen. I see one short. And who may I ask is that empty place for? Bankel's ghost. That is my dear Mr. Van Glober. He's for a beloved guest known to all of you. Beloved guest, huh? Well, let's see now. Well, well, hey, listen to this. This seat has indeed been reserved for one known to all of us. Who is it? It's been reserved for Marcia Tilleyu.  Come on, sit down right now. Marcia was never, she was too sensible to play ghosts. I am an old actor. With the audience seated and the curtain up, I find it hard to wait. Art is long, but time is fleeting. And there is one who bids me speak. Love, hear thou. How desolate the heart is ever calling, ever unanswered, and the dark ring falling then as now. You are wondering if I really believe my daughter Marcia is present in this galaxy of her friends. It may be the wandering wits of an old man, but I see her sitting there, tragic and beautiful, about her the sound of rain and of sweet bells jangling out of tune. Forgive me. You have not come here tonight to hear a doting father spread his miseries before you, but for a stern of hisness, which from your courtesy or attentiveness, I feel sure you have guessed. Mr. Schutler asked me to tell him this matter privately, but I refused. For you were all her friends, her honorable friends, and I wanted you present. Build my daughter! Who will conquer life? There's the question. I have the answer. Yes, Mr. Schutler. The murderer is here. He sits here among us now at my table. Shall I lock the door now, Mr. Tilley? Yes. Yes, lock the door. Lock it tight. Leave no chance for escape. It's too late now. No power in heaven or earth can save him. All right, Mr. Tilley, the door's locked. My friends, is this not like a play? Your face is waiting for the name... the name of... Iscariot the Judas. That's it. That's it. Clear your throat. Switch it to worm. Look about you. Who knows? The man may be right beside you. Who knows but that you may be his next victim. I keep my promise, Mr. Schutler. I have the proof, Solomon, enough to send the murderer from this table to the gallows. The one who killed Marsha is looking at me now. Ah! The blood on his hands. The terror in his eyes. I'll tell you his name. His name is... Let me go! Not that! A knife! A knife! Oh, my God! Oh, my God! Where are you? He's killing me. He's killing... The handle protruded from old Tilley's crimson shirt front. His eyes were closed. We carried him into the next room and waited outside while the doctor worked over him. Mr. Hecht. I'm Ben Hecht, doctor. Will you come in, please? He's asking for you. The knife pierced the heart. He hasn't much longer. Ben... Ben, is that you, Ben? Yes, it's me. Who did it? Lean over so I can see your face. Satisfied? Let me fall out of my pocket. What is that? I must have stuck it in the pocket of this suit the last time I wore it. What's in that letter, Ben? I don't know. I haven't even opened it. That's Marshall's handwriting. A letter from the dead. Open it, Ben. Read it to me. You mustn't excite yourself. When was that letter mailed? It's a postmarked attempt. It must have been the day before... Read, read the letter, Ben. All right. What does it say, Ben? Read it. Well, it says, um... Dear Ben, this is to remind you of the opening at the Broadhurst tonight. I hope you will be there because I sincerely believe that this is one of the greatest roles I have ever played. And I'm so anxious to make good in it because of Father's faith in me. Really? She had been proud of your performance in there this evening, too, Pop. You were great. Thank you, Ben. Thank you. Doctor! Doctor! Well, that's that. He was quite an actor in his day, wasn't he? Yes. Quite an actor. How's he doing? What'd he say? He said anything? He's dead. I've got a letter here that will explain everything. It's a pity I didn't find it sooner. I haven't had this dinner set on since the night of Marshall's opening. It fell out of my pocket when I leaned over the bed in there. It was written by Marsha Tillyou. Today she died.  I'd stay a while longer, but death seems easier and simpler than life. What are a few pills more or less to one who has swallowed so much? Take care of Father. He liked you the best for the last time, Marsha. Suicide. It's a suicide note. But what about the bullet? Can't you guess? The old man worshipped her. She was his star.  Only failures do that. So he fired three bullets into her dead body, slashed the painting, and wrecked the place to make it look like a crime of passion. He must have been mad as a hater. No, he was sane. I think he really saw her as murdered by all of us. Her so-called friends who had let her down when she needed the most. Do you realize that that old barnstormer was playing his death scene from the moment he came into this room tonight? He'd rehearsed it in his bedroom for days, sharpening away at Macbeth's old toadstabber. He had his lines down pat. He staged this elaborate scene this evening and killed himself in such a way that we'd all be raked over the coals, not only for Marsha's murder, but for his own as well. It was a lovely piece of old-fashioned miming, but as fruitless of dramas I ever had them as fortunate to witness. You're right, O'Shea.  We could have helped him a lot with the construction, but it was a great glass night. And so closes Actors Blood, written and narrated by Ben Hecht and starring Frederick March. Tonight's study in Suspense. Suspense is produced and directed by William Spear. Have you discovered, as thousands have, how much Roma wines add to the enjoyment of your meals? How their superb flavor makes special occasion feasts out of everyday meals? Well, find out for yourself. Start off the meal with that delightful appetizer, Roma California sherry, then place on the table a well-chilled bottle of Roma California table wine, delicate sautern, hearty burgundy, or tart, tasty claret. You'll be amazed at the tremendous difference Roma wine makes in the enjoyment of your foods. Don't overlook this easy and expensive way to add thrilling extra enjoyment of everyday living. Remember, Roma wines cost only pennies a glass. Take a tip from the millions who enjoy Roma wines at meals when entertaining. Ask for R-O-M-A. Roma wines, America's largest selling wines, made in California for enjoyment throughout the world. Next Thursday, same time, you will hear Brian Donlivia, star of Suspense. Presented by Roma Wines, R-O-M-A, made in California for enjoyment throughout the world. This is CBS, the Columbia Broadcasting System.


Friends, Myself Sandeep Javeri, Assistant Professor of the Department of Civil Engineering from the Washington Institute of Technology, Sholapur. In today's session, we are going to discuss problem on conservation of momentum. The learning outcome at the end of this session, students will be able to solve problem on conservation of momentum. Now let us consider the principle. The principle of conservation of momentum may be stated as the momentum is conserved in a system in which resultant force is 0. In other words, in a system if the resultant force is 0, initial momentum will remain equals to final momentum. Here we should note that this law is valid for entire system, not for single element. It is valid for entire system. Now let us consider the problem on law of conservation of momentum. The statement is a bullet having weight 0.5 Newton and moving with a velocity of 400 meter per second hits centrally a 30 Newton block of wood which is moving away at 15 meter per second and gets embedded in it. Then the velocity of the bullet after the impact and the amount of kinetic energy lost. So here the two bodies given one is bullet another is block. So they are moving with different velocity we are supposed to find out the velocity of bullet after the impact and also we are supposed to find out the amount of kinetic energy lost. Let us consider the solution for this even problem. So we have bullet is given which has velocity as 400 meter per second. So let us the velocity of bullet is even which is equals to 400 meter per second. And another body that is a wooden block is given having a velocity of say u2 is equal to 15 meter per second. The rate of bullet is given as 0.5 Newton. The rate of block is given as 30 Newton. Now after impact this bullet is going to embedded in the block and both bullet and block are moving with a common velocity say V. So here the total mass of bullet and total mass of bullet and block while considering the weight of the body or mass of the body. Now this is a 30 Newton that is a weight of block and this weight of bullet is 0.5 Newton. So according to law of conservation of momentum initial momentum is equals to final momentum. So if you consider this is a initial momentum and this part as final momentum. So we obtain the expression for initial momentum as m1 u1 plus m2 u2 which is equals to capital M that is total mass of block and bullet we have to consider into the common velocities V. We know the mass is obtained as weight divided by acceleration due to gravity. So here m1 is nothing but w1 upon g into u1 plus m2 is w2 upon g into u2 which is equals to now the capital M is replaced by w1 plus w2 divided by small g. So here w1 is nothing but the weight of bullet w2 is weight of block which is 30 Newton. So writing the values this is 0.5 divided by 9.81 plus 30 divided by 9.81. So this is multiplied with the velocity that is 430 divided by 9.81 multiplied by the velocity of block is 15 which is equals to w1 weight of bullet plus weight of block is w2 which is 30 divided by 9.81 multiplied by the velocity that is common velocity V. So here w1 is a weight of bullet that is 0.5 divided by g is 9.81 velocity of bullet is 400 and weight of block is w2 that is 30 Newton and acceleration due to gravity g is 9.81 and u2 that is the velocity of block as 15 meter per second. So in this equation the unknown is the common velocity so this common velocity V is equal to V is equal to we are getting 21.37 meter per second. Now let us consider so we are getting the value as 21.31 meter per second. Now let us find kinetic energy lost so it is obtained by using expression initial kinetic energy minus final kinetic energy. So initial kinetic energy that means we have to consider the motion of bullet as well as motion of block and final kinetic energy we have to consider combined effect of motion of block as well as bullet. So we know the kinetic energy is obtained by using the expression half mv square so initial kinetic energy will be equals to half of m1 u1 square plus half of m2 u2 square this is kinetic energy of bullet this is kinetic energy of block minus the combined effect of block and bullet. So it is half of mv square where mass is a combined weight of or combined mass of bullet and block and V is a common velocity so which is equals to half of w1 upon g into u1 square plus half of w2 upon g into u2 square minus half of w1 plus w2 upon g into v square. So by putting this value we are getting the expression half of 0.5 divided by 9.81 into 400 square plus half of 30 divided by 9.81 multiplied by 30 15 square this velocity of block is 15 minus half of 0.5 plus 30 divided by 9.81 into 21.31 square. So we are getting the kinetic energy lost is equals to 3715.47 joule which is equals to 3.715 kilo joule so this is a required answer that we obtained. So you are supposed to pause the video and answer this question this is the answer. So in this question a bullet having weight 1 Newton which is moving with a velocity of 500 meter per second which hits centrally a 50 Newton block of wood which is moving away at 10 meter per second and gets embedded in it find the velocity of the bullet after the impact. So here we are going to use the expression for law of conservation of momentum that is initial momentum is equal to final momentum by putting the values of velocities of block and bullet we can obtain the final velocity of the bullet after impact and which is obtained as 19.60 meter per second. So this is the reference that we use for the creation of this video. Thank you.