냐컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� +-+-+-+-+-+-+-+-+ 栢栢栢栢昉께께굇굇굅같�|O|u|t|b|r|e|a|k|臍같굇굇굉께께栢栢栢� +-+-+-+-+-+-+-+-+ Issue #5 - Page 7 of 13 냐컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� Cryptoanalysis of an affine cipher ---------------------------------- by: Encrypted The objective of cryptoanalysis is to "crack the code", ex. - to recover the plaintext from the ciphertext, and also to find which key was used. I will discuss some methods of cryptoanalysis. Understanding the methods of cryptoanalysis is important not only for the cipher breaker "alpha", but also for the cipher users "bravo" and "charlie", since they want to make sure that their communication is reasonably secure. The Kerckhoff's Principle. The Kerckhoff's Principle is the general assumption that the opponent, Alpha", knows which cryptosystem is being used. There are different levels of attacks on a cryptosystem. Ciphertext-only attack. We are assuming the opponent possesses a string of ciphertexts Known plaintext. The opponent possesses a string of plaintexts, and the corresponding string of ciphertexts. Chosen plaintext. The opponent has a temporary access to the encryption machinery, so that he can choose a plaintext string and construct the corresponding ciphertext string. The weakest type of attacts is the ciphertext-only attack. If the keyspace of the cryptosystem is small, then the method of exhaustive search can be applied. In the case of a large keyspace, there exist other methods which are based on the statistical properties of languages. Statistical properties of the English. We assume that plaintext and cyphertext characters are characters of the English alphabet, and that the plaintext is an ordinary English text. Frequency of appearance of a character. The English characters do not appear in ordinary texts with the same frequency. People have estimated relative frequencies of the 26 English characters by compiling statistics from books, magazines. Below is a table I found somewhere on the net. I didnt make it im not that smart. A B C D E F G H I J K L M .082 .015 .028 .043 .127 .022 .020 .061 .070 .002 .008 .040 .024 N O P Q R S T U V W X Y Z .067 .075 .019 .001 .060 .063 .091 .028 .010 .023 .001 .020 .001 Probability of occurence (i hope that iz worded right. heh) 1. E ( probability .127). 2. T,A, O, I, N, S, H, R ( probability between 0.06 and 0.09). 3. D, L (probability around 0.04). 4. C,U, M, W, F, G, Y, P, B (probability between 0.015 and 0.023). 5. V,K,J,X,Q,Z ( probability less than 0.01). There are also combinations of two and three letters, called digrams and trigrams, that are frenquently met. In decreasing order, the most common digrams and trigrams are: TH HE IN ER AN RE ED ON ES ST EN AT TO NT HA ND OU EA NG AS OR TI IS ET IT AR TE SE HI OF THE ING AND HER ERE ENT THA NTH WAS ETH FOR DTH These statistical properties can be used effectively for attacks on ciphers having a relatively large keyspace. Cryptoanalysis of the Affine Cipher An example of cryptanalysis of an affine cipher. Suppose the ciphertext obtained from an affine cipher is: fmxvedkaphferbndkrxrsrefmorudsdkdvshvufedkaprkdlyevlrhhrh count the number of occurrences of the 26 ciphertext letters a b c d e f g h i j k l m 2 1 0 6 5 4 0 5 0 0 5 2 2 n o p q r s t u v w x y z 1 1 3 0 8 3 0 2 4 0 2 1 0 reaarange the ciphertext characters in the following table of decreasing number of occurences r 8 occurrences d 6 occurences e,h,k 5 occurrences f,s,v 4 occurrence Comparing with the table of frenquencies of English alphabet characters, our first guess is that r is an encryption of E and d is an encryption of T. Ok. Here are some formulas to decipher the code, but they are kinda hard to udnerstand and you need to understand Algebra really well. It kinda hard to display them in the correct diagram also since im using notepad but ill give it a try. These were gathered from various websites and programs so these arent my equations. Im not that smart. Fuck it took me months to understnad the dam equations myself. All information below this line iz copied and not my original work (didnt want to be a thief) _____________________________________________________________________________ Comparing with the table of frenquencies of English alphabet characters, our first guess is that r is an encryption of E and d is an encryption of T. If this were true, we would have EK(E) = r, EK(T) = d, or EK(4) = 17, EK(19) = 3. Recall that for affine ciphers EK(x) = ax+b mod 26 so we have 4a+b = 17 19a +b = 3 (heh, if you understand any of this shit email me and ill send u txts on deciphering more advanced keys. heh.) Our next guess is EK(E) = r, EK(T) = e. This gives EK(4) = 17, EK(19) = 4, and the corresponding system so we have 4a+b = 17 19a +b = 4 (heh, your gettin into more than u can handle aint u) The next possibility is EK(E) = r, EK(T) = h. This gives EK(4) = 17, EK(19) = 7, and the system so we have 4a+b = 17 19a +b = 7 (lol, your still reading? i hope u understand algebra. heh) The next guess is EK(E) = r, EK(T) = k, or EK(4) = 17, EK(19) = 10, and the system so we have 4a+b = 17 19a +b = 10 Solving this system gives a = 3, b = 5. Since gcd(3,26) = 1, this is an eligible pair. So we test for the key K = (3,5), use the decryption function associated with this key to decrypt the message to see if it has any sense _________________________________________________________________________________________________ Well thats it for cracking an affine cipher. Next months issue will be on Cryptoanalysis of the Substitution Cipher. If you want all the cryptoanalysis txt's then plz email me. If you dont understand algebra then plz dont try to learn cryptoanalysis, all your gonna do iz fail. -[encrypted] prokzide@charter.net