You can change your choice at any time on our, Modular Multiplicative Inverse Calculator. The bad key a=2 yields an ambiguous message as we saw in the introductory example: each A turns into 0 (=a) since 2*0 = 0 MOD 26 just as each N turns into 0 since 2*13 = 26 = 0 MOD 26. The conversion to letters takes place modulo to the alphabet length: If a 1 is added to the last character, the result of the sum is the first character of the alphabet. This encoding and decoding is working based on alphabet shifting & transforming the letters into numbers . Viewed 4k times . You can observe this order-doesnt-matter rule in the original 26x26 multiplication table: The diagonal line from the top left to the bottom right forms a reflection line. How to pick a symmetric cipher for a given cipher text size? Copyright 1998 - 2023 CrypTool Contributors. which we used in our virus carrier example. Step 1: For decryption first we need to find the multiplication inverse of the key. He decodes all the other cipher letters by finding their corresponding number in the 23rd row (see above) and then goes up that column to find the original plain letter. } color: #ffffff; For the English alphabet, where m = 26, this means a cannot be 2, 4, 6, 8 (any even number) or 13. b ^ ^ ^ 8 ^ a G n n n n n R R R f h h h h h h $ u R ` R R R n n n n 7 R j n n n f R f k \ ^ % n n `d P ^ v$ .$ r % T 0 G $ r 2 % n n n n Chapter 2 Multiplicative Cipher In this chapter we will study the Multiplicative Cipher. The reason for that is that a prime number has per definition no prime divisor except for 1 and itself. Information Security Stack Exchange is a question and answer site for information security professionals. Cipher textanromrjukahhouha=1ANROMRJUKAHHOUHa=3ANXWEXDYMALLWYLa=5ANTISTHECARRIERa=7ANVCYVFOUABBCOBa=9ANZQKZBIEAVVQIVa=11ANLGULPQIADDGQDa=15ANPUGPLKSAXXUKXa=17ANBKQBZSWAFFKSFa=19ANFYCFVMGAZZYMZa=21ANHSIHTWYAJJSWJa=23ANDEWDXCOAPPECPa=25ANJMOJRGQATTMGT MS Excel as a simple encryption and decryption tool: I created the following table in MS Excel with the CHAR and the MOD function: Cipher textanromrjukahhouhaa-101317141217920100771420739ANXWEXDYMALLWYL521ANTISTHECARRIER715ANVCYVFOUABBCOB93ANZQKZBIEAVVQIV1119ANLGULPQIADDGQD157ANPUGPLKSAXXUKX1723ANBKQBZSWAFFKSF1911ANFYCFVMGAZZYMZ215ANHSIHTWYAJJSWJ2317ANDEWDXCOAPPECP2525ANJMOJRGQATTMGT For example, I created the T in the row a=5 using the Excel-formula =CHAR(65+MOD(E$2*$B4,26)) where the cell E$2 contains 17 and the cell $B4 contains 21 as the decoding key a-1. This allows us to force results to belong to the same alphabet. The encryption function looks like this: f (x)= ax+b mod . Modular Multiplicative Inverse a -1. h2 { Write to dCode! In fact, I always have to subtract 101 from each entered lower case plain letter to get its corresponding number. Each character in the message is multiplied with this key. If we extract those rows with the good keys a = 1,3,5,7,9,11,15,17,19,21,23,25 and their corresponding columns, we obtain: 13579111517192123251135791115171921232533915211719255111723551525919323717111217721923112511531751999119113215231572517111173252117951231915151519231591721253711171725715235213111919191951731512511239217212111117723319925155232317115251971211593252523211917151197531 This reduced table shows i.e. So on for each letter, the final encrypted message is ZIEZQ. Invented by Lester S. Hill in 1929, it was the first polygraphic cipher in which it was practical (though barely) to operate on more than three symbols at once. Simply: Z26* = {1,3,5,7,9,11,15,17,19,21,23,25}. Example3: Now, it is your turn. So are 2 and 3, 2 and 5, 3 and 10, 26 and 27, 45 and 16. For a check: the eight integers 1,5,7,11,13,17,19,23 are relative prime to 24 and thus the good keys for M=24. Option 2: Cracking the cipher code using trial and error (brute force) Knowing that there are just 12 possible unique encryptions MOD 26, the journalist produces the corresponding 12 rows in the 26 x 26 multiplication table and cracks the code easily.
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