Question

1. Poly-alphabetic Cipher

For this question, we consider the Hill cipher given in the textbook on an alphabet

A consisting of 26 English characters (A-Z), 10 numeric characters (0-9) and space,

which corresponds to integers 0 to 36. Here the plaintext is processed successively in

blocks of size m. The encryption algorithm takes a block with m plaintext digits and

transforms into a cipher block of size m using a key matrix of size mÅ~m by the linear

transformation, which is given by:

c1 = (k1,1p1 + k1,2p2 + . . . + k1,mpm) mod 37

c2 = (k2,1p1 + k2,2p2 + . . . + k2,mpm) mod 37

. . .

cm = (km,1p1 + km,2p2 + . . . + km,mpm) mod 37

Note: For this question, correspondence between plaintext and number modulo 37 are

as follows “A” ↔ 0, “B” ↔ 1, “C” ↔ 2, . . . , “Z” ↔ 25, “0” ↔ 26, “1” ↔ 27,

“2” ↔ 28, . . . , “9” ↔ 35 and “ ” (space) ↔ 36

(a) How many different keys are possible in this system?

(b) This cipher is easily broken with a known plaintext attack. An adversary discovers

the following ciphertext is encrypted using this cipher with m = 5 (55

characters in total, no spaces):

A8VS3XRDEON6JEVXGJID13C07L4C1R4Q965XWRA5DQGYWTNHYO4ND8Z

If the following combination of plaintext and ciphertext is given (please replace

both “?????” by the last five digits of your student number), decrypt the cipher

by giving the plaintext as well as both encryption and decryption keys.

Plaintext X9B6T6JAW3UEY7FHIW?????5Z

Ciphertext 2Q59ZZ1Z?????UMDNY2JHINTS

You need to show step-by-step details of your working. Make sure to include

the details of any package, functions used, and/or programs developed. Simply

showing the final result and/or a program would not receive marks.

Answer 1

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