consider the affine cipher that transforms a message M into ciphertext C as (19 - M + 6) mod 31. message can be recovered by an affine transformation of the form M = (a C +b) mod 31. ermine the constants a and b.

Consider a very simple symmetric block encryption algorithm in which 32-bits blocks of plaintext are encrypted using a 64-bit key. Encryption is defined as C = (PK₁) K₁ where C = ciphertext, K = secret key, Ko = leftmost 64 bits of K, K₁ = rightmost 64 bits of K,+ = bitwise exclusive OR, and is addition mod 264. a. Show the decryption equation. That is, show the equation for P as a function of C, Ko, and K₁. b. Suppose and adversary has access to two sets of plaintexts and their correspond- ing ciphertexts and wishes to determine K. We have the two equations: C = (PK) K₁; C = (PK) K₁ First, derive an equation in one unknown (e.g., Ko). Is it possible to proceed fur- ther to solve for Ko?

If an encryption function er is identical to the decryption function dg, then the key K is said to be an involutory key. (a) Let K = (a, b) be a key in an affine cipher over Z/nZ. Show that K is an involutory key if and only if a- = a (mod n) and b(a+1) = 0 (mod n).

Use a coding matrix A of your choice. Use a graphing utility to find the multiplicative inverse of your coding matrix. Write a cryptogram for each message. C perform all necessary matrix multiplications. DGE OU T AHEAD BR 2 18 4 75 0 15 21 20 0 1 8 5 1 4 .... 1 1 -12 32 -15 Using the coding matrix the coded message is.····☐☐☐☐☐☐☐☐☐☐ 2 2 1 5 4 4 4 7 (Simplify your answers.) 61