Affine cipher extended to (Z/pZ) and it's application in images

A New Approach of Crypto-compression on MPEG Format

“…Transposition means that permuting the letters of the message to make it unintelligible. Over the centuries, many systems of cryptographic Telecare Medicine Information System (TMIS) have developed more perfection more clever (Benlcouiri et al, 2013).…”

“…Congruence: For u, v in Z and n an integer ≥2, the notation u ≡ v mod(n) reads u congruent to v modulo n and means that (u − v) is divisible by n which is equivalent to say that u and v have the same retained when divided by n, for example 17 = 5 (3) but also -1 = 1 (2). (Benlcouiri et al, 2013): u, v, r, s belong to ℤ and n an integer ≥2 if u ≡ v (n) and r ≡ s (n) so: u + r ≡ v + s (n); u-r ≡ v-s (n); u×r ≡ v×s (n) and for all k Є ℤ we have u ≡ v + kn (n) if u and v are two integers belonging to {0; 1; 2;… n-1} so u ≡ v (n) implies u ≡ v…”

“…Recalling that if d is the Greatest Common Divisor (GCD) of a and b, there exists the whole u and v such that au + bv = d. The Euclidean algorithm allows calculating these u and v coefficients. Simply go up the calculations by expressing the GCD d as a function of other numbers (Benlcouiri et al, 2013).…”

“…Noting that E = {0; 1; 2… 25}, ܽ and ܾ are integers selected from E. Coding is affine, after numbered from 0 to 25 letters of the alphabet, to encode a letter (called source) number x by the letter number y, where y is the remainder of the division of ax + b by 26. The encoding function associated affine associated with the coefficients a and b is the function f from E to E in which x matches to f (x) = y. f (x) is the only element of the set E = {0, 1, 2... 25} which is congruent to ax + b modulo 26, f (x) ≡ ax + b mod (26) (Benlcouiri et al, 2013).…”

“…Choo et al (2007) have introduced a Crypto-system for uncompressed raw MPEG data, called Secure Real-time Media Transmission (SRMT), by using two transposition steps and one of XOR operation. In 2013, Benlcouiri et al (2013) have presented a randomized encryption method, which is based on the puzzle principle and the extended affine cipher on field ℤ/‫‬ℤ to scramble the puzzle. The advantages of this method are its randomness concerning the choice of key as well as the execution time which is proportional to the number of puzzle pieces.…”