Cryptanalysis of Observer Based Discrete-Time Chaotic Encryption Schemes

Abstract

This paper investigates the weaknesses of cryptosystems that use observer based synchronized chaotic systems. It is shown that known plaintext and chosen plaintext attacks can successfully be launched against such cryptosystems to recover the system parameters and subsequently eavesdrop on the message transmission. The methods employed rely only on the basic mathematical relations that exist between the output sequence and the message sequence of the transmitter system and require very less computations.

A differential cryptanalysis of Yen–Chen–Wu multimedia cryptography system

“…have been recovered, which happens with high probability as shown in the previous subsection, the first 15 bytes in f (16) 0⊕1 (k) can be freely chosen by choosing f (15) 0⊕1 (k). The last byte in each 16-byte block f (16) 0⊕1 (k, 15) may not be chosen, if it is equal to Secret.…”

“…Without loss of generality, assume that N can be exactly divided by 15. Then, the plaintext has N/15 blocks: f = (f (15) , where f (15) (k) = (f (15) (k, j)) 14 j=0 = (f (15k + j)) 14 j=0 . Similarly, denote the ciphertext by f = (f (i)) (N/15)·16−1 i=0 = (f (16) , where f (16) (k) = (f (16) (k, j)) 15 j=0 = (f (16k + j)) 15 j=0 denotes the expanded cipher-block.…”

“…Then, perform the byte swapping operation for the following 32 values of (i, j, l) one after another: (0,8,4), (1,9,5), (2,10,6), (3,11,7), (4,12,8), (5,13,9), (6,14,10), (7,15,11), (0,4,12), (1,5,13), (2,6,14), (3,7,15), (8,12,16), (9,13,17), (10,14,18), (11,15,19), (0,2,20), (1,3,21), (4,6,22), (5,7,23), (8,…”

“…From Properties 3 and 4, and the proof of Property 2, one can see that there are 8 · 15 = 120 binary bits of f (16) 0⊕1 (k) come from f (15) 0⊕1 (k) and other eight bits come from f (15) 0⊕1 (k − 1, l(k − 1)) for k ≥ 1 (the eight expanded bits are all 0-bits when k = 0). Since all the other steps do not change the Hamming weight of each 16-byte block, we can get f…”

“…Due to the subtle similarity between chaos and cryptography, some of multimedia encryption schemes were designed based on one or more chaotic systems [3,4,5,8,9,11]. Meanwhile, a lot of cryptanalytic work has also been reported, showing that many encryption schemes were not designed carefully and are prone to various kinds of attacks [12,13,14,15,16,17,18,19,20,21,22,23].…”