An Improved Public Key Cryptosystem Based on Chebyshev Chaotic Map Over Finite Field

Public key cryptosystem based on multiple chaotic maps for image encryption

“…The Chebyshev map used specifically in order to generate secret shared keys between Alice and Bob, where the generation of the secret shared keys depends on the modified algorithm introduced by [25] in order to solve the multi-keys problem.…”

“…The very important issue in both proposed algorithms is that the key space for both algorithms depends on the parameter n (number of keys) that makes the two algorithms have very large key space. This makes the attack on the two systems is very complicated because the third party must not find only one correct key to break the system as in the single map cryptosystem [25] but he must find ( ) correct keys. The key space of the two proposed systems was described according to the method of attack by the third party, either attacks the system by finding the secret keys or attacks the system by finding the shared secret keys directly.…”

“…Kocarev et al [21], [22] were the first who proposed the use of the Chebyshev map in public-key encryption but the use of this map made the algorithms suffer from multi-keys problem (more than one key may decrypt the system) [23], [24]. This problem was solved by [25] by introducing a new parameter to the original algorithm.…”