A Secret Key Cryptosystem by Iterating a Chaotic Map

Abstract

Chaos is introduced to cryptology. As an example of the applications, a secret key cryptosystem by iterating a one dimensional chaotic map is proposed. This system is based on the characteristics of chaos, which are sensitivity of parameters, sensitivity of initial points, and randomness of sequences obtained by iterating a chaotic map. A ciphertext is obtained by the iteration of a inverse chaotic map from an initial point, which denotes a plaintext. If the times of the iteration is large enough, the randohinets of the encryption and the decryption function is so large that attackers cannot break this cryptosystem by statistic characteristics. In addition t o the security of the statistical point, even if the cryptosystern is composed by a tent map, which is one of the simplest chaotic maps, setting a finite computation size avoids a ciphertext only attack. The most attractive point of the cryptosystem is that the cryptosystem is composed by only iterating a simple calculations though the information rate of the cryptosystem is about 0.5.

Lessons Learnt from the Cryptanalysis of Chaos-Based Ciphers

“…This type of chaos-based ciphers are usually known as digital chaos-based cryptosystems or digital chaotic ciphers. One typical type of digital chaotic ciphers amounts to numerically computing a great number of iterations of a discrete chaotic system, using the message and/or the key as initial data (see [46,43] and references therein). This is basically also the strategy in [18], [102], where periodic approximations of chaotic automorphisms are used to define substitutions (so-called S-boxes) resistant to linear and differential cryptanalysis.…”

“…The implementation of Shannon's intuitions had to wait till the development of Chaos Theory in the 1980s. Indeed, it was around 1990 when the first chaos-based ciphers were proposed (e.g., [78], [46]). Moreover, in 1990 chaos synchronization [91] entered the scene and shortly thereafter, the first applications to secure communications followed [56,37].…”

Rabbit: A New High-Performance Stream Cipher

“…However, even though chaotic systems exhibit random-like behavior, they are not necessarily cryptographically secure in their discretized form, see e.g. [3,4]. The reason partly being that discretized chaotic functions do not automatically yield sufficiently complex behavior of the corresponding binary functions, which is a prerequisite for cryptographic security.…”

“…In the C file, rabbit.c, the logical rotation function, _rotl, is used, however, for some compilers it may not be defined. In such case, the logical rotation function can be defined as: [3]; p_instance->x [6] = g [6] + _rotl(g [5],16) + _rotl(g [4],16); p_instance->x [7] = g [7] + _rotl(g [6], 8) + g [5]; } // key_setup void key_setup(t_instance *p_instance, const byte *p_key) { // Temporary data uint32 k0, k1, k2, k3, i; // Generate four subkeys k0 = *(uint32*)(p_key+ 0); k1 = *(uint32*)(p_key+ 4); k2 = *(uint32* …”

Applied cryptography: Protocols, algorithms, and source code in C

“…Four Japanese cryptographers presented an algorithm based on chaotic maps at Eurocrypt '91 [687,688]; Biham cryptanalyzed the algorithm at the same conference [157]. Another algorithm relies on subsets of a particular set of random codes [693].…”