Problems with a Probabilistic Encryption Scheme Based on Chaotic Systems

It has been well-known that tight relationship exists between chaos and cryptography [Brown & Chua, 1996]. Many fundamental characteristics of chaos, such as ergodicity, mixing property and sensitivity to initial conditions/control parameters [Hao, 1993], can be connected with some cryptographic properties of good ciphers, such as confusion/diffusion, balance and avalanche property [Schneier, 1996]. As a new source of cryptography, chaos has attracted much attention in recent years. Besides secure communication approaches based on chaos synchronization technique [G. Alvarez et al., 1999], the ideas of using digital (i.e., discrete-value discrete-time) chaotic systems to construct cryptosystems have also been proposed [E. Alvarez et al., 1999; Baptista, 1998; Frey, 1993; Fridrich, 1998; Habutsu et al., 1991; Hong & Xieting, 1997; Jakimoski & Kocarev, 2001a; Kocarev et al., 1998; Kocarev & Jakimoski, 2001; S. Li et al., 2001a, 2002a; Masuda & Aihara, 2002; Matthews, 1989; Papadimitriou et al., 1997, 1999, 2001; L. Shujun et al., 2001; Tao et al., 1998a,b; Zhou & Ling,