Deeper Investigating Adequate

Cellular automata (CA) are particularly well suited for cryptographic application and there are several previous studies in this topic (Benkiniouar & Benmohamed, 2004; Gutowitz, 1995; Kari, 1992; Nandi et al., 1994; Oliveira et al., 2004; 2008; Seredynski et al., 2003; Tomassini & Perrenoud, 2000; Wuensche, 2008; Wolfram, 1986). Since CA rule is simple, local and discrete, it can be executed in easily-constructed massively-parallel hardware at fast speeds. Basically, the CA-based cryptographic models can be divided into three classes: (i) models that use CA to generate binary sequences with good pseudo-random properties, which are used as cryptographic keys, but the effective ciphering process is made by another function (Benkiniouar & Benmohamed, 2004; Seredynski et al., 2003; Tomassini & Perrenoud, 2000; Wolfram, 1986); (ii) models based on additive, non-homogeneous and reversible CA, that use algebraic properties of this kind of rules to generate automata of maximum and/or known cycle (Kari, 1992; Nandi et al., 1994); and (iii) models based on irreversible CA, which uses the backward interaction of cellular automata in the ciphering process and the forward interaction to decipher (Gutowitz, 1995; Oliveira et al., 2004; 2008; 2010a; Wuensche, 2008), as the cryptographic model discussed here. Gutowitz has previously proposed a cryptographic model based on backward evolution of irreversible CA (Gutowitz, 1995). A toggle CA rule transition is used as the secret key in his model. A pre-image of an arbitrary lattice is calculated adding extra bits in each side of the lattice. This increment is pointed as the major flaw in the model. CA backward interaction is also known as pre-image computation and an efficient reverse algorithm was proposed by Wuensche and Lesser (Wuensche & Lesser, 1992) for a periodic boundary condition, keeping the pre-image with the same size of the image. Such algorithm was evaluated as encryption method in (Oliveira et al., 2008). However, its usage has the disadvantage that there is no guarantee of pre-image existence for any given lattice and any given rule. The only rules with assurance of pre-image existence are not appropriate for ciphering because they do not exhibit a chaotic dynamics. Thus, a new approach was proposed, which alternates the original reverse algorithm and the variation that uses extra bits, using the second only when the pre-image computation fails. This variation is similar to pre-image computation adopted in Gutowitz model (Gutowitz, 1995). Although this approach needs to add bits to the ciphertext when a failure occurs, it is Deeper Investigating Adequate Secret Key Specifications for a Variable Length Cryptographic Cellular Automata Based Model 12