Public key cryptosystems based on Iterated Functions Systems

09/12/2023

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by   Jacques Peyriere, et al.

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Let f=(f_0,f_1,…, f_ν-1) be a collection of one-to-one functions from some space X into itself such that the sets f_j(X) are disjoint. If w=w_1w_2⋯ w_k is a word on the alphabet {0,1,…,ν-1}, let Φ_f,w = f_w_1∘ f_w_2∘⋯∘ f_w_k. Given a function F of which we know that it can be written as Φ_f,w, it is easy to recover w. We give some examples of this situation where everything can be scrambled up by using some private key to get a new system g=(g_1,g_2,…,g_ν-1) on another set Y in such a way that the images of the g_j are no longer disjoint. We define a cryptosystem whose public key is g. The message to be encrypted is a word w and the associated cryptogram is Φ_g,w. The private key allows to recover Φ_f,w from Φ_g,w.