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The automated inverse theory in cryptography, points to autonomous finite automata, which is relative to the canonical form for one-key cryptosystems based on finite automata, the public key encryption based on finite automata for one-key cipher can be executed by finite automata.
A finite automaton is considered as a natural model for ciphers. The method of converting Ra Rb has been introduced to deal with the structural problem of such automata; then, the public key encryption based on finite automata and a focal type for one key cipher that can be executed by finite automates with limited error propagation and without spreading data is provided.

What is the application of Finite Automata in cryptography?

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    $\begingroup$ There is a book with the exact same title as this question. You might want to read it for a more thorough answer. $\endgroup$
    – fkraiem
    Commented Sep 28, 2018 at 12:37
  • $\begingroup$ Finite Automata and Application to Cryptography (shorturl.at/fnAW0) $\endgroup$
    – R1w
    Commented May 10 at 11:32

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In the area of symmetric cryptography , finite automaton have been applied to model the additive differential probability of exclusive-or and the differential analysis of S-function ref 1 ref 2

another example of automata application on linear model of modular addition ref

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You can find the Znàm's problem which following Wikipedia have application in Non deterministic automaton and so in cryptography and this.

Related reference are Brocard-Ramanujan's problem since :

$$5040/7^2+1/7=103,5041=71^2$$

Here I gave a sketch of proof in a special case which can be extend using Selberg sieve see Sum of two squares problem

Other point of view :

At the crossroads with these differents fields there is also the matrix for a near reference see

Homomorphic Encryption for Finite Automata

As other key-words : Hermitian matrix

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  • $\begingroup$ Thank you, good job Miss and Mister cassoulet char $\endgroup$
    – R1w
    Commented May 10 at 8:29
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    $\begingroup$ You're welcome to conclude see Uncertainty relation with three angular momentum components $\endgroup$ Commented May 10 at 12:45

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