On a public-key cryptosystem based on iterated morphisms and substitutions
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A course in computational algebraic number theory
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Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
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The main purpose of this paper is to examine applications of group theoretical concepts to cryptography. We construct a backward deterministic system employing the action of the modular group on the upper half plane and the amalgamated free product structure of the group. We invent a geometrical algorithm that finds the normal form of an element of the modular group effectively. This algorithm makes our backward deterministic system tractable. Using the backward deterministic system, we invent a public-key cryptosystem in terms of a functional cryptosystem.