# Nondeterministic Algorithm for Breaking Diffie-Hellman Key Exchange using Self-Assembly of DNA Tiles

## Keywords:

Modular multiplication, Discrete logarithm, Nondeterministic, Diffie- Hellman, Key exchange, Self-assembly, DNA tiles## Abstract

The computation based on DNA tile self-assembly has been demonstrated to be scalable, which is consider as a promising technique for computation. In this work, I first show how the tile self-assembly process can be used for computing the modular multiplication by mainly constructing three small systems including addition system, subtraction system and comparing system which can also be parallely implemented the discrete logarithm problem in the finite field GF(p). Then the nondeterministic algorithm is successfully performed to break Diffie-Hellman key exchange with the computation time complexity of Î˜(p), and the probability of finding the successful solutions among many parallel executions is proved to be arbitrarily close to 1.

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