Abstract
Abstract. Classical Diffie-Hellman protocol of the key establishment was the basis of the development of several key exchange protocols. But this protocol is not secure and it is not protected against the “man in the middle†attack. The purpose of this article is to offer a secure and practical noncommutative analogue of the Diffie–Hellman protocol that is reliably protected not only against “man in the middle†attack but also against the quantum computer attack
Highlights
Security of the most popular present-day public key cryptosystems is based on the computational complexity of the some problems in number theory
The creation of the sufficiently powerful quantum computer will make these cryptosystems useless, since at present there are quantum algorithms that solve these problems in polynomial time [1]
Due to the need to develop new approaches in cryptography to protect against the potential threat posed by the quantum computer works have appeared that use noncommutative algebraic objects as a platform for building cryptosystems
Summary
Security of the most popular present-day public key cryptosystems is based on the computational complexity of the some problems in number theory. Two of these problems are the most common: the factorization problem and the discrete logarithm problem. Due to the need to develop new approaches in cryptography to protect against the potential threat posed by the quantum computer works have appeared that use noncommutative algebraic objects (groups and rings) as a platform for building cryptosystems. There is a need for secure noncommutative public key cryptosystems, which could be used in the construction of noncommutative analogue of the Diffie– Hellman key establishment protocol for protection against "man in the middle" attack. 1,..., N 4 selects session keys - the random integers ri ,ti satisfying f (n) 2 ri ,ti f (n) 2
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