Welcome to the resource topic for 2025/1757
Title:
New key establishment protocol based on random 1 walks in infinite forest
Authors: Vasyl Ustimenko, Tymoteusz Chojecki
Abstract:We suggest post quantum secure protocol based on pseudorandom walk on infinite q-regular forest D(q) where q = 2^m, m > 1. Correspondents share positive integer n, pseudorandom tuple from (Fq) ^n and two pseudorandom input words in the alphabet F_q of length O(1). They use the group of cubic multivariate transformations of the vector space of points of D(q) induced by walks on the forest of
even length as the platform for the implementation of modified Twisted Diffie-Hellman protocol of Noncommutative Cryptography based on the complexity of the Conjugacy Power Problem. The output of the protocol is a vector from (F_q)^n. In fact the action of the group on the partition set of the bipartite homomorphic image D(n, q) of the forest is used. Correspondents elaborate the collision vector in time O(n^2) in the case when the length of input words is O(1) and the size of private integer parameters is O(n). If length of the input words is also O(n) then the complexity of protocol will be O(n^3). We suggest also the obfuscation of the scheme with hidden graph of the
1complexity O(n^5) for which the output of the algorithm is a symbolic cubic transformation F of (Fq)^n. It can be used symbiotically with the symmetric encryption via the adding to the ciphertext from (F_q)^n the vector F(b_1, b_2, . . . , b_n) where the tuple (b_1, b_2, . . . , b_n) of pseudorandom nature is known publicly.
ePrint: https://eprint.iacr.org/2025/1757
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .