Paper 2019/468
The Mersenne Low Hamming Combination Search Problem can be reduced to an ILP Problem
Abstract
In 2017, Aggarwal, Joux, Prakash, and Santha proposed an innovative NTRU-like public-key cryptosystem that was believed to be quantum resistant, based on Mersenne prime numbers q = 2^N-1. After a successful attack designed by Beunardeau, Connolly, Geraud, and Naccache, the authors revised the protocol which was accepted for Round 1 of the Post-Quantum Cryptography Standardization Process organized by NIST. The security of this protocol is based on the assumption that a so-called Mersenne Low Hamming Combination Search Problem (MLHCombSP) is hard to solve. In this work, we present a reduction of MLHCombSP to Integer Linear Programming (ILP). This opens new research directions for assessing the concrete robustness of such cryptosystem. In particular, we uncover a new family of weak keys, for whose our attack runs in polynomial time.
Note: Fixed typos, removed one section, reviewed statement.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. AfricaCrypt 2019
- Keywords
- Post-Quantum Cryptography Cryptanalysis Public-Key Cryptography Integer Linear Programming Mersenne-Based Cryptosystem
- Contact author(s)
-
budroni alessandro @ gmail com
andreat tenti @ gmail com - History
- 2022-10-06: last of 3 revisions
- 2019-05-10: received
- See all versions
- Short URL
- https://ia.cr/2019/468
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2019/468,
author = {Alessandro Budroni and Andrea Tenti},
title = {The Mersenne Low Hamming Combination Search Problem can be reduced to an {ILP} Problem},
howpublished = {Cryptology {ePrint} Archive, Paper 2019/468},
year = {2019},
url = {https://eprint.iacr.org/2019/468}
}
