Cryptanalysis of the Cryptosystems Based on the Generalized Hidden Discrete Logarithm Problem

Ma Yanlong

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Paper 2021/1701

Cryptanalysis of the Cryptosystems Based on the Generalized Hidden Discrete Logarithm Problem

Ma Yanlong

Abstract

In this paper, we will show the hidden discrete logarithm problem(HDLP) and the generalized form of HDLP(GHDLP) over non-commutative associative algebras (FNAAs) can be reduced to discrete logarithm problem(DLP) in a finite field through analyzing the eigenvalues of the representation matrix. Through the analysis of computational complexity, we will show that HDLP and GHDLP is not are not good improvements of DLP.With all the instruments in hand, we will show how some schemes based on GHDLP can be broken. Thus we can conclude that, all ideas of constructing cryptographic schemes based on the two problem are of no practical significance.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: HLDP，GHDLP，digital signature，matrix
Contact author(s): 1543537831 @ qq com
History: 2023-06-27: revised; 2021-12-31: received; See all versions
Short URL: https://ia.cr/2021/1701
License: CC BY

BibTeX

@misc{cryptoeprint:2021/1701,
      author = {Ma Yanlong},
      title = {Cryptanalysis of the Cryptosystems Based on the Generalized Hidden Discrete Logarithm Problem},
      howpublished = {Cryptology ePrint Archive, Paper 2021/1701},
      year = {2021},
      note = {\url{https://eprint.iacr.org/2021/1701}},
      url = {https://eprint.iacr.org/2021/1701}
}