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Cryptanalysis of the cryptosystems based on the generalized hidden discrete logarithm problem
Authors: Yanlong Ma
Keywords: hidden discrete logarithm; generalized hidden discrete logarithm; digital signature; matrix representation.
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Keywords: hidden discrete logarithm; generalized hidden discrete logarithm; digital signature; matrix representation.
Abstract
In this paper, we will solve an important form of hidden discrete logarithm problem (HDLP) and a generalized form of HDLP (GHDLP) over non-commutative associative algebras (FNAAs). We will reduce them 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 are not good improvements of DLP. With all the instruments in hand, we will break a series of corresponding schemes. Thus, we can conclude that all ideas of constructing cryptographic schemes based on the two solved problems are of no practical significance.ORCID: https://orcid.org/0009-0003-1278-1879
Department of Mathematical Sciences Tsinghua University
No.30, Shuangqing Road, Haidian District
Beijing, China
Postcode: 100084
E-mail:
Department of Mathematical Sciences Tsinghua University
No.30, Shuangqing Road, Haidian District
Beijing, China
Postcode: 100084
E-mail:
DOI
https://doi.org/10.56415/csjm.v32.15Fulltext
– 0.31 Mb
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- Cryptanalysis of the cryptosystems based on the generalized hidden discrete logarithm problem
