Cryptanalysis of a public key cryptosystem based on Diophantine equations via weighted LLL reduction View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-11

AUTHORS

Jintai Ding, Momonari Kudo, Shinya Okumura, Tsuyoshi Takagi, Chengdong Tao

ABSTRACT

Researching post-quantum cryptography is now an important task in cryptography. Although various candidates of post-quantum cryptosystems (PQC) have been constructed, sizes of their public keys are large. Okumura constructed a candidate of PQC whose security is expected to be based on certain Diophantine equations (DEC). Okumura analysis suggests that DEC achieves the high security with small public key sizes. This paper proposes a polynomial time-attack on the one-way property of DEC. We reduce the security of DEC to finding special short lattice points of some low-rank lattices derived from public data. The usual LLL algorithm could not find the most important lattice point in our experiments because of certain properties of the lattice point. Our heuristic analysis leads us to using a variant of the LLL algorithm, called a weighted LLL algorithm by us. Our experiments suggest that DEC with 128 bit security becomes insecure by our attack. More... »

PAGES

1123-1152

References to SciGraph publications

  • 1997-09. Small Solutions to Polynomial Equations, and Low Exponent RSA Vulnerabilities in JOURNAL OF CRYPTOLOGY
  • 2015-12. A public key cryptosystem based on diophantine equations of degree increasing type in PACIFIC JOURNAL OF MATHEMATICS FOR INDUSTRY
  • 1986-03. On Lovász’ lattice reduction and the nearest lattice point problem in COMBINATORICA
  • 2010. Algebraic Cryptanalysis of the PKC’2009 Algebraic Surface Cryptosystem in PUBLIC KEY CRYPTOGRAPHY – PKC 2010
  • 2013. Simple Matrix Scheme for Encryption in POST-QUANTUM CRYPTOGRAPHY
  • 2010. On Ideal Lattices and Learning with Errors over Rings in ADVANCES IN CRYPTOLOGY – EUROCRYPT 2010
  • 2009. An Algebraic Surface Cryptosystem in PUBLIC KEY CRYPTOGRAPHY – PKC 2009
  • 1991-12. Hilbert's Tenth Problem for fields of rational functions over finite fields in INVENTIONES MATHEMATICAE
  • 1982-12. Factoring polynomials with rational coefficients in MATHEMATISCHE ANNALEN
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    http://scigraph.springernature.com/pub.10.1007/s13160-018-0316-x

    DOI

    http://dx.doi.org/10.1007/s13160-018-0316-x

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