The Discrete Logarithm Problem

1993 ◽  
pp. 49-59
Author(s):  
Alfred Menezes
Keyword(s):  
Discrete Logarithm ◽  
Discrete Logarithm Problem

scholarly journals On the first fall degree of summation polynomials

2019 ◽  
Vol 13 (3-4) ◽  
pp. 229-237
Author(s):  
Stavros Kousidis ◽  
Andreas Wiemers
Keyword(s):  
Elliptic Curve ◽  
Gröbner Basis ◽  
Discrete Logarithm ◽  
Polynomial Systems ◽  
Discrete Logarithm Problem ◽  
Grobner Basis ◽  
Weil Descent ◽  
Degree Bound

Abstract We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.

scholarly journals Partial Lifting and the Elliptic Curve Discrete Logarithm Problem

Algorithmica ◽  
2006 ◽  
Vol 46 (1) ◽  
pp. 59-68 ◽  
Author(s):  
Qi Cheng ◽  
Ming-Deh Huang
Keyword(s):  
Elliptic Curve ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem

scholarly journals Cryptographic aspects of real hyperelliptic curves

2010 ◽  
Vol 47 (1) ◽  
pp. 31-65 ◽  
Author(s):  
Michael J. Jacobson ◽  
Renate Scheidler ◽  
Andreas Stein
Keyword(s):  
Hyperelliptic Curve ◽  
Discrete Logarithm ◽  
Mathematical Structure ◽  
Hyperelliptic Curves ◽  
Cryptographic Protocols ◽  
Discrete Logarithm Problem ◽  
Explicit Formulas ◽  
Genus 2

Abstract In this paper, we give an overview of cryptographic applications using real hyperelliptic curves. We review previously proposed cryptographic protocols and discuss the infrastructure of a real hyperelliptic curve, the mathematical structure underlying all these protocols. We then describe recent improvements to infrastructure arithmetic, including explicit formulas for divisor arithmetic in genus 2, and advances in solving the infrastructure discrete logarithm problem, whose presumed intractability is the basis of security for the related cryptographic protocols.

Discrete Logarithm Problem

2019 ◽  
pp. 47-57
Author(s):  
Khaleel Ahmad ◽  
Afsar Kamal ◽  
Khairol Amali Bin Ahmad
Keyword(s):  
Discrete Logarithm ◽  
Discrete Logarithm Problem

scholarly journals On the discrete logarithm problem for prime-field elliptic curves

2018 ◽  
Vol 51 ◽  
pp. 168-182 ◽  
Author(s):  
Alessandro Amadori ◽  
Federico Pintore ◽  
Massimiliano Sala
Keyword(s):  
Elliptic Curves ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Prime Field
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