Index Calculus Method for Solving Elliptic Curve Discrete Logarithm Problem Using Quantum Annealing

2021 ◽  
pp. 149-155
Author(s):  
Michał Wroński
Keyword(s):  
Elliptic Curve ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Quantum Annealing ◽  
Index Calculus

scholarly journals Quasi-subfield Polynomials and the Elliptic Curve Discrete Logarithm Problem

2020 ◽  
Vol 14 (1) ◽  
pp. 25-38
Author(s):  
Ming-Deh Huang ◽  
Michiel Kosters ◽  
Christophe Petit ◽  
Sze Ling Yeo ◽  
Yang Yun
Keyword(s):  
Elliptic Curve ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Complexity Bounds ◽  
New Class ◽  
Index Calculus

AbstractWe initiate the study of a new class of polynomials which we call quasi-subfield polynomials. First, we show that this class of polynomials could lead to more efficient attacks for the elliptic curve discrete logarithm problem via the index calculus approach. Specifically, we use these polynomials to construct factor bases for the index calculus approach and we provide explicit complexity bounds. Next, we investigate the existence of quasi-subfield polynomials.

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

Problems in Cryptography and Cryptanalysis

2018 ◽  
pp. 23-39
Author(s):  
Kannan Balasubramanian ◽  
Rajakani M.
Keyword(s):  
Elliptic Curve ◽  
Optimization Problems ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Random Number Generators ◽  
Factorization Problem ◽  
Diffie Hellman ◽  
Integer Factorization Problem ◽  
Diffie Hellman Key Exchange ◽  
Membership Problems

The integer factorization problem used in the RSA cryptosystem, the discrete logarithm problem used in Diffie-Hellman Key Exchange protocol and the Elliptic Curve Discrete Logarithm problem used in Elliptic Curve Cryptography are traditionally considered the difficult problems and used extensively in the design of cryptographic algorithms. We provide a number of other computationally difficult problems in the areas of Cryptography and Cryptanalysis. A class of problems called the Search problems, Group membership problems, and the Discrete Optimization problems are examples of such problems. A number of computationally difficult problems in Cryptanalysis have also been identified including the Cryptanalysis of Block ciphers, Pseudo-Random Number Generators and Hash functions.

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