TY - GEN
T1 - Acceleration of index calculus for solving ECDLP over prime fields and its limitation
AU - Kudo, Momonari
AU - Yokota, Yuki
AU - Takahashi, Yasushi
AU - Yasuda, Masaya
N1 - Funding Information:
�This work was supported by JST CREST Grant Number JPMJCR14D6, Japan.
Funding Information:
supported by JST CREST Grant Number
Publisher Copyright:
© Springer Nature Switzerland AG 2018.
PY - 2018
Y1 - 2018
N2 - In 2018, Amadori et al. proposed a new variant of index calculus to solve the elliptic curve discrete logarithm problem (ECDLP), using Semaev’s summation polynomials. The variant drastically decreases the number of required Gröbner basis computations, and it outperforms other index calculus algorithms for the ECDLP over prime fields. In this paper, we provide several improvements to accelerate to solve systems of multivariate equations arising in the variant. A main improvement is to apply the hybrid method, which mixes exhaustive search and Gröbner bases techniques to solve multivariate systems over finite fields. We also make use of symmetries of summation polynomials. We show experimental results of our improvements, and give their complexity analysis to discuss a limitation of our acceleration in both theory and practice.
AB - In 2018, Amadori et al. proposed a new variant of index calculus to solve the elliptic curve discrete logarithm problem (ECDLP), using Semaev’s summation polynomials. The variant drastically decreases the number of required Gröbner basis computations, and it outperforms other index calculus algorithms for the ECDLP over prime fields. In this paper, we provide several improvements to accelerate to solve systems of multivariate equations arising in the variant. A main improvement is to apply the hybrid method, which mixes exhaustive search and Gröbner bases techniques to solve multivariate systems over finite fields. We also make use of symmetries of summation polynomials. We show experimental results of our improvements, and give their complexity analysis to discuss a limitation of our acceleration in both theory and practice.
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U2 - 10.1007/978-3-030-00434-7_19
DO - 10.1007/978-3-030-00434-7_19
M3 - Conference contribution
AN - SCOPUS:85057335292
SN - 9783030004330
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 377
EP - 393
BT - Cryptology and Network Security - 17th International Conference, CANS 2018, Proceedings
A2 - Papadimitratos, Panos
A2 - Camenisch, Jan
PB - Springer Verlag
T2 - 17th International Conference on Cryptology and Network Security, CANS 2018
Y2 - 30 September 2018 through 3 October 2018
ER -