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

PY - 2018/1/1

Y1 - 2018/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=85057335292&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85057335292&partnerID=8YFLogxK

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 -