Computational hardness of IFP and ECDLP

Masaya Yasuda, Takeshi Shimoyama, Jun Kogure, Tetsuya Izu

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The RSA cryptosystem and elliptic curve cryptography (ECC) have been used practically and widely in public key cryptography. The security of RSA and ECC respectively relies on the computational hardness of the integer factorization problem (IFP) and the elliptic curve discrete logarithm problem (ECDLP). In this paper, we give an estimate of computing power required to solve each problem by state-of-the-art of theory and experiments. By comparing computing power required to solve the IFP and the ECDLP, we also estimate bit sizes of the two problems that can provide the same security level.

Original languageEnglish
Pages (from-to)493-521
Number of pages29
JournalApplicable Algebra in Engineering, Communications and Computing
Volume27
Issue number6
DOIs
Publication statusPublished - Dec 1 2016

Fingerprint

Integer Factorization
Discrete Logarithm Problem
Factorization
Elliptic Curves
Hardness
Cryptography
Public key cryptography
RSA Cryptosystem
Public Key Cryptography
Computing
Estimate
Experiments
Experiment

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Applied Mathematics

Cite this

Computational hardness of IFP and ECDLP. / Yasuda, Masaya; Shimoyama, Takeshi; Kogure, Jun; Izu, Tetsuya.

In: Applicable Algebra in Engineering, Communications and Computing, Vol. 27, No. 6, 01.12.2016, p. 493-521.

Research output: Contribution to journalArticle

Yasuda, Masaya ; Shimoyama, Takeshi ; Kogure, Jun ; Izu, Tetsuya. / Computational hardness of IFP and ECDLP. In: Applicable Algebra in Engineering, Communications and Computing. 2016 ; Vol. 27, No. 6. pp. 493-521.
@article{e511fcef4c5c4facb171e9bad10b2897,
title = "Computational hardness of IFP and ECDLP",
abstract = "The RSA cryptosystem and elliptic curve cryptography (ECC) have been used practically and widely in public key cryptography. The security of RSA and ECC respectively relies on the computational hardness of the integer factorization problem (IFP) and the elliptic curve discrete logarithm problem (ECDLP). In this paper, we give an estimate of computing power required to solve each problem by state-of-the-art of theory and experiments. By comparing computing power required to solve the IFP and the ECDLP, we also estimate bit sizes of the two problems that can provide the same security level.",
author = "Masaya Yasuda and Takeshi Shimoyama and Jun Kogure and Tetsuya Izu",
year = "2016",
month = "12",
day = "1",
doi = "10.1007/s00200-016-0291-x",
language = "English",
volume = "27",
pages = "493--521",
journal = "Applicable Algebra in Engineering, Communications and Computing",
issn = "0938-1279",
publisher = "Springer Verlag",
number = "6",

}

TY - JOUR

T1 - Computational hardness of IFP and ECDLP

AU - Yasuda, Masaya

AU - Shimoyama, Takeshi

AU - Kogure, Jun

AU - Izu, Tetsuya

PY - 2016/12/1

Y1 - 2016/12/1

N2 - The RSA cryptosystem and elliptic curve cryptography (ECC) have been used practically and widely in public key cryptography. The security of RSA and ECC respectively relies on the computational hardness of the integer factorization problem (IFP) and the elliptic curve discrete logarithm problem (ECDLP). In this paper, we give an estimate of computing power required to solve each problem by state-of-the-art of theory and experiments. By comparing computing power required to solve the IFP and the ECDLP, we also estimate bit sizes of the two problems that can provide the same security level.

AB - The RSA cryptosystem and elliptic curve cryptography (ECC) have been used practically and widely in public key cryptography. The security of RSA and ECC respectively relies on the computational hardness of the integer factorization problem (IFP) and the elliptic curve discrete logarithm problem (ECDLP). In this paper, we give an estimate of computing power required to solve each problem by state-of-the-art of theory and experiments. By comparing computing power required to solve the IFP and the ECDLP, we also estimate bit sizes of the two problems that can provide the same security level.

UR - http://www.scopus.com/inward/record.url?scp=84964091834&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964091834&partnerID=8YFLogxK

U2 - 10.1007/s00200-016-0291-x

DO - 10.1007/s00200-016-0291-x

M3 - Article

AN - SCOPUS:84964091834

VL - 27

SP - 493

EP - 521

JO - Applicable Algebra in Engineering, Communications and Computing

JF - Applicable Algebra in Engineering, Communications and Computing

SN - 0938-1279

IS - 6

ER -