Exponentiation inversion problem reduced from fixed argument pairing inversion on twistable ate pairing and its difficulty

Shoichi Akagi, Yasuyuki Nogami

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

As one of problems that guarantee the security of pairing-based cryptography, pairing inversion problem is studied. Some recent works have reduced fixed argument pairing inversion (FAPI) problem to exponentiation inversion (EI) problem. According to the results, FAPI problem is solved if EI problem of exponent (qk - 1)/Φk (q) is solved, where q, k, and r are the characteristic, embedding degree, and order of pairing group, respectively. Φk(x) is the cyclotomic polynomial of order k. This paper shows an approach for reducing the exponent of EI problem to q - 1 especially on Ate pairing. For many embedding degrees, it is considerably reduced from the previous result (qk - 1)/Φk(q). After that, the difficulty of the reduced EI problem is discussed based on the distribution of correct (q - 1)-th roots on a small example.

Original languageEnglish
Pages (from-to)240-249
Number of pages10
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8639 LNCS
DOIs
Publication statusPublished - 2014

Fingerprint

Exponentiation
Pairing
Cryptography
Inversion
Polynomials
Exponent
Pairing-based Cryptography
Cyclotomic Polynomials
Roots

Keywords

  • Barreto-Naehrig curve
  • pairing inversion problem
  • trace

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

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title = "Exponentiation inversion problem reduced from fixed argument pairing inversion on twistable ate pairing and its difficulty",
abstract = "As one of problems that guarantee the security of pairing-based cryptography, pairing inversion problem is studied. Some recent works have reduced fixed argument pairing inversion (FAPI) problem to exponentiation inversion (EI) problem. According to the results, FAPI problem is solved if EI problem of exponent (qk - 1)/Φk (q) is solved, where q, k, and r are the characteristic, embedding degree, and order of pairing group, respectively. Φk(x) is the cyclotomic polynomial of order k. This paper shows an approach for reducing the exponent of EI problem to q - 1 especially on Ate pairing. For many embedding degrees, it is considerably reduced from the previous result (qk - 1)/Φk(q). After that, the difficulty of the reduced EI problem is discussed based on the distribution of correct (q - 1)-th roots on a small example.",
keywords = "Barreto-Naehrig curve, pairing inversion problem, trace",
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AU - Nogami, Yasuyuki

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AB - As one of problems that guarantee the security of pairing-based cryptography, pairing inversion problem is studied. Some recent works have reduced fixed argument pairing inversion (FAPI) problem to exponentiation inversion (EI) problem. According to the results, FAPI problem is solved if EI problem of exponent (qk - 1)/Φk (q) is solved, where q, k, and r are the characteristic, embedding degree, and order of pairing group, respectively. Φk(x) is the cyclotomic polynomial of order k. This paper shows an approach for reducing the exponent of EI problem to q - 1 especially on Ate pairing. For many embedding degrees, it is considerably reduced from the previous result (qk - 1)/Φk(q). After that, the difficulty of the reduced EI problem is discussed based on the distribution of correct (q - 1)-th roots on a small example.

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