A complete and explicit security reduction algorithm for RSA-based cryptosystems

Kaoru Kurosawa, Katja Schmidt-Samoa, Tsuyoshi Takagi

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)

Abstract

In this paper, we introduce a conceptually very simple and demonstrative algorithm for finding small solutions (x,y) of ax + y = c mod N, where gcd(a, N) = 1. Our new algorithm is a variant of the Euclidian algorithm. Unlike former methods, it finds a small solution whenever such a solution exists. Further it runs in time script O sign((logN)3), which is the same as the best known previous techniques, e.g. lattice-based solutions. We then apply our algorithm to RSA-OAEP and RSA-Paillier to obtain better security proofs. We believe that there will be many future applications of this algorithm in cryptography.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsChi Sung Laih
PublisherSpringer Verlag
Pages474-491
Number of pages18
ISBN (Print)3540205926
DOIs
Publication statusPublished - 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2894
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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