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

Kaoru Kurosawa; Katja Schmidt-Samoa; Tsuyoshi Takagi

doi:10.1007/978-3-540-40061-5_30

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

Kaoru Kurosawa, Katja Schmidt-Samoa, Tsuyoshi Takagi

Laboratory of Mathematical Design for Advanced Cryptography

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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 language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Chi Sung Laih
Publisher	Springer Verlag
Pages	474-491
Number of pages	18
ISBN (Print)	3540205926
DOIs	https://doi.org/10.1007/978-3-540-40061-5_30
Publication status	Published - 2003

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2894
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-540-40061-5_30

Cite this

Kurosawa, K., Schmidt-Samoa, K., & Takagi, T. (2003). A complete and explicit security reduction algorithm for RSA-based cryptosystems. In C. S. Laih (Ed.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 474-491). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2894). Springer Verlag. https://doi.org/10.1007/978-3-540-40061-5_30

A complete and explicit security reduction algorithm for RSA-based cryptosystems. / Kurosawa, Kaoru; Schmidt-Samoa, Katja; Takagi, Tsuyoshi.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / Chi Sung Laih. Springer Verlag, 2003. p. 474-491 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2894).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Kurosawa, K, Schmidt-Samoa, K & Takagi, T 2003, A complete and explicit security reduction algorithm for RSA-based cryptosystems. in CS Laih (ed.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2894, Springer Verlag, pp. 474-491. https://doi.org/10.1007/978-3-540-40061-5_30

Kurosawa K, Schmidt-Samoa K, Takagi T. A complete and explicit security reduction algorithm for RSA-based cryptosystems. In Laih CS, editor, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2003. p. 474-491. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-40061-5_30

Kurosawa, Kaoru ; Schmidt-Samoa, Katja ; Takagi, Tsuyoshi. / A complete and explicit security reduction algorithm for RSA-based cryptosystems. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / Chi Sung Laih. Springer Verlag, 2003. pp. 474-491 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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

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