New semantically secure public-key cryptosystems from the rsa-primitive

Kouichi Sakurai, Tsuyoshi Takagi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Citations (Scopus)

Abstract

We analyze the security of the simplified Paillier (S-Paillier) cryptosystem, which was proposed by Catalano et al. We prove that the one-wayness of the S-Paillier scheme is as intractable as the standard RSA problem. We also prove that an adversary, which breaks the semantic security, can compute the least significant bits of the nonce. This observation is interesting, because the least significant bit of the nonce is the hard core bit of the encryption function. Moreover, we proposed a novel semantically secure cryptosystem, based on the one-way function fe,nMSBZ(l) (r) = (r−MSBl(r))emod n, where (e, n) is the RSA public-key and r −MSBl(r) means that the l most significant bits of r are zeroed. We proved that the one-wayness of the proposed scheme is as intractable as the standard RSA problem. An adversary, which breaks the semantic security of the proposed scheme, can break the least significant bits of the nonce. These security results of the proposed scheme are similar to those of the S-Paillier cryptosystem. However, the proposed scheme is more efficient than the S-Paillier cryptosystem.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsDavid Naccache, Pascal Paillier
PublisherSpringer Verlag
Pages1-16
Number of pages16
ISBN (Print)3540431683, 9783540431688
DOIs
Publication statusPublished - Jan 1 2002
Event5th International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2002 - Paris, France
Duration: Feb 12 2002Feb 14 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2274
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other5th International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2002
CountryFrance
CityParis
Period2/12/022/14/02

Fingerprint

Public-key Cryptosystem
Cryptography
Cryptosystem
Semantic Security
Semantics
One-way Function
Public key
Encryption

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Sakurai, K., & Takagi, T. (2002). New semantically secure public-key cryptosystems from the rsa-primitive. In D. Naccache, & P. Paillier (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 1-16). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2274). Springer Verlag. https://doi.org/10.1007/3-540-45664-3_1

New semantically secure public-key cryptosystems from the rsa-primitive. / Sakurai, Kouichi; Takagi, Tsuyoshi.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / David Naccache; Pascal Paillier. Springer Verlag, 2002. p. 1-16 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2274).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sakurai, K & Takagi, T 2002, New semantically secure public-key cryptosystems from the rsa-primitive. in D Naccache & P Paillier (eds), 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. 2274, Springer Verlag, pp. 1-16, 5th International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2002, Paris, France, 2/12/02. https://doi.org/10.1007/3-540-45664-3_1
Sakurai K, Takagi T. New semantically secure public-key cryptosystems from the rsa-primitive. In Naccache D, Paillier P, editors, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2002. p. 1-16. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-45664-3_1
Sakurai, Kouichi ; Takagi, Tsuyoshi. / New semantically secure public-key cryptosystems from the rsa-primitive. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / David Naccache ; Pascal Paillier. Springer Verlag, 2002. pp. 1-16 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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