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New Semantically Secure Public-Key Cryptosystems from the RSA-Primitive

  • Kouichi Sakurai
  • Tsuyoshi Takagi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2274)

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 {i1-01} mod n, where (e, n) is the RSA public-key and rMSB l (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.

Keywords

Encryption Scheme Random Integer Encryption Function Modular Exponentiation Choose Ciphertext Attack 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Kouichi Sakurai
    • 1
  • Tsuyoshi Takagi
    • 2
  1. 1.Department of Computer Science and Communication EngineeringKyushu UniversityFukuokaJapan
  2. 2.Fachbereich InformatikTechnische Universität DarmstadtDarmstadtGermany

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