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On the Lossiness of 2k-th Power and the Instantiability of Rabin-OAEP

  • Haiyang Xue
  • Bao Li
  • Xianhui Lu
  • Kunpeng Wang
  • Yamin Liu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8813)

Abstract

Seurin (PKC 2014) proposed the 2-Φ/4-hiding assumption which asserts the indistinguishability of Blum Numbers from pseudo Blum Numbers. In this paper, we investigate the lossiness of 2 k -th power based on the 2 k -Φ/4-hiding assumption, which is an extension of the 2-Φ/4-hiding assumption. And we prove that 2 k -th power function is a lossy trapdoor permutation over Quadratic Residuosity group. This new lossy trapdoor function has 2k-bits lossiness for k-bits exponent, while the RSA lossy trapdoor function given by Kiltz et al. (Crypto 2010) has k-bits lossiness for k-bits exponent under Φ-hiding assumption in lossy mode. We modify the square function in Rabin-OAEP by 2 k -th power and show the instantiability of this Modified Rabin-OAEP by the technique of Kiltz et al. (Crypto 2010). The Modified Rabin-OAEP is more efficient than the RSA-OAEP scheme for the same secure bits. With the secure parameter being 80 bits and the modulus being 2048 bits, Modified Rabin-OAEP can encrypt roughly 454 bits of message, while RSA-OAEP can roughly encrypt 274 bits.

Keywords

Rabin OAEP Lossy trapdoor function Φ-hiding 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Haiyang Xue
    • 1
    • 2
    • 3
  • Bao Li
    • 1
    • 2
  • Xianhui Lu
    • 1
    • 2
  • Kunpeng Wang
    • 1
    • 2
  • Yamin Liu
    • 1
    • 2
  1. 1.Data Assurance and Communication Security Research CenterChinese Academy of SciencesBeijingChina
  2. 2.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  3. 3.University of Chinese Academy of SciencesBeijingChina

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