Efficient public key encryption with smallest ciphertext expansion from factoring

  • Authors:
  • Haifeng Qian;Yuan Zhou;Zhibin Li;Zecheng Wang;Bing Zhang

  • Affiliations:
  • Computer Science and Technology Department, East China Normal University, Shanghai, China 200062;National Computer Network Emergency Response Technical Team (Coordination Center of China), Beijing, China;Computer Science and Technology Department, East China Normal University, Shanghai, China 200062 and Institute of Theoretical Computing, East China Normal University, Shanghai, China 200062;Computer Science and Technology Department, East China Normal University, Shanghai, China 200062;National Computer Network Emergency Response Technical Team (Coordination Center of China), Beijing, China

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2008

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Abstract

For public key encryption schemes, adaptive chosen ciphertext security is a widely accepted security notion since it captures a wide range of attacks. SAEP and SAEP+ are asymmetric encryption schemes which were proven to achieve semantic security against adaptive chosen ciphertext attacks. However, the bandwidth for message is essentially worse, that is the ciphertext expansion (the length difference between the ciphertext and the plaintext) is too large. In most of the mobile networks and bandwidth constrained communication systems, it is necessary to securely send as many messages as possible. In this article, we propose two chosen-ciphertext secure asymmetric encryption schemes. The first scheme is a generic asymmetric encryption padding scheme based on trapdoor permutations. The second one is its application to the Rabin-Williams function which has a very fast encryption algorithm. These asymmetric encryption schemes both achieve the optimal bandwidth w.r.t. the ciphertext expansion, namely with the smallest ciphertext expansion. Further, tight security reductions are shown to prove the security of these encryption schemes.