Public-Key Cryptographic Primitives Provably as Secure as Subset Sum

Abstract. We propose a semantically-secure public-key encryption scheme whose security is polynomialtime equivalent to the hardness of solving random instances of the subset sum problem. The subset sum assumption required for the security of our scheme is weaker than that of existing subset-sum based encryption schemes, namely the lattice-based schemes of Ajtai and Dwork (STOC ’97), Regev (STOC ’03, STOC ’05), and Peikert (STOC ’09). Additionally, our proof of security is simple and direct. We also present a natural variant of our scheme that is secure against key-leakage attacks, as well as an oblivious transfer protocol that is secure against semi-honest adversaries.

• Type: Conference
• Year: 2010
• Where: TCC
• Authors: Vadim Lyubashevsky, Adriana Palacio, Gil Segev
• Keywords: Cryptography, Public-key Encryption Scheme, Subset Sum Assumption, Subset Sum Problem, TCC 2010