Security

Public-Key Cryptographic Primitives Provably as Secure as Subset Sum

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Executive Summary

The authors propose a semantically-secure public-key encryption scheme whose security is polynomial-time equivalent to the hardness of solving random instances of the subset sum problem. The subset sum assumption required for the security of the 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, the proof of security is simple and direct. They also present a natural variant of the scheme that is secure against key-leakage attacks, as well as an oblivious transfer protocol that is secure against semi-honest adversaries.

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