Non-Constructivity in Security Proofs
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In the field of cryptography, one generally obtains assurances for the security of a cryptographic protocol by giving a reductionist security proof, which is comprised of a reduction from breaking a mathematical problem (that is well-studied and widely believed to be intractable) to the breaking of the cryptographic protocol. While such reductions are generally constructive, some authors give non-constructive reductions (also called non-uniform reductions) in order to reduce the tightness gap of the reduction. However, in order to assess the concrete security that the proof provides, one also needs to assess the intractability of the underlying mathematical problem against non-constructive attacks. Unfortunately, there has been very little work in the literature on non-constructive attacks on these problems, and sometimes non-constructive attacks are found that are much faster than their constructive counterparts. Thus, it is sometimes very difficult to obtain meaningful security assurances about a cryptographic protocol from a non-constructive reductionist security proof. In this thesis, we examine three instances of non-constructive security proofs for cryptographic protocols in the literature: (1) a password-based key derivation function; (2) an HMAC-related message authentication code scheme; and (3) a round-optimal blind signature scheme.
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Priya Soundararajan (2018). Non-Constructivity in Security Proofs. UWSpace. http://hdl.handle.net/10012/13770