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Information and Computation

A multivariate convertible undeniable signature scheme

Satyam Omar, Sahadeo Padhye, Dhananjoy Dey, Devansh Mehrotra

Published Feb 21, 2025• 1 citation
Publisher
DOI
10.1016/j.ic.2025.105286

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Security assumptions in post-quantum cryptography

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This thesis analyses the assumptions present in security proofs of post-quantum cryptosystems using Koblitz and Menezes' critique to guide the focus points. The classical analysis focusses in particular on isogeny-based and multivariate polynomial cryptosystems. Firstly, we present attacks against hardness assumptions on derivative computational problems arising in protocols for isogeny-based undeniable signature schemes. Secondly, we provide upper bounds on the solving degree of over-determined systems of n+l multivariate polynomials in n variables as an alternative to the degree of regularity, which gives a heuristic upper bound. We finish with an analysis of the resources of a quantum adversary, providing an improved method for quantum gate approximation that gives shorter sequences by a factor of 9/7.

•Jan 1, 2021•0 citations
This thesis analyses the assumptions present in security proofs of post-quantum cryptosystems using Koblitz and Menezes' critique to guide the focus points. The classical analysis focusses in particular on isogeny-based and multivariate polynomial cryptosystems. Firstly, we present attacks against hardness assumptions on derivative computational problems arising in protocols for isogeny-based undeniable signature schemes. Secondly, we provide upper bounds on the solving degree of over-determined systems of n+l multivariate polynomials in n variables as an alternative to the degree of regularity, which gives a heuristic upper bound. We finish with an analysis of the resources of a quantum adversary, providing an improved method for quantum gate approximation that gives shorter sequences by a factor of 9/7.