Gligoroski, D. (2023). A Transformation for Lifting Discrete Logarithm Based Cryptography to Post-Quantum Cryptography, Cryptology ePrint Archive.
Added by: Jack (3/6/23, 10:24 PM) Last edited by: Jack (3/6/23, 10:32 PM)
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Abstract
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We construct algebraic structures where rising to the non-associative power indices is no longer tied with the Discrete Logarithm Problem but with a problem that has been analysed in the last two decades and does not have a quantum polynomial algorithm that solves it. The problem is called Exponential Congruences Problem. By this, we disprove the claims presented in the ePrint report 2021/583 titled "Entropoids: Groups in Disguise" by Lorenz Panny that "all instantiations of the entropoid framework should be breakable in polynomial time on a quantum computer." Additionally, we construct an Arithmetic for power indices and propose generic recipe guidelines that we call "Entropic-Lift" for transforming some of the existing classical cryptographic schemes that depend on the hardness of Discrete Logarithm Problem to post-quantum cryptographic schemes that will base their security on the hardness of the Exponential Congruences Problem. As concrete examples, we show how to transform the classical Diffie-Hellman key exchange, DSA and Schnorr signature schemes. We also post one open problem: From the perspective of provable security, specifically from the standpoint of security of post-quantum cryptographic schemes, to precisely formalize and analyze the potentials and limits of the Entropic-Lift transformation.
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