Abstract
Applying Hensel’s lemma to the discrete logarithm problem over prime fields reveals the rich geometric and algebraic structure underlying the problem. It is shown that the problem has links to cocycles, connections, group extensions and crystalline cohomology. It is reminiscent of the recent use of Monsky-Washnitzer cohomology for counting points on hyperelliptic curves. Further some weak keys of the cryptosystems based on the hardness of the discrete logarithm problem over prime fields are discussed.
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Gadiyar, H.G., Maini, K.M.S., Padma, R. (2004). Cryptography, Connections, Cocycles and Crystals: A p-Adic Exploration of the Discrete Logarithm Problem. In: Canteaut, A., Viswanathan, K. (eds) Progress in Cryptology - INDOCRYPT 2004. INDOCRYPT 2004. Lecture Notes in Computer Science, vol 3348. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30556-9_24
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