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Discrete Logarithms

Aurore Guillevic 1 François Morain 1, 2 
1 GRACE - Geometry, arithmetic, algorithms, codes and encryption
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : The Discrete Logarithm Problem (DLP) is one of the most used mathematical problems in asymmetric cryptography design, the other one being the integer factorization. It is intrinsically related to the Diffie-Hellman problem (DHP). DLP can be stated in various groups. It must be hard in well-chosen groups, so that secure-enough cryptosystems can be built. In this chapter, we present the DLP, the various cryptographic problems based on it, the commonly used groups, and the major algorithms available at the moment to compute discrete logarithms in such groups. We also list the groups that must be avoided for security reasons. Our computational model will be that of classical computers. It is to be noted that in the quantum model, DLP can be solved in polynomial time for cyclic groups.
Keywords : discrete logarithms
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Submitted on : Wednesday, December 13, 2017 - 9:50:29 AM
Last modification on : Thursday, January 20, 2022 - 5:27:41 PM


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  • HAL Id : hal-01420485, version 2


Aurore Guillevic, François Morain. Discrete Logarithms. Nadia El Mrabet; Marc Joye. Guide to pairing-based cryptography, CRC Press - Taylor and Francis Group, pp.42, 2016, 9781498729505. ⟨hal-01420485v2⟩



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