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Supersingular Isogeny Diffie-Hellman: Finding the Distribution of the Secret Key by Computation of Brandt Matrices

van der Laan, Harmke (2018) Supersingular Isogeny Diffie-Hellman: Finding the Distribution of the Secret Key by Computation of Brandt Matrices. Bachelor's Thesis, Mathematics.

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Abstract

Quantum computing poses a threat to classical cryptosystems, so new protocols are needed. One possible candidate to replace currently used key exchange protocols is Supersingular Isogeny Diffie-Hellman (SIDH). The security of SIDH depends on a uniform distribution of the secret key, for which heuristic estimations exist. These heuristics have been verified by Thormarker (2017), via simulation of random walks on isogeny graphs. This thesis studies the theoretical background of SIDH and investigates the relation between supersingular elliptic curves and quaternion algebras. Through this relation it is shown that the distribution of the secret key in SIDH can be found by computing Brandt matrices. This is then compared to the results from the heuristic estimations.

Item Type: Thesis (Bachelor's Thesis)
Supervisor:
Supervisor nameSupervisor E mail
Muller, J.S.Steffen.Muller@rug.nl
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 16 Jul 2018
Last Modified: 30 Jul 2018 13:41
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/17892

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