Security Analysis of ElGamal Implementations

Mohamad El Laz; Benjamin Grégoire; Tamara Rezk

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Paper

Security Analysis of ElGamal Implementations

Topics: Applied Cryptography; Security Metrics and Measurement; Security Protocols; Security Requirements; Security Verification and Validation

In Proceedings of the 17th International Joint Conference on e-Business and Telecommunications SECRYPT - Volume 1, 310-321, 2020 , Lieusaint - Paris, France

Authors: Mohamad El Laz ; Benjamin Grégoire and Tamara Rezk

Affiliation: Inria Sophia-Antipolis Méditerranée, France

Keyword(s): ElGamal, DDH Assumption, Quadratic Residues, Voting Systems, Message Encoding.

Abstract: The ElGamal encryption scheme is not only the most extensively used alternative to RSA, but is also almost exclusively used in voting systems as an effective homomorphic encryption scheme. Being easily adaptable to a wide range of cryptographic groups, the ElGamal encryption scheme enjoys homomorphic properties while remaining semantically secure. This is subject to the upholding of the Decisional Diffie-Hellman (DDH) assumption on the chosen group. We analyze 26 libraries that implement the ElGamal encryption scheme and discover that 20 of them are semantically insecure as they do not respect the Decisional Diffie-Hellman (DDH) assumption. From the five libraries that do satisfy the DDH assumption, we identify and compare four different message encoding and decoding techniques.

CC BY-NC-ND 4.0

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Paper citation in several formats:

El Laz, M.; Grégoire, B. and Rezk, T. (2020). Security Analysis of ElGamal Implementations. In Proceedings of the 17th International Joint Conference on e-Business and Telecommunications - SECRYPT; ISBN 978-989-758-446-6; ISSN 2184-7711, SciTePress, pages 310-321. DOI: 10.5220/0009817103100321

@conference{secrypt20,
author={Mohamad {El Laz}. and Benjamin Grégoire. and Tamara Rezk.},
title={Security Analysis of ElGamal Implementations},
booktitle={Proceedings of the 17th International Joint Conference on e-Business and Telecommunications - SECRYPT},
year={2020},
pages={310-321},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0009817103100321},
isbn={978-989-758-446-6},
issn={2184-7711},
}

TY - CONF

JO - Proceedings of the 17th International Joint Conference on e-Business and Telecommunications - SECRYPT
TI - Security Analysis of ElGamal Implementations
SN - 978-989-758-446-6
IS - 2184-7711
AU - El Laz, M.
AU - Grégoire, B.
AU - Rezk, T.
PY - 2020
SP - 310
EP - 321
DO - 10.5220/0009817103100321
PB - SciTePress