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Lecture notes in computer science

Highly Efficient Key Exchange Protocols with Optimal Tightness

Katriel Cohn-Gordon, Cas J. F. Cremers, Kristian Gjøsteen, Håkon Jacobsen, Tibor Jager

Published Jan 1, 2019• 45 citations
Publisher
DOI
10.1007/978-3-030-26954-8_25

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Tight security is an important requirement of practical cryptographic schemes. Compared with loosely‐secure schemes, tightly‐secure schemes allow shorter security parameters hence are more efficient. In CRYPTO 2018, Gjøsteen and Jager proposed a tightly‐secure authenticated key exchange (AKE) protocol. They used ‘commitment trick’ to construct a tight security reduction for their protocol. However, this technique leads to a three‐pass execution in their protocol, and their protocol cannot achieve key confirmation unless it is modified to have a four‐pass execution. In this study, the authors propose a tightly‐secure two‐pass AKE protocol. They use the twin Diffie–Hellman problem and the ‘re‐patch’ trick of random oracles to construct a tight security reduction for their protocol. This technique allows their protocol to have a two‐pass execution. Their protocol provides several security properties such as key‐compromise‐impersonation security, unknown‐key‐share security, and weak perfect forward secrecy. Moreover, a three‐pass variant of their protocol provides key confirmation.

IET Information Security•Sep 14, 2020•4 citations
In this paper we give nearly-tight reductions for modern implicitly authenticated Diffie-Hellman protocols in the style of the Signal and Noise protocols which are extremely simple and efficient. Unlike previous approaches, the combination of nearly-tight proofs and efficient protocols enables the first real-world instantiations for which the parameters can be chosen in a theoretically sound manner. Our reductions have only a linear loss in the number of users, implying that our protocols are more efficient than the state of the art when instantiated with theoretically sound parameters. We also prove that our security proofs are optimal: a linear loss in the number of users is unavoidable for our protocols for a large and natural class of reductions.
Tight security is an important requirement of practical cryptographic schemes. Compared with loosely‐secure schemes, tightly‐secure schemes allow shorter security parameters hence are more efficient. In CRYPTO 2018, Gjøsteen and Jager proposed a tightly‐secure authenticated key exchange (AKE) protocol. They used ‘commitment trick’ to construct a tight security reduction for their protocol. However, this technique leads to a three‐pass execution in their protocol, and their protocol cannot achieve key confirmation unless it is modified to have a four‐pass execution. In this study, the authors propose a tightly‐secure two‐pass AKE protocol. They use the twin Diffie–Hellman problem and the ‘re‐patch’ trick of random oracles to construct a tight security reduction for their protocol. This technique allows their protocol to have a two‐pass execution. Their protocol provides several security properties such as key‐compromise‐impersonation security, unknown‐key‐share security, and weak perfect forward secrecy. Moreover, a three‐pass variant of their protocol provides key confirmation.