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Lecture notes in computer science

Tightly Secure Two-Pass Authenticated Key Exchange Protocol in the CK Model

Yuting Xiao, Rui Zhang, Hui Ma

Published Jan 1, 2020• 6 citations
Publisher
DOI
10.1007/978-3-030-40186-3_9

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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.

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Abstract. An unresolved problem in research on authenticated key exchange (AKE) is to construct a secure protocol against advanced attacks such as key compromise impersonation and maximal exposure attacks without relying on random oracles. HMQV, a state of the art AKE protocol, achieves both efficiency and the strong security proposed by Krawczyk (we call it the CK + model), which includes resistance to advanced attacks. However, the security proof is given under the random oracle model. We propose a generic construction of AKE from a key encapsulation mechanism (KEM). The construction is based on a chosen-ciphertext secure KEM, and the resultant AKE protocol is CK + secure in the standard model. The construction gives the first CK + secure AKE protocols based on the hardness of integer factorization problem, code-based problems, or learning problems with errors. In addition, instantiations under the Diffie-Hellman assumption or its variant can be proved to have strong security without non-standard assumptions such as πPRF and KEA1. Furthermore, we extend the CK + model to identity-based (called the id-CK + model), and propose a generic construction of identity-based AKE (ID-AKE) based on identity-based KEM, which satisfies id-CK + security. The construction leads first strongly secure ID-AKE protocols under the hardness of integer factorization problem, or learning problems with errors.

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Many recent protocols for Authenticated Key Exchange have been proven correct in the CK, CK-HMQV, or eCK security models. The exact relation between the security models, and hence between the security guarantees provided by the protocols, is unclear. We show that the CK, CK-HMQV, and eCK security models are formally incomparable for a number of reasons. Second, we show that these models are also practically incomparable, by providing for each model attacks on existing protocols that are not considered by the other models. Our analysis exposes many subtleties of these models, some of which can even be generalized to reveal shortcomings in security proofs in related AKE security models.

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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.
Abstract. An unresolved problem in research on authenticated key exchange (AKE) is to construct a secure protocol against advanced attacks such as key compromise impersonation and maximal exposure attacks without relying on random oracles. HMQV, a state of the art AKE protocol, achieves both efficiency and the strong security proposed by Krawczyk (we call it the CK + model), which includes resistance to advanced attacks. However, the security proof is given under the random oracle model. We propose a generic construction of AKE from a key encapsulation mechanism (KEM). The construction is based on a chosen-ciphertext secure KEM, and the resultant AKE protocol is CK + secure in the standard model. The construction gives the first CK + secure AKE protocols based on the hardness of integer factorization problem, code-based problems, or learning problems with errors. In addition, instantiations under the Diffie-Hellman assumption or its variant can be proved to have strong security without non-standard assumptions such as πPRF and KEA1. Furthermore, we extend the CK + model to identity-based (called the id-CK + model), and propose a generic construction of identity-based AKE (ID-AKE) based on identity-based KEM, which satisfies id-CK + security. The construction leads first strongly secure ID-AKE protocols under the hardness of integer factorization problem, or learning problems with errors.
Many recent protocols for Authenticated Key Exchange have been proven correct in the CK, CK-HMQV, or eCK security models. The exact relation between the security models, and hence between the security guarantees provided by the protocols, is unclear. We show that the CK, CK-HMQV, and eCK security models are formally incomparable for a number of reasons. Second, we show that these models are also practically incomparable, by providing for each model attacks on existing protocols that are not considered by the other models. Our analysis exposes many subtleties of these models, some of which can even be generalized to reveal shortcomings in security proofs in related AKE security models.