Obtaining a secure and efficient key agreement protocol from (H)MQV and NAXOS (extended version)

Updated (extended) and corrected version; see "Errata" and "Revisions" in the appendix for a summary of changes.LaMacchia, Lauter and Mityagin recently presented a strong security definition for authenticated key agreement strengthening the well-known Canetti-Krawczyk definition. They also described a protocol, called NAXOS, that enjoys a simple security proof in the new model. Compared to MQV and HMQV, NAXOS is less efficient and cannot be readily modified to obtain a one-pass protocol. On the other hand MQV does not have a security proof, and the HMQV security proof is extremely complicated. This paper proposes a new authenticated key agreement protocol, called CMQV (`Combined' MQV), which incorporates design principles from MQV, HMQV and NAXOS. The new protocol achieves the efficiency of HMQV and admits a natural one-pass variant. Moreover, we present a simple and intuitive proof that CMQV is secure in the LaMacchia-Lauter-Mityagin model

Forward Secrecy of SPAKE2

Currently, the Simple Password-Based Encrypted Key Exchange (SPAKE2) protocol of Abdalla and Pointcheval (CT-RSA 2005) is being considered by the IETF for standardization and integration in TLS 1.3. Although it has been proven secure in the Find-then-Guess model of Bellare, Pointcheval and Rogaway (EUROCRYPT 2000), whether it satisfies some notion of forward secrecy remains an open question. In this work, we prove that the SPAKE2 protocol satisfies the so-called weak forward secrecy introduced by Krawczyk (CRYPTO 2005). Furthermore, we demonstrate that the incorporation of key-confirmation codes in SPAKE2 results in a protocol that provably satisfies the stronger notion of perfect forward secrecy. As forward secrecy is an explicit requirement for cipher suites supported in the TLS handshake, we believe this work could fill the gap in the literature and facilitate the adoption of SPAKE2 in the recently approved TLS 1.3

Obtaining a secure and efficient key agreement protocol from (H)MQV and NAXOS

LaMacchia, Lauter and Mityagin recently presented a strong security definition for authenticated key agreement strengthening the well-known Canetti-Krawczyk definition. They also described a protocol, called NAXOS, that enjoys a simple security proof in the new model. Compared to MQV and HMQV, NAXOS is less efficient and cannot be readily modified to obtain a one-pass protocol. On the other hand MQV does not have a security proof, and the HMQV security proof is extremely complicated. This paper proposes a new authenticated key agreement protocol, called CMQV (`Combined\u27 MQV), which incorporates design principles from MQV, HMQV and NAXOS. The new protocol achieves the efficiency of HMQV and admits a natural one-pass variant. Moreover, we present a simple and intuitive proof that CMQV is secure in the LaMacchia-Lauter-Mityagin model

A New Security Model for Authenticated Key Agreement

The Canetti--Krawczyk (CK) and extended Canetti--Krawczyk (eCK) security models, are widely used to provide security arguments for key agreement protocols. We discuss security shades in the (e)CK models, and some practical attacks unconsidered in (e)CK--security arguments. We propose a strong security model which encompasses the eCK one. We also propose a new protocol, called Strengthened MQV (SMQV), which in addition to provide the same efficiency as the (H)MQV protocols, is particularly suited for distributed implementations wherein a tamper--proof device is used to store long--lived keys, while session keys are used on an untrusted host machine. The SMQV protocol meets our security definition under the Gap Diffie--Hellman assumption and the Random Oracle model

A Secure and Efficient Authenticated Diffie–Hellman Protocol

The Exponential Challenge Response (XRC) and Dual Exponential Challenge Response (DCR) signature schemes are the building blocks of the HMQV protocol. We propose a complementary analysis of these schemes; on the basis of this analysis we show how impersonation and man in the middle attacks can be mounted against the HMQV protocol when some session specific information leakages happen. We define the Full Exponential Challenge Response (FXRC) and Full Dual Exponential Challenge Response (FDCR) signature schemes; using these schemes we propose the Fully Hashed MQV protocol (with security arguments), which preserves the remarkable performance of the (H)MQV protocols and resists the attacks we present

Simple oblivious transfer protocols compatible with Kummer and supersingular isogenies

The key exchange protocol of Diffie and Hellman, which can be defined for any group, has the special feature of using only exponentiations. In particular, it can also be instantiated in Kummer varieties, which are not groups, and in the post-quantum isogeny-based setting with the supersingular isogeny DH scheme of De Feo, Jao and Plût (SIDH). In this article, we propose a new simple oblivious transfer (OT) protocol, based on the Diffie-Hellman key exchange, that only uses exponentiations; we also revisit the older Wu-Zhang-Wang scheme. Both protocols can be directly instantiated on fast Kummer varieties; more importantly, they can also be transposed in the post-quantum SIDH setting. The semantic security of our proposals relies on the hardness of non-standard versions of the (supersingular) Diffie-Hellman problem, that are investigated within this article. To the best of our knowledge, these protocols are the simplest secure discrete-log based OT schemes using only exponentiations, and the first isogeny-based OT schemes

Secure Blind Decryption

Abstract. In this work we construct public key encryption schemes that admit a protocol for blindly decrypting ciphertexts. In a blind decryp-tion protocol, a user with a ciphertext interacts with a secret keyholder such that the user obtains the decryption of the ciphertext and the key-holder learns nothing about what it decrypted. While we are not the first to consider this problem, previous works provided only weak secu-rity guarantees against malicious users. We provide, to our knowledge, the first practical blind decryption schemes that are secure under a strong CCA security definition. We prove our construction secure in the stan-dard model under simple, well-studied assumptions in bilinear groups. To motivate the usefulness of this primitive we discuss several applica-tions including privacy-preserving distributed file systems and Oblivious Transfer schemes that admit public contribution.

About the Security of MTI/C0 and MQV

Abstract. The main application of cryptography is the establishment of secure channels. The most classical way to achieve this goal is definitely the use of variants of the signed Diffie-Hellman protocol. It applies a signature algorithm on the flows of the basic Diffie-Hellman key exchange, in order to achieve authentication. However, signature-less authenticated key exchange have numerous advantages, and namely from the efficiency point of view. They are thus well-suited for some constrained environments. On the other hand, this efficiency comes at the cost of some uncertainty about the actual security. This paper focuses on the two most famous signature-less authenticated key exchange protocols, MTI/C0 and MQV. While the formal security of MTI/C0 has never been studied, results for the plain MQV protocol are still debated. We point out algorithmic assumptions on which some security proofs can be built in the random oracle model. The stress is put on implementation aspects that must be properly dealt with in order to obtain the expected security. Some formalizations about authenticated key exchange, and the generic model, are of independent interest. Key words: Key Exchange, MTI, MQV, Diffie-Hellman, Security Proof.