7 research outputs found
Formal Verification of a Post-Quantum Signal Protocol with Tamarin
No full textInternational audienceThe Signal protocol is used by billions of people for instant messaging in applications such as Facebook Messenger, Google Messages, Signal,Skype, and WhatsApp. However, advances in quantum computing threaten thesecurity of the cornerstone of this protocol: the Diffie-Hellman key exchange.There actually are resistant alternatives, called post-quantum secure, but replacing the Diffie-Hellman key exchange with these new primitives requires a deeprevision of the associated security proof. While the security of the current Signalprotocol has been extensively studied with hand-written proofs and computerverified symbolic analyses, its quantum-resistant variants lack symbolic securityanalyses.In this work, we present the first symbolic security model for post-quantum variants of the Signal protocol. Our model focuses on the core state machines of thetwo main sub-protocols of Signal: the X3DH handshake, and the so-called double ratchet protocol. Then we show, with an automated proof using the Tamarinprover, that instantiated with the Hashimoto-Katsumata-Kwiatkowski-Prest postquantum Signal’s handshake from PKC’21, and the Alwen-Coretti-Dodis KEMbased double ratchet from EUROCRYPT’19, the resulting post-quantum Signalprotocol has equivalent security properties to its current classical counterpart
GeT a CAKE: Generic Transformations from Key Encaspulation Mechanisms to Password Authenticated Key Exchanges
No full textInternational audiencePassword Authenticated Key Exchange (PAKE) have become a key building block in many security products as they provide interesting efficiency/security trade-offs. Indeed, a PAKE allows to dispense with the heavy public key infrastructures and its efficiency and portability make it well suited for applications such as Internet of Things or e-passports. With the emerging quantum threat and the effervescent development of post-quantum public key algorithms in the last five years, one would wonder how to modify existing password authenticated key exchange protocols that currently rely on Diffie-Hellman problems in order to include newly introduced and soon-to-be-standardized post-quantum key encapsulation mechanisms (KEM). A generic solution is desirable for maintaining modularity and adaptability with the many post-quantum KEM that have been introduced.In this paper, we propose two new generic and natural constructions proven in the Universal Composability (UC) model to transform, in a black-box manner, a KEM into a PAKE with very limited performance overhead: one or two extra symmetric encryptions. Behind the simplicity of the designs, establishing security proofs in the UC model is actually non-trivial and requires some additional properties on the underlying KEM like fuzziness and anonymity. Luckily, post-quantum KEM protocols often enjoy these two extra properties. As a demonstration, we prove that it is possible to apply our transformations to Crystals-Kyber, a lattice-based post-quantum KEM that will soon be standardized by the National Institute of Standards and Technology (NIST)
Polytopes in the Fiat-Shamir with Aborts Paradigm
No full textThe Fiat-Shamir with Aborts paradigm (FSwA) uses rejection sampling to remove a secret’s dependency on a given source distribution. Recent results revealed that unlike the uniform distribution in the hypercube, both the continuous Gaussian and the uniform distribution within the hypersphere minimise the rejection rate and the size of the proof of knowledge. However, in practice both these distributions suffer from the complexity of their sampler. So far, those three distributions are the only available alternatives, but none of them offer the best of all worlds: competitive proof of knowledge size and rejection rate with a simple sampler.
We introduce a new generic framework for FSwA using polytope based rejection sampling to enable a wider variety of constructions. As a matter of fact, this framework is the first to generalise these results to integral distributions. To complement the lack of alternatives, we also propose a new polytope construction, whose uniform sampler approaches in simplicity that of the hypercube. At the same time, it provides competitive proof of knowledge size compared to that obtained from the Gaussian distribution. Concurrently, we share some experimental improvements of our construction to further reduce the proof size. Finally, we propose a signature based on the FSwA paradigm using both our framework and construction. We prove it to be competitive with Haetae in signature size and with Dilithium on sampler simplicity
GeT a CAKE: Generic Transformations from Key Encaspulation Mechanisms to Password Authenticated Key Exchanges
No full textPassword Authenticated Key Exchange (PAKE) have become a key building block in many security products as they provide interesting efficiency/security trade-offs. Indeed, a PAKE allows to dispense with the heavy public key infrastructures and its efficiency and portability make it well suited for applications such as Internet of Things or e-passports.
With the emerging quantum threat and the effervescent development of post-quantum public key algorithms in the last five years, one would wonder how to modify existing password authenticated key exchange protocols that currently rely on Diffie-Hellman problems in order to include newly introduced and soon-to-be-standardized post-quantum key encapsulation mechanisms (KEM).
A generic solution is desirable for maintaining modularity and adaptability with the many post-quantum KEM that have been introduced.
In this paper, we propose two new generic and natural constructions proven in the Universal Composability (UC) model to transform, in a black-box manner, a KEM into a PAKE with very limited performance overhead: one or two extra symmetric encryptions. Behind the simplicity of the designs, establishing security proofs in the UC model is actually non-trivial and requires some additional properties on the underlying KEM like fuzziness and anonymity. Luckily, post-quantum KEM protocols often enjoy these two extra properties. As a demonstration, we prove that it is possible to apply our transformations to Crystals-Kyber, a lattice-based post-quantum KEM that will soon be standardized by the National Institute of Standards and Technology (NIST).
In a nutshell, this work opens up the possibility to securely include post-quantum cryptography in PAKE-based real-world protocols
Polytopes in the Fiat-Shamir with Aborts Paradigm
No full textInternational audienceThe Fiat-Shamir with Aborts paradigm (FSwA) uses rejection sampling to remove a secret’s dependency on a given source distribution. Recent results revealed that unlike the uniform distribution in the hypercube, both the continuous Gaussian and the uniform distribution within the hypersphere minimise the rejection rate and the size of the proof of knowledge. However, in practice both these distributions suffer from the complexity of their sampler. So far, those three distributions are the only available alternatives, but none of them offer the best of all worlds: competitive proof of knowledge size and rejection rate with a simple sampler.We introduce a new generic framework for FSwA using polytope based rejection sampling to enable a wider variety of constructions. As a matter of fact, this framework is the first to generalise these results to integral distributions. To complement the lack of alternatives, we also propose a new polytope construction, whose uniform sampler approaches in simplicity that of the hypercube. At the same time, it provides competitive proof of knowledge size compared to that obtained from the Gaussian distribution. Concurrently, we share some experimental improvements of our construction to further reduce the proof size. Finally, we propose a signature based on the FSwA paradigm using both our framework and construction. We prove it to be competitive with Haetae in signature size and with Dilithium on sampler simplicity
DAKE: Bandwidth-Efficient (U)AKE from Double-KEM
No full textBandwidth remains a major bottleneck in post-quantum cryptography, particularly for authenticated key exchange (AKE) protocols. In this work, we present DAKE, a bandwidth-efficient AKE framework built from double-KEM constructions. DAKE comes in two main versions achieving, respectively, weak and full perfect forward secrecy, as well as explicit authentication. It further admits two variants: a unilateral version, and another where a signature scheme replaces a KEM. They are proven secure in the standard model under eCKw and eCK-PFS, two strong variants of the extended Canetti–Krawczyk framework.
DAKE employs a double-KEM, a primitive that encapsulates a single key under two public keys simultaneously. Such constructions can achieve smaller encapsulation sizes than two independent KEM encapsulations, offering a significant bandwidth advantage.
To facilitate the design of double-KEMs compatible with DAKE, we introduce a chosen-key Fujisaki–Okamoto (CK-FO) transform proven in the QROM, which upgrades IND-CPA double-PKEs to IND-CCA double-KEMs while ensuring the one-sided chosen-key security required by DAKE.
As a concrete instantiation, we propose Maul, a compact double-KEM derived from ML-KEM under the Hint-MLWE assumption. Maul reuses ciphertext components to cut encapsulation size by up to 42% compared to two parallel ML-KEMs. When instantiated with Maul, DAKE achieves overall communication reductions of about 16% (mutual authentication) and 21% (unilateral), outperforming both the double-KEM AKE of Xue et al. (ASIACRYPT 2018) and standard ML-KEM-based AKEs
