The McEliece cryptosystem is one of the few systems to be considered secure against attacks by Quantum computers. The original scheme is built upon Goppa codes and produces very large keys, hence recent research has focused mainly on trying to reduce the public key size. Previous proposals tried to replace the class of Goppa codes with other families of codes, but this was revealed to be an insecure choice. In this paper we introduce a construction based on Generalized Srivastava codes, a large class which includes Goppa codes as a special case, that allows relatively short public keys without being vulnerable to known structural attacks.

Abstract. In this paper we present efficient implementations of McEliece variants using quasi-dyadic codes. We provide secure parameters for a classical McEliece encryption scheme based on quasi-dyadic generalized Srivastava codes, and successively convert our scheme to a CCA2-secure protocol in the random oracle model applying the Fujisaki-Okamoto transform. In contrast with all other CCA2-secure code-based cryptosystems that work in the random oracle model, our conversion does not require a constant weight encoding function. We present results for both 128-bit and 80-bit security level, and for the latter we also feature an implementation for an embedded device.

We revisit the construction of IND-CCA secure key encapsulation mechanisms (KEM) from public-key encryption schemes (PKE). We give new, tighter security reductions for several constructions. Our main result is an improved reduction for the security of the U ⊥ -transform of Hofheinz, Hövelmanns, and Kiltz (TCC'17) which turns OW-CPA secure deterministic PKEs into IND-CCA secure KEMs. This result is enabled by a new one-way to hiding (O2H) lemma which gives a tighter bound than previous O2H lemmas in certain settings and might be of independent interest. We extend this result also to the case of PKEs with non-zero decryption failure probability and non-deterministic PKEs. However, we assume that the derandomized PKE is injective with overwhelming probability. In addition, we analyze the impact of different variations of the U ⊥transform discussed in the literature on the security of the final scheme. We consider the difference between explicit (U ⊥ ) and implicit (U ⊥ ) rejection, proving that security of the former implies security of the latter. We show that the opposite direction holds if the scheme with explicit rejection also uses key confirmation. Finally, we prove that (at least from a theoretic point of view) security is independent of whether the session keys are derived from message and ciphertext (U ⊥ ) or just from the message (U ⊥ m ).

The design of a practical code-based signature scheme is an open problem in post-quantum cryptography. This paper is the full version of a work appeared at SIN’18 as a short paper, which introduced a simple and efficient one-time secure signature scheme based on quasi-cyclic codes. As such, this paper features, in a fully self-contained way, an accurate description of the scheme setting and related previous work, a detailed security analysis, and an extensive comparison and performance discussion.

Current widely-used key exchange (KE) mechanisms will be vulnerable to quantum attacks when sufficiently strong quantum computers become available. Therefore, devising quantum-resistant replacements that combine efficiency with solid security guarantees is an important and challenging task. This paper proposes several contributions towards this goal. First, we introduce "CAKE", a key encapsulation algorithm based on the QC-MDPC McEliece encryption scheme, with two major improvements: a) the use of ephemeral keys that defeats a recent reaction attack against MDPC decoding of the corresponding encryption scheme and b) a highly efficient key generation procedure for QC-MDPCbased cryptosystems. Then, we present an authenticated key exchange protocol based on CAKE, which is suitable for the Internet Key Exchange (IKE) standard. We prove that CAKE is IND-CPA secure, that the protocol is SK-Secure, and suggest practical parameters. Compared to other post-quantum schemes, we believe that CAKE is a promising candidate for post-quantum key exchange standardization.

Code-based cryptography is one of the main areas of interest for NIST’s Post-Quantum Cryptography Standardization call. In this paper, we introduce DAGS, a Key Encapsulation Mechanism (KEM) based on quasi-dyadic generalized Srivastava codes. The scheme is proved to be IND-CCA secure in both random oracle model and quantum random oracle model. We believe that DAGS will offer competitive performance, especially when compared with other existing code-based schemes, and represent a valid candidate for post-quantum standardization.

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Code-based cryptographic schemes are highly regarded among the quantum-safe alternatives to current standards. Yet, designing codebased signatures using traditional methods has always been a challenging task, and current proposals are still far from the target set by other postquantum primitives (e.g. lattice-based). In this paper, we revisit a recent work using an innovative approach for signing, based on the hardness of the code equivalence problem. We introduce some optimizations and provide a security analysis for all variants considered. We then show that the new parameters produce instances of practical interest.Recently, cryptographic group actions came into the spotlight again, with several improvements over the original work of Couveignes [10] and Stolbunov [20]. This enabled many improvements in the field of isogeny-based cryptography, including primitives that were previously missing in the post-quantum scenario such as static-static key exchange protocols.