Small Field Attack, and Revisiting RLWE-Based Authenticated Key Exchange from Eurocrypt\u2715

Authenticated key-exchange (AKE) plays a fundamental role in modern cryptography. Up to now, the HMQV protocol family is among the most efficient provably secure AKE protocols, which has been widely standardized and in use. Given recent advances in quantum computing, it would be highly desirable to develop lattice-based HMQV-analogue protocols for the possible upcoming post-quantum era. Towards this goal, an important step is recently made by Zhang et al. at Eurocrypt\u2715. Similar to HMQV, the HMQV-analogue protocols proposed there consists of two variants: a two-pass protocol $\Pi_2$, as well as a one-pass protocol $\Pi_1$ that implies, in turn, a signcryption scheme (named as deniable encryption ). All these protocols are claimed to be provably secure under the ring-LWE (RLWE) assumption. In this work, we propose a new type of attack, referred to as small field attack (SFA), against the one-pass protocol $\Pi_1$, as well as its resultant deniable encryption scheme. With SFA, a malicious user can efficiently recover the static private key of the honest victim user in $\Pi_1$ with overwhelming probability. Moreover, the SFA attack is realistic and powerful in practice, in the sense that it is almost impossible for the honest user to prevent, or even detect, the attack. Besides, some new property regarding the CRT basis of $R_q$ is also developed in this work, which is essential for our small field attack and may be of independent interest. The security proof of the two-pass protocol $\Pi_2$ is then revisited. We are stuck at Claim 16 in [ZZDS14], with a gap identified and discussed in the security proof. To us, we do not know how to fix the gap, which traces back to some critical differences between the security proof of HMQV and that of its RLWE-based analogue

Lattice-Based Signature from Key Consensus

Given the current research status in lattice-based cryptography, it is commonly suggested that lattice-based signature could be subtler and harder to achieve. Among them, Dilithium is one of the most promising signature candidates for the post-quantum era, for its simplicity, efficiency, small public key size, and resistance against side channel attacks. The design of Dilithium is based on a list of pioneering works (e.g.,[VL09,VL12,BG14]), and has very remarkable performance by very careful and comprehensive optimizations in implementation and parameter selection. Whether better trade-offs on the already remarkable performance of Dilithium can be made is left in \cite{CRYSTALS} as an interesting open question. In this work, we provide new insights in interpreting the design of Dilithium, in terms of key consensus previously proposed in the literature for key encapsulation mechanisms (KEM) and key exchange (KEX). Based on the deterministic version of the optimal key consensus with noise (OKCN) mechanism, originally developed in [JZ16] for KEM/KEX, we present \emph{signature from key consensus with noise} (SKCN), which could be viewed as generalization and optimization of Dilithium. The construction of SKCN is generic, modular and flexible, which in particular allows a much broader range of parameters for searching better tradeoffs among security, computational efficiency, and bandwidth. For example, on the recommended parameters, compared with Dilithium our SKCN scheme is more efficient both in computation and in bandwidth, while preserving the same level of post-quantum security. In addition, using the same routine of OKCN for both KEM/KEX and digital signature eases (hardware) implementation and deployment in practice, and is useful to simplify the system complexity of lattice-based cryptography in general

Acclimation to soil flooding - sensing and signal-transduction

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