The HFEv- signature scheme is one of the most studied multivariate schemes and one of the major candidates for the upcoming standardization of post-quantum digital signature schemes. In this paper, we propose three new attack strategies against HFEv-, each of them using the idea of projection. Especially our third attack is very effective and is, for some parameter sets, the most efficient known attack against HFEv-. Furthermore, our attack requires much less memory than direct and rank attacks. By our work, we therefore give new insights in the security of the HFEv- signature scheme and restrictions for the parameter choice of a possible future standardized HFEv- instance.

A review of the current state of multivariate public-key cryptosystems compares and contrasts the most promising multivariate schemes in digital signatures and public-key encryption as well as their security.

Secure Remote Password (SRP) protocol is an augmented Password-based Authenticated Key Exchange (PAKE) protocol based on discrete logarithm problem (DLP) with various attractive security features. Compared with basic PAKE protocols, SRP does not require server to store user’s password and user does not send password to server to authenticate. These features are desirable for secure client-server applications. SRP has gained extensive real-world deployment, including Apple iCloud, 1Password etc. However, with the advent of quantum computer and Shor’s algorithm, classic DLP-based public key cryptography algorithms are no longer secure, including SRP. Motivated by importance of SRP and threat from quantum attacks, we propose a RLWE-based SRP protocol (RLWE-SRP) which inherit advantages from SRP and elegant design from RLWE key exchange. We also present parameter choice and efficient portable C++ implementation of RLWE-SRP. Implementation of our 209-bit secure RLWE-SRP is more than 3x faster than 112-bit secure original SRP protocol, 5.5x faster than 80-bit secure J-PAKE and 14x faster than two 184-bit secure RLWE-based PAKE protocols with more desired properties.

Authenticated Key Exchange (AKE) is a cryptographic scheme with the aim to establish a high-entropy and secret session key over a insecure communications network. Password-Authenticated Key Exchange (PAKE) assumes that the parties in play share a simple password, which is cheap and human-memorable and is used to achieve the authentication. PAKEs are practically relevant as these features are extremely appealing in an age where most people access sensitive personal data remotely from more-and-more pervasive hand-held devices. Theoretically, PAKEs allow the secure computation and authentication of a high-entropy piece of data using a low-entropy string as a starting point. In this paper, we apply the recently proposed technique introduced in [19] to construct two lattice-based PAKE protocols enjoying a very simple and elegant design that is an parallel extension of the class of Random Oracle Model (ROM)-based protocols PAK and PPK [13, 41], but in the lattice-based setting. The new protocol resembling PAK is three-pass, and provides mutual explicit authentication, while the protocol following the structure of PPK is two-pass, and provides implicit authentication. Our protocols rely on the Ring-Learning-with-Errors (RLWE) assumption, and exploit the additive structure of the underlying ring. They have a comparable level of efficiency to PAK and PPK, which makes them highly attractive. We present a preliminary implementation of our protocols to demonstrate that they are both efficient and practical. We believe they are suitable quantum safe replacements for PAK and PPK.

In this paper, we show that the signal function used in Ring-Learning with Errors (RLWE) key exchange could leak information to find the secret s of a reused public key p = as+2e. This work is motivated by an attack proposed in [1] and gives an insight into how public keys reused for long term in RLWE key exchange protocols can be exploited. This work specifically focuses on the attack on the KE protocol in [2] by initiating multiple sessions with the honest party and analyze the output of the signal function. Experiments have confirmed the success of our attack in recovering the secret.