The HFE cryptosystem is one of the most popular multi- variate schemes. Especially in the area of digital signatures, the HFEv- variant offers short signatures and high performance. Recently, an instance of the HFEv- signature scheme called GeMSS was selected as one of the alternative candidates for signature schemes in the third round of the NIST Post-Quantum Crypto (PQC) Standardization Project. In this paper, we propose a new key recovery attack on the HFEv- signature scheme. Our attack shows that both the Minus and the Vinegar modification do not enhance the security of the basic HFE scheme significantly. This shows that it is very difficult to build a secure and efficient signature scheme on the basis of HFE. In particular, we use our attack to show that the proposed parameters of the GeMSS scheme are not as secure as claimed.

In 2017, Ward Beullens et al. submitted Lifted Unbalanced Oil and Vinegar [3], which is a modification to the Unbalanced Oil and Vinegar Scheme by Patarin. Previously, Ding et al. proposed the Subfield Differential Attack [22] which prompted a change of parameters by the authors of LUOV for the second round of the NIST post quantum standardization competition [4]. In this paper we propose a modification to the Subfield Differential Attack called the Nested Subset Differential Attack which fully breaks half of the parameter sets put forward. We also show by experimentation that this attack is practically possible to do in under 210 min for the level I security parameters and not just a theoretical attack. The Nested Subset Differential attack is a large improvement of the Subfield differential attack which can be used in real world circumstances. Moreover, we will only use what is called the “lifted” structure of LUOV, and our attack can be thought as a development of solving “lifted” quadratic systems.

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In 2017, Ward Beullens et al. submitted Lifted Unbalanced Oil and Vinegar (LUOV) [4], a signature scheme based on the famous multivariate public key cryptosystem (MPKC) called Unbalanced Oil and Vinegar (UOV), to NIST for the competition for post-quantum public key scheme standardization. The defining feature of LUOV is that, though the public key P works in the extension field of degree r of F_2, the coefficients of P come from F_2. This is done to significantly reduce the size of P. The LUOV scheme is now in the second round of the NIST PQC standardization process. In this paper we introduce a new attack on LUOV. It exploits the “lifted” structure of LUOV to reduce direct attacks on it to those over a subfield. We show that this reduces the complexity below the targeted security for the NIST post-quantum standardization competition.

In 2017 Kyung-Ah Shim et al. proposed a multivariate signature scheme called Himq-3 which is a submission to National Institute of Standards and Technology (NIST) standardization process of post-quantum cryptosystems. The Himq-3 signature scheme can be classified into the oil vinegar signature scheme family. Similar to the rainbow signature scheme, the Himq-3 signature scheme uses a multilayer structure to shorten the signature size. Moreover the signing process is very fast due to a special system called L-inveritble cycle system that is used to invert the central map. In this paper, we provide a complete cryptanalysis to the Himq-3 signature scheme. We describe a new attack method called the singularity attack. This attack is based on the observation that the variables in the L-invertible cycle system are not allowed to be zero in a valid signature. For the completeness, we show step by step how variables and layers can be separated so that signature forgery can be performed. We claim that the complexity of our attack is much lower than the proposed security level.

In this paper, we proposed an idea to construct a general multivariate public key cryptographic (MPKC) scheme based on a user’s identity. In our construction, each user is distributed a unique identity by the key distribution center (KDC) and we use this key to generate user’s private keys. Thereafter, we use these private keys to produce the corresponding public key. This method can make key generating process easier so that the public key will reduce from dozens of Kilobyte to several bits. We then use our general scheme to construct practical identity-based signature schemes named ID-UOV and ID-Rainbow based on two well-known and promising MPKC signature schemes, respectively. Finally, we present the security analysis and give experiments for all of our proposed schemes and the baseline schemes. Comparison shows that our schemes are both efficient and practical.

In this paper, we first present a theoretical analysis model on the Proof-of-Work (PoW) for cryptocurrency blockchain. Based on this analysis, we present a new type of PoW, which relies on the hardness of solving a set of random quadratic equations over the finite field GF(2). We will present the advantages of such a PoW, in particular, in terms of its impact on decentralization and the incentives involved, and therefore demonstrate that this is a new good alternative as a new type for PoW in blockchain applications.

In this paper, we introduce a new provably secure ephemeral-only RLWE+Rounding-based key exchange protocol and a proper approach to more accurately estimate the security level of the RLWE problem with only one sample. Since our scheme is an ephemeral-only key exchange, it generates only one RLWE sample from protocol execution. We carefully analyze how to estimate the practical security of the RLWE problem with only one sample, which we call the ONE-sample RLWE problem. Our approach is different from existing approaches that are based on estimation with multiple RLWE samples. Though our analysis is based on some recently developed techniques in Darmstadt, our type of practical security estimate was never done before and it produces security estimates substantial different from the estimates before based on multiple RLWE samples. We show that the new design improves the security and reduce the communication cost of the protocol simultaneously by using one RLWE+Rounding sample technique. We also present two parameter choices ensuring 2^{−60} key exchange failure probability which cover security of AES-128/192/256 with concrete security analysis and implementation. We believe that our construction is secure, simple, efficient and elegant with wide application prospects.

Short integer solution (SIS) and learning with errors (LWE) are two hard lattice problems. These two problems are believed having huge potential in application of cryptography. In 2012, Ding et al. [5] introduced the first provably secure key exchange based on LWE problem. On the other hand, we believe that it is very difficult to do key exchange on SIS problem only. In 2014, Wang et al. [6] did an attempt, but it was not successful. Mao et al. [7] broke the protocol by an attack based on CBi-SIS problem in 2016. However, their attack is not efficient. In this paper, we present a extremely straightforward and simple attack to Wang’s key exchange and then we will construct a key exchange based on SIS and LWE problems.

In CT-RSA 2019, Bauer et al. have analyzed the case when the public key is reused for the NewHope key encapsulation mechanism (KEM), a second-round candidate in the NIST Post-quantum Standard process. They proposed an elegant method to recover coefficients ranging from −6 to 4 in the secret key. We repeat their experiments but there are two fundamental problems. First, even for coefficients in [−6, 4] we cannot recover at least 262 of them in each secret key with 1024 coefficients. Second, for the coefficient outside [−6, 4], they suggested an exhaustive search. But for each secret key on average there are 10 coefficients that need to be exhaustively searched, and each of them has 6 possibilities. This makes Bauer et al.’s method highly inefficient. We propose an improved method, which with 99.22% probability recovers all the coefficients ranging from −6 to 4 in the secret key. Then, inspired by Ding et al.’s key mismatch attack, we propose an efficient strategy which with a probability of 96.88% succeeds in recovering all the coefficients in the secret key. Experiments show that our proposed method is very efficient, which completes the attack in about 137.56 ms using the NewHope parameters.