Cryptanalysis of The Lifted Unbalanced Oil Vinegar Signature Scheme

In 2017, Ward Beullens \textit{et al.} submitted Lifted Unbalanced Oil and Vinegar (LUOV)\cite{beullens2017field}, 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 $\mathcal{P}$ works in the extension field of degree $r$ of $\mathbb{F}_2$, the coefficients of $\mathcal{P}$ come from $\mathbb{F}_2$. This is done to significantly reduce the size of $\mathcal{P}$. 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

Retrofitting Post-Quantum Cryptography in Internet Protocols:A Case Study of DNSSEC

Quantum computing is threatening current cryptography, especially the asymmetric algorithms used in many Internet protocols. More secure algorithms, colloquially referred to as Post-Quantum Cryptography (PQC), are under active development. These new algorithms differ significantly from current ones. They can have larger signatures or keys, and often require more computational power. This means we cannot just replace existing algorithms by PQC alternatives, but need to evaluate if they meet the requirements of the Internet protocols that rely on them. In this paper we provide a case study, analyzing the impact of PQC on the Domain Name System (DNS) and its Security Extensions (DNSSEC). In its main role, DNS translates human-readable domain names to IP addresses and DNSSEC guarantees message integrity and authenticity. DNSSEC is particularly challenging to transition to PQC, since DNSSEC and its underlying transport protocols require small signatures and keys and efficient validation. We evaluate current candidate PQC signature algorithms in the third round of the NIST competition on their suitability for use in DNSSEC. We show that three algorithms, partially, meet DNSSEC’s requirements but also show where and how we would still need to adapt DNSSEC. Thus, our research lays the foundation for making DNSSEC, and protocols with similar constraints ready for PQC

QuantumHammer: A Practical Hybrid Attack on the LUOV Signature Scheme

Post-quantum schemes are expected to replace existing public-key schemes within a decade in billions of devices. To facilitate the transition, the US National Institute for Standards and Technology (NIST) is running a standardization process. Multivariate signatures is one of the main categories in NIST\u27s post-quantum cryptography competition. Among the four candidates in this category, the LUOV and Rainbow schemes are based on the Oil and Vinegar scheme, first introduced in 1997 which has withstood over two decades of cryptanalysis. Beyond mathematical security and efficiency, security against side-channel attacks is a major concern in the competition. The current sentiment is that post-quantum schemes may be more resistant to fault-injection attacks due to their large key sizes and the lack of algebraic structure. We show that this is not true. We introduce a novel hybrid attack, QuantumHammer, and demonstrate it on the constant-time implementation of LUOV currently in Round 2 of the NIST post-quantum competition. The QuantumHammer attack is a combination of two attacks, a bit-tracing attack enabled via Rowhammer fault injection and a divide and conquer attack that uses bit-tracing as an oracle. Using bit-tracing, an attacker with access to faulty signatures collected using Rowhammer attack, can recover secret key bits albeit slowly. We employ a divide and conquer attack which exploits the structure in the key generation part of LUOV and solves the system of equations for the secret key more efficiently with few key bits recovered via bit-tracing. We have demonstrated the first successful in-the-wild attack on LUOV recovering all 11K key bits with less than 4 hours of an active Rowhammer attack. The post-processing part is highly parallel and thus can be trivially sped up using modest resources. QuantumHammer does not make any unrealistic assumptions, only requires software co-location (no physical access), and therefore can be used to target shared cloud servers or in other sandboxed environments