Unbalanced Oil And Vinegar Research Articles

Analysis of the complexity of attacks on multivariate cryptographic transformations using algebraic field structure

In recent years, interest in cryptosystems based on multidimensional quadratic transformations (MQ transformations) has grown significantly. This is primarily due to the NIST PQC competition [1] and the need for practical electronic signature schemes that are resistant to attacks on quantum computers. Despite the fact that the world community has done a lot of work on cryptanalysis of the presented schemes, many issues need further clarification. NIST specialists are very cautious about the standardization process and urge cryptologists [4] in the next 3 years to conduct a comprehensive analysis of the finalists of the NIST PQC competition before their standardization.
 One of the finalists is the Rainbow electronic signature scheme [2]. It is a generalization of the UOV (Unbalanced Oil and Vinegar) scheme [3]. Recently, another generalization of this scheme – LUOV (Lifted UOV) [5] was found to attack [6], which in polynomial time is able to recover completely the private key. The peculiarity of this attack is the use of the algebraic structure of the field over which the MQ transformation is given. This line of attack has emerged recently and it is still unclear whether it is possible to use the field structure in the Rainbow scheme.
 The aim of this work is to systematize the techniques used in attacks using the algebraic field structure for UOV-based cryptosystems and to analyze the obstacles for their generalization to the Rainbow scheme.

Choosing subfields for LUOV and lifting fields for rainbow

Multivariate public key cryptography is one of the main candidates for post-quantum cryptography. Rainbow, an improved (multi-layer) version of unbalanced oil and vinegar (UOV), is one of the most famous multivariate signature schemes that is a promising candidate for NIST standardisation. At INDOCRYPT 2017, Beullens and Preneel introduced a new variant LUOV of UOV. Their idea is to generate a UOV scheme over the binary field and then lift it into a bigger field and hence dramatically reduce the public key size. In this study, the authors first theoretically deduce the choice for the subfield L (which is different from ) which results in smaller signature sizes (up to 40%). Moreover, they extend the idea to Rainbow and theoretically yield the optimal choice for the subfield L over which a Rainbow is generated before being lifted to K. As a result, they can reduce the public key size of the obtained Rainbow scheme up to at least 36%.

An Improved Identity-Based Multivariate Signature Scheme Based on Rainbow

Multivariate Public Key Cryptography (MPKC) is one of the main candidates for post-quantum cryptography, especially in the area of signature schemes. In this paper, we instantiate a certificate Identity-Based Signature (IBS) scheme based on Rainbow, one of the most efficient and secure multivariate signature schemes. In addition, we revise the previous identity-based signature scheme IBUOV based on the Unbalanced Oil and Vinegar (UOV) scheme on the security and choice of parameters and obtain that our scheme is more efficient than IBUOV in terms of key sizes and signature sizes.

Side-Channel Attacks on Post-Quantum Signature Schemes based on Multivariate Quadratic Equations

In this paper, we investigate the security of Rainbow and Unbalanced Oil-and-Vinegar (UOV) signature schemes based on multivariate quadratic equations, which is one of the most promising alternatives for post-quantum signature schemes, against side-channel attacks. We describe correlation power analysis (CPA) on the schemes that yield full secret key recoveries. First, we identify a secret leakage of secret affine maps S and T during matrix-vector products in signing when Rainbow is implemented with equivalent keys rather than random affine maps for optimal implementations. In this case, the simple structure of the equivalent keys leads to the retrieval of the entire secret affine map T. Next, we extend the full secret key recovery to the general case using random affine maps via a hybrid attack: after recovering S by performing CPA, we recover T by mounting algebraic key recovery attacks. We demonstrate how this leakage on Rainbow can be practically exploited on an 8-bit AVR microcontroller using CPA. Consequently, our CPA can be applied to Rainbow-like multi-layered schemes regardless of the use of the simple-structured equivalent keys and UOV-like single layer schemes with the implementations using the equivalent keys of the simple structure. This is the first result on the security of multivariate quadratic equations-based signature schemes using only CPA. Our result can be applied to Rainbow-like multi-layered schemes and UOV-like single layer schemes submitted to NIST for Post-Quantum Cryptography Standardization.

Side-channel security analysis of UOV signature for cloud-based Internet of Things

Among Internet of Things (IoTs), cloud-based IoTs help retain the confidentiality of both device-to-cloud and cloud-to-device messages by setting up individual identities and credentials for each IoT devices. As recently been emphasized by two American institutes, National Institute of Standards and Technology (NIST) and National Security Agency (NSA), cloud-based IoTs that use RSA and ECC signatures are insecure under quantum computer attacks. To ensure the security in the cloud-based IoTs under quantum computer attacks, there is a critical need for implementations of new quantum-resistance signature systems, such as Unbalanced Oil and Vinegar (UOV), for making the cloud-based IoTs more secure and reliable. In order to analyze the security of UOV for cloud-based IoTs, we present an efficient algorithm based on side channel analysis of UOV, which combines inducing faults and Hamming distance power analysis. We implement UOV signature schemes on Sakura-G FPGA board via using Verilog-HDL code and Xilinx ISE software, where the power collection uses a 350 MHz Keysights oscilloscope. Based on the experimental results, we successfully recover all the secret keys of UOV signature, which shows that we should protect UOV and related signatures against side channel attacks when they are adopted in cloud-based IoTs.

On the Equivalent Keys in Multivariate Cryptosystems

The number of equivalent keys in multivariate cryptosystem is closely related to the scheme security. This study analyzes the structure of the private key space in some multivariate schemes. The result gives the lower bounds on the number of equivalent keys of some variants of the hidden field equation (HFE) scheme including plus, minus-plus, embedding, and internal perturbation. This method estimates the number of invertible transformations which maintain the form of the central map invariant. Furthermore, a formal proof shows that the two modifications of fixing and embedding are equivalent in security analyses of multivariate schemes. Also this paper corrects previous proofs in Wolf's work on the number of equivalent keys in HFEv, the unbalanced oil and vinegar (UOV) scheme, and the stepwise triangular systems (STS).