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IEEE Symposium on Computers and Communications (ISCC)

Attack Analysis on Two-party Signature and Threshold Signature Based on Dilithium

Xiang Wu, Bohao Li, Boyang Zhang, Xiaofan Liu, Wei Ren, Kim‐Kwang Raymond Choo

Published Jul 9, 2023• 1 citation
Publisher

Abstract

With the rapid development of post-quantum cryptography study, the Crystals-Dilithium digital signature algorithm based on the lattice has received much attention, and many extended studies have appeared on its basis. In this paper, we focus on the two-party signature protocol and$(t,\ n)$-threshold signature protocol based on Dilithium, and analyze their feasibility and security. After repeated experiments with the official rejection sampling code of the Aigis-sig scheme, it is shown that the two-party signature protocol basically cannot pass rejection sampling verification properly and is not feasible. At the same time, both protocols have a security risk that private key is divulged and internal members forge signatures. Through security analysis and experimental results, we found that there is close to 100% possibility that the internal members can crack the y value and private key information to complete the signature forgery. It will make the security of signatures unable to be guaranteed.

DOI
10.1109/iscc58397.2023.10217977

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With the rapid development of post-quantum cryptography study, the Crystals-Dilithium digital signature algorithm based on the lattice has received much attention, and many extended studies have appeared on its basis. In this paper, we focus on the two-party signature protocol and(t, n)(t,\ n)(t, n)-threshold signature protocol based on Dilithium, and analyze their feasibility and security. After repeated experiments with the official rejection sampling code of the Aigis-sig scheme, it is shown that the two-party signature protocol basically cannot pass rejection sampling verification properly and is not feasible. At the same time, both protocols have a security risk that private key is divulged and internal members forge signatures. Through security analysis and experimental results, we found that there is close to 100% possibility that the internal members can crack the y value and private key information to complete the signature forgery. It will make the security of signatures unable to be guaranteed.
Abstract The development of threshold protocols based on lattice-signature schemes has been of increasing interest in the past several years. The main research focus was towards protocols constructed for various variants of Crystals-Dilithium, future NIST digital signature standard known as ML-DSA. In this work, we propose TOPCOAT, a two-party lattice-based signature algorithm that embodies Dilithium's compression techniques. The aforesaid result is achieved by introducing a new hinting mechanism that allows parties to collaboratively calculate HighBits\textsf{HighBits}HighBits. Our hinting mechanism allows public key compression similar to Dilithium. Additionally, we suggest an optimization technique to minimize number of restarts both parties need to produce a valid signature. We prove security of our scheme under MLWE and MSIS assumptions in ROM, and provide implementation of our proposed scheme. As additional contribution, we present vulnerabilities and inconsistencies found in Liu et al. work which aimed to construct distributed lattice-based signature protocol.
The National Institute of Standards and Technology is in the process of selecting post-quantum public-key cryptography (PQC) algorithms through a public competition-like process. Dilithium, a lattice-based signature scheme, is a PQC candidate submitted to the NIST. It offers a fairly good performance with relatively straightforward implementation. In this study, we considered a secure two-party Dilithium signing protocol. We described how to build a distributed key generation and distributed signing protocol for Dilithium. Our protocol achieves a coordinated two-party Dilithium signature generation using Brakersiki/Fan-Vercauteren homomorphic encryption scheme. Our protocol is proven secure against active adversaries corrupting one of the players. Compared with other protocols, our protocol has advantage in resisting quantum computing attacks.
The long-term security of public blockchains strictly depends on the hardness assumptions of the underlying digital signature schemes. In the current scenario, most deployed cryptocurrencies and blockchain platforms rely on elliptic-curve cryptography, which is vulnerable to quantum attacks due to Shor's algorithm. Therefore, it is important to understand how post-quantum (PQ) digital signatures behave when integrated into real blockchain systems. This report presents a blockchain prototype that supports multiple quantum-secure signature algorithms, focusing on CRYSTALS-Dilithium, Falcon and Hawk as lattice-based schemes. This report also describes the design of the prototype and discusses the performance metrics, which include key generation, signing, verification times, key sizes and signature sizes. This report covers the problem, background, and experimental methodology, also providing a detailed comparison of quantum-secure signatures in a blockchain context and extending the analysis to schemes such as HAETAE.
In this paper, we propose DiLizium: a new lattice-based two-party signature scheme. Our scheme is constructed from a variant of the Crystals-Dilithium post-quantum signature scheme. This allows for more efficient two-party implementation compared with the original but still derives its post-quantum security directly from the Module Learning With Errors and Module Short Integer Solution problems. We discuss our design rationale, describe the protocol in full detail, and provide performance estimates and a comparison with previous schemes. We also provide a security proof for the two-party signature computation protocol against a classical adversary. Extending this proof to a quantum adversary is subject to future studies. However, our scheme is secure against a quantum attacker who has access to just the public key and not the two-party signature creation protocol.
Rejection sampling technology is a core tool in the design of lattice-based signatures with ‘Fiat–Shamir with Aborts’ structure, and it is related to signing efficiency and signature, size as well as security. In the rejection sampling theorem proposed by Lyubashevsky, the masking vector of rejection sampling is chosen from discrete Gaussian distribution. However, in practical designs, the masking vector is more likely to be chosen from bounded uniform distribution due to better efficiency and simpler implementation. Besides, as one of the third-round candidate signatures in the NIST postquantum cryptography standardization process, the 3rd round version of CRYSTALS-Dilithium has proposed a new method to decrease the rejection probability in order to achieve better efficiency and smaller signature size by decreasing the number of nonzero coefficients of the challenge polynomial according to the security levels. However, it is seen that small entropies in this new method may lead to higher risk of forgery attack compared with former schemes proposed in its 2nd version. Thus, in this paper, we first analyze the complexity of forgery attack for small entropies and then introduce a new method to decrease the rejection probability without loss of security including the security against forgery attack. This method is achieved by introducing a new rejection sampling theorem with tighter bound by utilizing Rényi divergence where masking vector follows uniform distribution. By observing large gaps between the security claim and actual security bound in CRYSTALS-Dilithium, we propose two series of adapted parameters for CRYSTALS-Dilithium. The first set can improve the efficiency of the signing process in CRYSTALS-Dilithium by factors of 61.7 % and 41.7 % , according to the security levels, and ensure the security against known attacks, including forgery attack. And, the second set can reduce the signature size by a factor of 14.09 % with small improvements in efficiency at the same security level.
Abstract Traditional threshold signature schemes, which are based on number-theoretic problems, are vulnerable to attacks in quantum computing environments. Moreover, these schemes incur high communication and computational costs among nodes, which pose significant challenges for meeting the stringent requirements of interactive security and real-time performance in power grid load regulation systems. To address these challenges, this paper introduces a post-quantum threshold signature scheme based on CRYSTALS-Dilithium (CDTS) specifically designed for power grid load regulation systems. Constructed within the Fiat-Shamir framework and integrating a CRYSTALS-Dilithium-based threshold signature, this scheme effectively ensures the system’s fault tolerance and security in the face of quantum computing threats. In terms of efficiency, the CDTS scheme significantly reduces computational overheads through the introduction of rejection sampling techniques and the optimization of the number-theoretic transform algorithm. To further enhance the scheme’s adaptability to the dynamic nature of power grid load regulation, an innovative dynamic threshold adjustment mechanism is proposed. This mechanism monitors load changes in real-time within a ΔT\Delta TΔT Δ T time window, allowing for flexible adjustments to the threshold parameters. Security analysis confirms that the proposed scheme satisfies the security requirements of power grid load regulation systems, making it a robust solution for ensuring secure and efficient load regulation in the quantum era. We conducted rigorous experimental comparisons under the same security level (NIST Level 3) and system scale ( th=5,n=10th=5, n=10th=5,n=10 t h = 5 , n = 10 ), the sizes of the public key (1.32 KB), private key (2.01 KB), and signature (2.45 KB) of the CDTS scheme are almost identical to those of the original Dilithium scheme. This data demonstrates that the threshold construction we proposed is nearly lossless in terms of storage efficiency, significantly outperforming the exponential overhead growth typically brought by traditional scheme. Through rigorous software testing and verification, we evaluated the performance of the CDTS scheme by randomly generating a 59-byte message and iteratively executing the signing process 10,000 times. The results indicate that the CDTS scheme achieves a complete signature and verification process in an average of 506.73 microseconds. This efficiency makes the CDTS scheme highly feasible for practical applications, particularly in environments requiring rapid and secure transaction processing.