The classic Elliptic curve digital Signature Algorithm (ECDSA) uses one inversion operation in the process of signature and verification, which greatly reduces the efficiency of digital signatures. Up to now, most research schemes improve efficiency by reducing reverse operations, but they fail to attach importance to such issues as forgery signature attack. At the same time, in the blockchain, the weak randomness of ECDSA will lead to the attack of forging random numbers, which is a potential problem of digital currency transactions. In consideration of this reason, in this article, an improved provably secure elliptic curve digital signature scheme is constructed. First, the new scheme introduces double parameters in the signature process, that can effectively resist the weak randomness attack of ECDSA in Bitcoin, and can be applied to blockchain digital currency trading systems. Second, in the random oracle model, it is provably indistinguishable against Elliptic Curve Discrete Logarithm Problem (ECDLP) under the super type I and type II adversary. Third, the new scheme avoids the inverse operation in the signature and verification phase. Compared with the ECDSA, the running speed is optimized by 50.1%. Similarly, the proposed scheme has higher computational efficiency than other existing algorithms.
We propose a multi-party computation (MPC) protocol over \(\mathbb {Z}_{2^k}\) secure against actively corrupted majority from somewhat homomorphic encryption. The main technical contributions are: (i) a new efficient packing method for \(\mathbb {Z}_{2^k}\)-messages in lattice-based somewhat homomorphic encryption schemes, (ii) a simpler reshare protocol for level-dependent packings, (iii) a more efficient zero-knowledge proof of plaintext knowledge on cyclotomic rings \({\mathbb Z}[X]/\varPhi _M(X)\) with M being a prime. Integrating them, our protocol shows from 2.2x upto 4.8x improvements in amortized communication costs compared to the previous best results. Our techniques not only improve the efficiency of MPC over \(\mathbb {Z}_{2^k}\) considerably, but also provide a toolkit that can be leveraged when designing other cryptographic primitives over \(\mathbb {Z}_{2^k}\).
Elliptic curve digital signature algorithm (ECDSA) is the simulation of digital signature algorithm (DSA) algorithm on elliptic curve. Compared with DSA, ECDSA has higher security and is the only widely accepted ECDSA, which has been adopted by many standardisation organisations. Based on the study of the original ECDSA scheme, this paper attempts to propose a new improved scheme. The proposed scheme has one main improvement. That is, considering that the original scheme has a finite field inversion process in the signature equation, the time-consuming inversion operation is completely avoided in the design. The proposed scheme has faster computation speed and reduces the ratio of verifying signature to signature generation time. The algorithm has certain significance for improving the efficiency of elliptic curve cryptography. Our simulation results show that the scheme runs faster and has higher signature and verification efficiency than that of the original scheme without compromising security. What's more, we also explore its application in bitcoin and Internet of Things (IoT).
Lorenzo Andolfo, Luigi Coppolino, Salvatore D’Antonio, Giovanni Mazzeo · 8 authors
The majority of financial organizations managing confidential data are aware of security threats and leverage widely accepted solutions (e.g., storage encryption, transport-level encryption, intrusion detection systems) to prevent or detect attacks. Yet these hardening measures do little to face even worse threats posed on data-in-use. Solutions such as Homomorphic Encryption (HE) and hardware-assisted Trusted Execution Environment (TEE) are nowadays among the preferred approaches for mitigating this type of threat. However, given the high-performance overhead of HE, financial institutions -- whose processing rate requirements are stringent -- are more oriented towards TEE-based solutions. The X-Margin Inc. company, for example, offers secure financial computations by combining the Intel SGX TEE technology and HE-based Zero-Knowledge Proofs, which shield customers' data-in-use even against malicious insiders, i.e., users having privileged access to the system. Despite such a solution offers strong security guarantees, it is constrained by having to trust Intel and by the SGX hardware extension availability. In this paper, we evaluate a new frontier for X-Margin, i.e., performing privacy-preserving credit risk scoring via an emerging cryptographic scheme: Functional Encryption (FE), which allows a user to only learn a function of the encrypted data. We describe how the X-Margin application can benefit from this innovative approach and -- most importantly -- evaluate its performance impact.
Christoph Dobraunig, Lorenzo Grassi, Anna Guinet, Daniël Kuijsters
Motivated by new applications such as secure Multi-Party Computation (MPC), Fully Homomorphic Encryption (FHE), and Zero-Knowledge proofs (ZK), the need for symmetric encryption schemes that minimize the number of field multiplications in their natural algorithmic description is apparent. This development has brought forward many dedicated symmetric encryption schemes that minimize the number of multiplications in \( \mathbb {F}_{2^n} \) or \( \mathbb {F}_{p} \), with p being prime. These novel schemes have lead to new cryptanalytic insights that have broken many of said schemes. Interestingly, to the best of our knowledge, all of the newly proposed schemes that minimize the number of multiplications use those multiplications exclusively in S-boxes based on a power mapping that is typically \(x^3\) or \(x^{-1}\). Furthermore, most of those schemes rely on complex and resource-intensive linear layers to achieve a low multiplication count. In this paper, we present Ciminion, an encryption scheme minimizing the number of field multiplications in large binary or prime fields, while using a very lightweight linear layer. In contrast to other schemes that aim to minimize field multiplications in \( \mathbb {F}_{2^n} \) or \( \mathbb {F}_{p} \), Ciminion relies on the Toffoli gate to improve the non-linear diffusion of the overall design. In addition, we have tailored the primitive for the use in a Farfalle-like construction in order to minimize the number of rounds of the used primitive, and hence, the number of field multiplications as far as possible.
After the work of Impagliazzo and Rudich (STOC, 1989), the black box framework has become one of the main research domain of cryptography. However black box techniques say nothing about non-black box techniques such as making use of zero-knowledge proofs. Brakerski et al. introduced a new black box framework named augmented black box framework, in which they gave a zero-knowledge proof oracle in addition to a base primitive oracle (TCC, 2011). They showed a construction of a non-interactive zero knowledge proof system based on a witness indistinguishable proof system oracle. They presented augmented black box construction of chosen ciphertext secure public key encryption scheme based on chosen plaintext secure public key encryption scheme and augmented black box separation between one-way function and key agreement. In this paper we simplify the work of Brakerski et al. by introducing a proof system oracle without witness indistinguishability, named coin-free proof system oracle, that aims to give the same construction and separation results of previous work. As a result, the augmented black box framework becomes easier to handle. Since our oracle is not witness indistinguishable, our result encompasses the result of previous work.
How someone can get health insurance without sharing his health infor-mation? How you can get a loan without disclosing your credit score? There is a method to certify certain attributes of various data, either this is health metrics or finance information, without revealing the data itself or any other kind of personal data. This method is known as “zero-knowledge proofs”. Zero-Knowledge techniques are mathematical methods used to verify things without sharing or revealing underlying data. Zero-Knowledge protocols have vast applications from simple identity schemes and blockchains to de-fense research programs and nuclear arms control. In this article we present the basic principles behind ZKP technology, possible applications and the threats and vulnerabilities that it is subject to and we review proposed securi-ty solutions.
Zero-Knowledge Proofs (ZKPs) have emerged as a revolutionary cryptographic technique that enables one party to prove knowledge of a statement without revealing any underlying information. ZKPs play a crucial role in enhancing cybersecurity by enabling privacy-preserving authentication, secure transactions, and data integrity verification. This paper explores the fundamentals of zero-knowledge proofs, including their classifications—interactive, non-interactive, and succinct proofs—along with real-world applications in secure communications, blockchain security, and identity verification. Furthermore, we discuss the challenges of implementing ZKPs and the potential future advancements in this cryptographic field
We introduce in this paper the algorithmic aspect of elliptic curves together with their applications. We also recall one of the promising application in the field of zero knowledge proofs with concrete implementations.
Robustness features are essential for any black-box or non-black box security mechanism in cryptography. Zero-knowledge proofs is an example of non-black box security mechanism used in cryptography. In this paper, we have explored and analyzed zero-knowledge proofs using discrete logarithm problem and compared it with integer factoring problem to check its robustness and compatibility for higher security in cryptography. The upper bound of Pollard's rho algorithm for discrete logarithm is growing faster in comparison with Pollard's rho factoring algorithm. The covariance between asymptotic notations of two different algorithms for zero-knowledge proofs are computed and positive covariance result is obtained, which clearly shows that random variants used for both algorithms are growing in same direction and have similar behavior. The functional value line segment of Pollard's rho algorithm for discrete logarithm converges with the functional value line segment of Pollard's rho factoring algorithm at a point.
Muhammed F. Esgin, Ngoc Khanh Nguyen, Gregor Seiler
We propose a very fast lattice-based zero-knowledge proof system for exactly proving knowledge of a ternary solution \(\vec {s} \in \{-1,0,1\}^n\) to a linear equation \(A\vec {s}=\vec {u}\) over \(\mathbb {Z}_q\), which improves upon the protocol by Bootle, Lyubashevsky and Seiler (CRYPTO 2019) by producing proofs that are shorter by a factor of 8.