An Efficient Double Parameter Elliptic Curve Digital Signature Algorithm for Blockchain

Abstract

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.INDEX TERMS ECDSA, Blockchain, ECDLP, random oracles, weak randomness.

Lightweight Authentication Model for IoT Environments Based on Enhanced Elliptic Curve Digital Signature and Shamir Secret Share

“…In [14], Thomas pronin suggests deterministic methods to calculate 𝑘 for each transaction rather than choice randomly, the deterministic scheme, in a specific aspect, depends on the hash value of the message, so this solution considered specific applications, such as Bitcoin, and there are no guarantees to apply it in different applications such as applications that involves a lot of messages sent as control signals, for example, when user object request some critical information from temperature sensor, by sending constant queries message as a remotecontrol . SHUANG-GEN LIU [15] signature creation phase, one of them used to generate a digital signature, and another used in the verification procedure, also, this proposed eliminating the modular inverse calculation in signature and verification phases to decreases the algorithm's complexity and enhance its run time. The theoretical analysis proves that the random integer decomposition into two integers couldn't throw out the random integer reusing weakness, since this Scheme leads to retrieving the private key when used twice.…”

“…As mentioned in sec.2, there are three research works [11,15,16], that proposed a modification to the standard ECSDA, these modifications are made to improve the run time efficiency, or to reduce the probability of the private key steal. The theoretical analysis for these modifications has been proven weakness points also.…”

“…Following a comparison between the proposed algorithm and the related works in [15,16], the comparison takes into it account the number of cryptography computations as a benchmark, some operations don't take into account, because of the trivial cost (such as XOR operation). So, two operations that are considered in Table3, inverse multiplication of modular arithmetic (IM), and scalar (point) multiplication (SM), those taken place in three different stages, parameters generation stage (PG), sign generation stage (SG), and sign verification stage (SV).…”

Blockchain-Based BIM Digital Project Management Mechanism Research

“…At the same time, the author also proposes a method of using smart contract to manage and track transactions initiated by participants participating in DTS creation. Liu et al [25] constructed an improved provably secure elliptic curve digital signature scheme to solve the problem that the weak randomness of elliptic curve digital signature algorithm (ECDSA) in blockchain technology will lead to the attack of forging random numbers. Firstly, two parameters are introduced into the scheme, which can effectively resist the weak randomness attack of Bitcoin ECDSA; Secondly, the scheme uses the Hamming weight of Hash function instead of Hash value to sign, which avoids the inverse operation in the signing and verification stage.…”

A Modification of ECDSA to Avoid the Rho Method Attack

“…In 2020, Hussein and Kashmar modified ECDSA by using two private keys 𝑑 1 and 𝑑 2 [6]. Later on, in 2021, Liu, Chen, and Liu modified ECDSA by using two random number 𝑘 and 𝑘 1 [7].…”