Gottfried Herold, Max Hoffmann, Michael Klooß, Carla Ràfols · 5 authors
Bilinear groups form the algebraic setting for a multitude of important cryptographic protocols including anonymous credentials, e-cash, e-voting, e-coupon, and loyalty systems. It is typical of such crypto protocols that participating parties need to repeatedly verify that certain equations over bilinear groups are satisfied, e.g., to check that computed signatures are valid, commitments can be opened, or non-interactive zero-knowledge proofs verify correctly. Depending on the form and number of equations this part can quickly become a performance bottleneck due to the costly evaluation of the bilinear map.
The Elliptic Curve Digital Signature Algorithm (ECDSA), de nes a technique for generating and validating digital signatures. We start by reviewing the mathematics behind the Digital Signature Algorithm (DSA) and its elliptic curve analogue (ECDSA). Secondly, we describe how the ECDSA is used in Bitcoin technology.
Yi Liu, Ruilin Li, Xingtong Liu, Jian Wang · 7 authors
With widely adoption of Bitcoin, Many malicious software trying to steal bitcoins through network has emerged in a large scale. Bitcoin makes heavy use of elliptic curve digital signature algorithm to guarantee transactions security. Each user can have lots of addresses hashed from his public keys to receive coins, and need private keys associated with these addresses to authorize spending those coins. A Bitcoin wallet give a good assistance to manage and preserve all private keys belong to its owner. However, saving complete private keys on local storage meets a big challenge in case of theft. For the purpose of securing user's private keys, we propose an efficient method to enhance Bitcoin wallet security. We combine random seeds and a passphrase for user easy to keep in mind to generate private keys whenever needed. It is only need to reserve a list of random seeds on local storage instead of complete private keys. Nobody could generate the whole private keys just relying on random seeds without the passphrase. Therefore, our method increases the difficulty for attackers to steal bitcoins. We also introduce a key recovery approach in case of the passphrase being forgotten. Our method does not incur any additional operations and is convenient to use by a common customer without professional knowledge.
Advanced Steganography and Watermarking Techniques
Increasingly digital technology in the present helped many people lives. Unlike the electoral system, there are many conventional uses of paper in its implementation. The aspect of security and transparency is a threat from still widespread election with the conventional system (offline). General elections still use a centralized system, there is one organization that manages it. Some of the problems that can occur in traditional electoral systems is with an organization that has full control over the database and system, it is possible to tamper with the database of considerable opportunities. Blockchain technology is one of solutions, because it embraces a decentralized system and the entire database are owned by many users. Blockchain itself has been used in the Bitcoin system known as the decentralized Bank system. By adopting blockchain in the distribution of databases on e-voting systems can reduce one of the cheating sources of database manipulation. This research discusses the recording of voting result using blockchain algorithm from every place of election. Unlike Bitcoin with its Proof of Work, this thesis proposed a method based on a predetermined turn on the system for each node in the built of blockchain.
This document describes the Schnorr non-interactive zero-knowledge
(NIZK) proof, a non-interactive variant of the three-pass Schnorr
identification scheme. The Schnorr NIZK proof allows one to prove the
knowledge of a discrete logarithm without leaking any information
about its value. It can serve as a useful building block for many
cryptographic protocols to ensure that participants follow the
protocol specification honestly. This document specifies the Schnorr
NIZK proof in both the finite field and the elliptic curve settings.
Jul 1, 2017·22017 IEEE International Conference on Computational Science and Engineering (CSE) and IEEE International Conference on Embedded and Ubiquitous Computing (EUC)
In this paper, we propose a CPA-Secure encryption scheme with equality test. Unlike other public key solutions, in our scheme, only the data owner can encrypt the message and get the comparable ciphertext, and only the tester with token who can perform the equality test. Our encryption scheme is based on multiplicative homomorphism of ElGamal Encryption and Non Interactive Zero Knowledge proof of Discrete Log. We proof that the proposed scheme is OW-CPA security under the attack of the adversary who has equality test token, and IND-CPA security under the attack of adversary who can not test the equality. The proposed scheme only suppose to compare two ciphertexts encrypted by same user, though it is less of flexibility, it is efficient and more suitable for data outsourcing scenario.
The systematic introduction to zero knowledge proof protocol has important theoretical guidance and practical significance on attracting more scholars involved in research as well as expanding application fields. Zero-knowledge proofs were first conceived in 1985 by Shafi Golwasser, Silvio Micalli and Charles Rackoff in a draft of the knowledge complexity of interactive proof systems. The goal of the present paper is to introduce a new identity based scheme which is a combination of zero-knowledge interactive proof and weil pairing on elliptic curves. The concept of weil pairing was first introduced by Andre Weil in 1940. It plays an important role in the theoretical study of the arithmetic of elliptic curves and Abelian varieties. It has also recently become extremely useful in cryptologic constructions related to these objects.
With the rise of Bitcoin, blockchain which is the core technology of Bitcoin has received increasing attention. Privacy preserving and performance on blockchain are two research points in academia and business, but there are still some unresolved issues in both respects. An aggregate signature scheme is a digital signature that supports making signatures on many different messages generated by many different users. Using aggregate signature, the size of the signature could be shortened by compressing multiple signatures into a single signature. In this paper, a new signature scheme for transactions on blockchain based on the aggregate signature was proposed. It was worth noting that elliptic curve discrete logarithm problem and bilinear maps played major roles in our signature scheme. And the security properties of our signature scheme were proved. In our signature scheme, the amount will be hidden especially in the transactions which contain multiple inputs and outputs. Additionally, the size of the signature on transaction is constant regardless of the number of inputs and outputs that the transaction contains, which can improve the performance of signature. Finally, we gave an application scenario for our signature scheme which aims to achieve the transactions of big data on blockchain.
With the rise of Bitcoin, cryptographic currencies have attracted more and more attention. Subsequently, other cryptographic currencies were gradually created, such as Zcash, Moreno, Dash and so on. In cryptographic currency, privacy preserving and expansion are two key technical points. In terms of privacy preserving, more effective solutions were proposed in Zcach, Moreno, Dash and other cryptographic currencies systems, in which ring signature, zero knowledge proof and other cryptographic techniques played important roles. But these schemes mainly considered protecting the addresses of both sides of the transaction. In terms of expansion, lightning network and other projects also give solutions. But most of these projects will bring other problems. In this paper, a signature scheme based on the aggregate signature and the elliptic curve algorithm is proposed to hide the transaction value of a single sender and receiver in the transactions which contain multiple inputs and outputs. This signature scheme achieves the purpose of privacy preserving from the transaction value. Further, the correctness proof and security analysis are given in this paper. In addition to that, another signature scheme that combines aggregation signature with bilinear ring signature is proposed. This aggregate ring signature scheme gives another attempt to solve the problem of expansion in the cryptographic currency system only using cryptographic technologies. At the same time, the sender's addresses can be hidden. Similarly, we also confirmed the correctness of this signature scheme.
Innovative idea using ring theory is raised to build a new algorithm for zero knowledge (ZK) cryptosystem. In this paper we introduce an algorithm for zero knowledge protocol based on a specific kind of rings named weak Armendariz. On the other hand, the aim of this paper focuses on the category of noncommutative algebraic structures to describe a new algebraic scheme of zero knowledge proof using weak Armendariz rings. As a result, we employ for the first time weak Armendariz rings in the science of cryptographic which regards as a new application of this class of rings. Finally, we present a novel idea combining between abstract algebra and cryptography.
Youngho Yoo, Reza Azarderakhsh, Amir Jalali, David Jao · 5 authors
We present the first general-purpose digital signature scheme \nbased on supersingular elliptic curve isogenies secure against quantum \nadversaries in the quantum random oracle model with small key sizes. \nThis scheme is an application of Unruh’s construction of non-interactive \nzero-knowledge proofs to an interactive zero-knowledge proof proposed \nby De Feo, Jao, and Plut. We implement our proposed scheme on an x86- \n64 PC platform as well as an ARM-powered device. We exploit the stateof-the-art \ntechniques to speed up the computations for general C and \nassembly. Finally, we provide timing results for real world applications.
Bitcoin is a digital currency based on cryptographic algorithms. All the transactions of this currency are recorded and stored in a publically available database called blockchain. Since, these transactions are available to everyone, bitcoins must be stored in a secured wallet. These bitcoin wallets can be opened only by its secret key. And if once the secret key of the wallet is lost, it cannot be recovered because of the irreversible nature of bitcoin transaction. To root out this problem, Goldfeder et al. [4] proposed a solution of threshold signature scheme compatible with bitcoins signature by using Elliptic Curve Digital Signature Algorithm (ECDSA) providing security policy of shared control of a wallet in which each player gets only a single share. Considering an important point of priority/weightage of players, Dikshit and Singh [12] first proposed a scheme in which each player is given one or more shares of the secret key according to his weightage/priority. This scheme has a drawback of managing and handling many keys by each player. Suppose a player has weightage w, then he possesses w different shares of secret key. This problem is resolved in the proposed scheme in this paper. We propose a scheme in which all the players get single share and can accomplish the requirements of concept of weightage. We extend the weighted threshold ECDSA scheme in order to realize efficient weighted threshold ECDSA scheme.
When constructing practical zero-knowledge proofs based on the hardness of the Ring-LWE or the Ring-SIS problems over polynomial rings \(\mathbb {Z}_p[X]/(X^n+1)\), it is often necessary that the challenges come from a set \(\mathcal {C}\) that satisfies three properties: the set should be large (around \(2^{256}\)), the elements in it should have small norms, and all the non-zero elements in the difference set \(\mathcal {C}-\mathcal {C}\) should be invertible. The first two properties are straightforward to satisfy, while the third one requires us to make efficiency compromises. We can either work over rings where the polynomial \(X^n+1\) only splits into two irreducible factors modulo p, which makes the speed of the multiplication operation in the ring sub-optimal; or we can limit our challenge set to polynomials of smaller degree, which requires them to have (much) larger norms.
Recently, by changing security requirements of computer networks, many public key schemes are introduced. One major shortcoming of identity-based cryptosystems is key screw. Certificateless public key cryptosystems were introduced to solve this problem. In this paper, a certificateless, public-key, multiple-key-agreement scheme will be offered which has some significant security properties such as perfect forward secrecy, strong security, and zero-knowledge proof. This scheme produces far more shared hidden keys per session in comparison with many existing schemes. In this paper, the security and the efficiency of the proposed scheme will be compared with some well-known current schemes.
Nicolas T. Courtois, Guangyan Song, Ryan Castellucci
Abstract In this paper, we study and give the first detailed benchmarks on existing implementations of the secp256k1 elliptic curve used by at least hundreds of thousands of users in Bitcoin and other cryptocurrencies. Our implementation improves the state of the art by a factor of 2.5 with a focus on the cases, where side channel attacks are not a concern and a large quantity of RAM is available. As a result, we are able to scan the Bitcoin blockchain for weak keys faster than any previous implementation. We also give some examples of passwords which we have cracked, showing that brain wallets are not secure in practice even for quite complex passwords.
The purpose behind zero-knowledge proofs are to deliver a mystification to the verifier, so that the verifier will not comprehend the information sent by the prover. Cryptography and complexity theory have gained a lot of importance because of zero-knowledge proofs. An enigmatic outset was dignified, that lead to the foundation zero-knowledge proof systems. Zero-knowledge proofs are generally used to verify a prover's theorem to a verifier, in such a way that the verifier will not be able to discover any supplementary evidence other than the proof given to him. In this paper, we have reviewed different zero-knowledge argument / proof techniques. We have also reviewed the proof system implications in the presence of malicious prover and malicious verifier. We have removed the outliers of the experiment by using Mahalanobis distance. Examples associated to zero-knowledge argument systems are also given.
We have proved that zero-knowledge proofs technique using integer factorization problem has big-oh O(τ1/4)for factoring integers algorithm given by Pollard's rho in comparison with Henry for discrete logarithm problem that is τ+τ/lgτ. Also, we have positively presented covariance between our result and Henry which clearly implies the input variables used for both functions tend to show similar behavior.