CryptoMaze: Atomic Off-Chain Payments in Payment Channel Network

Payment protocols developed to realize off-chain transactions in Payment channel network (PCN) assumes the underlying routing algorithm transfers the payment via a single path. However, a path may not have sufficient capacity to route a transaction. It is inevitable to split the payment across multiple paths. If we run independent instances of the protocol on each path, the execution may fail in some of the paths, leading to partial transfer of funds. A payer has to reattempt the entire process for the residual amount. We propose a secure and privacy-preserving payment protocol, CryptoMaze. Instead of independent paths, the funds are transferred from sender to receiver across several payment channels responsible for routing, in a breadth-first fashion. Payments are resolved faster at reduced setup cost, compared to existing state-of-the-art. Correlation among the partial payments is captured, guaranteeing atomicity. Further, two party ECDSA signature is used for establishing scriptless locks among parties involved in the payment. It reduces space overhead by leveraging on core Bitcoin scripts. We provide a formal model in the Universal Composability framework and state the privacy goals achieved by CryptoMaze. We compare the performance of our protocol with the existing single path based payment protocol, Multi-hop HTLC, applied iteratively on one path at a time on several instances. It is observed that CryptoMaze requires less communication overhead and low execution time, demonstrating efficiency and scalability.Comment: 30 pages, 9 figures, 1 tabl

Bitcoin Security with a Twisted Edwards Curve

International audienceThe security of the Bitcoin cryptocurrency system depends on the Koblitz curve secp256k1 combined with the digital signature ECDSA and the hash function SHA-256. In this paper, we show that the security of Bitcoin with ECDSA and secp256k1 is not optimal and present a detailed study of the efficiency of Bitcoin with the digital signature algorithm Ed25519 combined with the twisted Edwards curve CurveEd25519 and the hash function SHA-512. We show that Bitcoin is more secure and more efficient with the digital signature algorithm Ed25519 and the twisted Edwards curve CurveEd25519. Subject Classifications: 94A6

An Improved Public Key Cryptography Based on the Elliiptic Curve

Elliptic curve cryptography offers two major benefits over RSA: more security per bit, and a suitable key size for hardware and modern communication. Thus, this results to smaller size of public key certificates, lower power requirements and smaller hardware processors. Three major approaches are used in this dissertation to enhance the elliptic curve cryptsystems: reducing the number of the elliptic curve group arithmetic operations, speeding up the underlying finite field operations and reducing the size of the transited parameters. A new addition formula in the projective coordinate is introduced, where the analysis for this formula shows that the number of multiplications over the finite field is reduced to nine general field element multiplications. Thus this reduction will speed up the computation of adding two points on the elliptic curve by 11 percent. Moreover, the new formula can be used more efficiently when it is combined with the suggested sparse elements algorithms. To speed up the underlying finite field operations, several new algorithms are introduced namely: selecting random sparse elements algorithm, finding sparse base points, sparse multiplication over polynomial basis, and sparse multiplication over normal basis. The complexity analysis shows that whenever the sparse techniques are used, the improvement rises to 33 percent compared to the standard projective coordinate formula and improvement of 38 percent compared to affine coordinate. A new algorithm to compress and decompress the sparse elements algorithms are introduced to reduce the size of the transited parameters. The enhancements are applied on three protocols and two applications. The protocols are Diffie-Hellman, ELGamal and elliptic curve digital signature. In these protocols the speed of encrypting, decrypting and signing the message are increased by 23 to 38 percent. Meanwhile, the size of the public keys are reduced by 37 to 48 percent. The improved algorithms are applied to the on-line and off-line electronic payments systems, which lead to probably the best solution to reduce the objects size and enhance the performance in both systems

A Novel Identity Based Blind Signature Scheme using DLP for E-Commerce

Abstract— Blind signatures are used in the most of the application where confidentiality and authenticity are the main issue. Blind signature scheme deals with concept where requester sends the request that the signer should sign on a blind message without looking at the content. Many ID based blind signature are proposed using bilinear pairings and elliptic curve. But the relative computation cost of the pairing in bilinear pairings and ID map into an elliptic curve are huge. In order to save the running time and the size of the signature, this paper proposed a scheme having the property of both concepts identity based blind signature that is based on Discrete Logarithm Problem, so as we know that DLP is a computational hard problem and hence the proposed scheme achieves all essential and secondary security prematurity. With the help of the proposed scheme, this paper implemented an E-commerce system in a secure way. E-commerce is one of the most concern applications of ID based blind signature scheme. E-commerce consisting selling and buying of products or services over the internet and open network. ID based blind signature scheme basically has been used enormously as a part of today’s focussed business. Our proposed scheme can be also be used in E-business, E-voting and E-cashing anywhere without any restriction DOI: 10.17762/ijritcc2321-8169.15060

SIGNCRYPTION ANALYZE

The aim of this paper is to provide an overview for the research that has been done so far in signcryption area. The paper also presents the extensions for the signcryption scheme and discusses the security in signcryption. The main contribution to this paper represents the implementation of the signcryption algorithm with the examples provided.ElGamal, elliptic curves, encryption, identity-based, proxy-signcryption, public key, ring-signcryption, RSA, signcryption

A Novel Blind Signature Based Upon ECDLP

Encryption and decryption techniques protect the condentiality of information exchanged in a network whereas digital signature is electronic signing of data that provide senders authentication using its secret key and verication using its public key and other domain parameters. A combination of encipherment and digital signing of message immunes it from most of the active attacks such as modification of data, masquerading and repudiation Elliptic curve discrete logarithmic problem (ECDLP) is the problem of finding the scalar multiplier knowing the corresponding points on an elliptic curve. ECDLP is very complex and dicult to solve compared to any standard inverse operation of a one-way-trapdoor function such as Discrete Logarithm Problem or Factorization problem. Blind signature allows a user to obtain a signature from an authority on any document, in such a way that the authority learns nothing about the message that is being signed. The blindness is an important property which distinguishes the blind signature from other signature schemes. Blind signature is an important cryptographic primitive used in protocols such as electronic voting systems and cash payment systems. Since an ECDLP enjoys a large space and time complexity and blind signature ensures anonymity of clients message while obtaining a signature from a trusted party, we aim at designing a blind signature scheme based upon ECDLP which is supposed to have a low computation cost and low communication overhead. The signature should be such that it has a small size, it is highly secured and is resistant to elliptic curve cryptography based attacks such as forgery attack, MOV attack etc

A formal analysis of the mimblewimble cryptocurrency protocol with a security approach

A cryptocurrency is a digital currency that can be exchanged online for goods and services. Cryptocurrencies are deployed over public blockchains which have the transactions duplicated and distributed across the nodes of a computer network. This decentralized mechanism is devised in order to achieve reliability in a network consisting of unreliable nodes. Privacy, anonymity and security have become crucial in this context. For that reason, formal and mathematical approaches are gaining popularity in order to guarantee the correctness of the cryptocurrency implementations. Mimblewimble is a privacy-oriented cryptocurrency technology which provides security and scalability properties that distinguish it from other protocols of its kind. It was proposed by an anonymous developer, who posted a link to a text file on the IRC channel by the name Tom Elvis Jedusor (french name for Voldemort) in mid-2016. Mimblewimble’s cryptographic approach is based on Elliptic Curve Cryptography which allows to verify a transaction without revealing any information about the transactional amount or the parties involved. Mimblewimble combines Confidential transactions, CoinJoin and cut-through to achieve a higher level of privacy and security, as well as, scalability. In this thesis, we present and discuss these security properties and outline the basis of a model-driven verification approach to address the certification of the correctness of the protocol implementations. In particular, we propose an idealized model that is key in the described verification process. The main components of our idealized model are transactions, blocks and chain. Then, we identify and precisely state the conditions for our model to ensure the verification of relevant security properties of Mimblewimble. In addition, we analyze the Grin and Beam implementations of Mimblewimble in their current state of development. We present detailed connections between our model and their implementations regarding the Mimblewimble structure and its security properties