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Attacking (EC)DSA scheme with ephemeral keys sharing specific bits

THEORETICAL COMPUTER SCIENCE 2024年 1001卷

作者： Adamoudis, M. Draziotis, K. A. Poulakis, D. Aristotle Univ Thessaloniki Dept Math Thessaloniki 54124 Greece Aristotle Univ Thessaloniki Dept Informat Thessaloniki 54124 Greece

In this paper, we present a deterministic attack on (EC)DSA signature scheme, providing that several signatures are known such that the corresponding ephemeral keys share a certain amount of bits without knowing their value. By eliminating the shared blocks of bits between the ephemeral keys, we get a lattice of dimension equal to the number of signatures having a vector containing the private key. We compute an upper bound for the distance of this vector from a target vector, and next, using Kannan's enumeration algorithm, we determine it and hence the secret key. The attack can be made highly efficient by appropriately selecting the number of shared bits and the number of signatures.

关键词： digital signature algorithm elliptic curve digital signature algorithm Lattice LLL algorithm Kannan's enumeration algorithm

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A simple and rapid authentication protocol in mobile networks

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SECURITY AND COMMUNICATION NETWORKS 2014年第12期7卷 2596-2601页

作者： Guo, Ming-Huang Shih Hsin Univ Dept Informat Management Taipei Taiwan

Recently, mobile networks are more and more popular in providing the most pursuing pervasive networking services. Many technologies are deployed in mobile networks, such as Universal Mobile Telecommunication System (UMTS). In these communication systems, user secrecy and privacy are important issues and should be managed seriously. To avoid security threats, many studies on authentication in the mobile networks are proposed. In 2008, Juang and Wu introduced an authentication scheme with user privacy protection in UMTS networks. It resisted and avoided many security attacks and threats, but there are still some problems, such as the incomplete defense against the impersonation attack and data with International Mobile Subscriber Identity exchanged outside home networks. In this paper, we proposed a simple and rapid authentication scheme in mobile networks. The proposal applies the elliptic curve Diffie-Hellman key agreement protocol to exchange the session key safely and elliptic curve digital signature algorithm to improve the mobile security. It also deploys the temporary key mechanism to speed up the authentication while user is roaming in the mobile networks. The analysis shows that our mechanism not only improves Juang and Wu's proposal but also is a more secure and simple authentication protocol. Copyright (c) 2011 John Wiley & Sons, Ltd.

关键词： mobile network Universal Mobile Telecommunication System authentication protocol elliptic curve Diffie-Hellman key agreement protocol elliptic curve digital signature algorithm

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Pseudo -random scalar multiplication based on group isomorphism

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JOURNAL OF INFORMATION SECURITY AND APPLICATIONS 2020年 53卷

作者： Li, Hui Beijing Univ Chem Technol Dept Comp Sci & Technol Beijing 100029 Peoples R China

elliptic curve cryptography is an essential cryptography which is widely used in data encryption, key agreement, digital signature, and other applications. Scalar multiplication is the fundamental operation in all ECC schemes, such as ECDSA, ECIES, and ECMQV. Even a slight improvement of scalar multiplication is precious. Various methods have been proposed for improving efficiency of the scalar multiplication, including the windows method, the NAF method, and the w-NAF method. However, the endeavour in this direction almost exhausted in the past several years since it is hard to find a method substantially better than the w-NAF method. This paper focuses on the scalar multiplication algorithm for the case when the scalar is a pseudo-random number. A faster pseudo-random scalar multiplication method is proposed based on a group isomorphism between the pseudo-random number group and elliptic curve point group. Experimental results show that the proposed method can considerably reduce the computation time compared with those traditional methods. The pseudo-random scalar multiplication accounts for a significant proportion of total scalar multiplication operations in almost all ECC schemes. Therefore, the proposed method is promising and applicable for various ECC applications in the fields such as Internet of things, edge computing, and swarm robotics.

关键词： Group isomorphism elliptic curve digital signature algorithm elliptic curve Menezes-Qu-Vanstone elliptic curve integrated encryption scheme Uniform random number generator

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Low-complexity parallel systolic Montgomery multipliers over GF(2^m) using Toeplitz matrix-vector representation

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2008年第6期E91A卷 1470-1477页

作者： Lee, Chiou-Yng Lunghwa Univ Sci & Technol Dept Comp Informat & Network Engn Tao Yuan Taiwan

In this paper, a generalized Montgomery multiplication algorithm in GF(2(m)) using the Toeplitz matrix-vector representation is presented. The hardware architectures derived from this algorithm provide low-complexity bit-parallel systolic multipliers with trinomials and pentanomials. The results reveal that our proposed multipliers reduce the space complexity of approximately 15% compared with an existing systolic Montgomery multiplier for trinomials. Moreover, the proposed architectures have the features of regularity, modularity, and local interconnection. Accordingly, they are well suited to VLSI implementation.

关键词： bit-parallel systolic multiplier Toeplitz matrix-vector elliptic curve digital signature algorithm trinomial pentanomial

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Attacking (EC)DSA with partially known multiples of nonces

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INFORMATION AND COMPUTATION 2024年 301卷

作者： Adamoudis, Marios Draziotis, Konstantinos A. Poulakis, Dimitrios Aristotle Univ Thessaloniki Dept Math Thessaloniki 54124 Greece Aristotle Univ Thessaloniki Dept Informat GR-54124 Thessaloniki Greece

In this paper, we introduce a series of attacks on DSA schemes that, under certain assumptions, can expose the secret key when one or more signed messages are accessible. By utilizing these signed messages, we construct a system of linear congruences with at most one solution smaller than a specific bound, which can be efficiently determined using Babai's Nearest Plane algorithm. As a case study, we provide a successful attack on secp161k1, assuming that a particular multiple of an ephemeral key is 161 bits long. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： digital signature algorithm elliptic curve digital signature algorithm LLL algorithm Babai's nearest plane algorithm

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Performance comparison between IBE-HWMP and ECDSA-HWMP

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SECURITY AND COMMUNICATION NETWORKS 2013年第4期6卷 437-449页

作者： Benitez, Yesica Imelda Saavedra Ben-Othman, Jalel Claude, Jean-Pierre Univ Versailles Lab CNRS Prism F-78000 Versailles France Univ Paris Nord Lab L2TI Paris France John Wiley & Sons Ltd Journals Prod Dept Chichester PO19 8SQ W Sussex England

Wireless mesh networks (WMNs) are one of the key technologies that will dominate wireless networking in the few years. The main characteristics of WMNs permit network connectivity anywhere anytime with simplicity and low cost. Their capability for self-organization significantly reduces the complexity of network deployment. The draft standard of IEEE P802.11s/D4.0 is not considered secure for the routing protocol. In this paper, we propose a secure Hybrid-Wireless-Mesh Protocol using an elliptic curve digital signature algorithm (ECDSA-HWMP). We then compare the ECDSA-based HWMP against identity-based encryption (IBE)-based HWMP. This study has been carried out to show the great benefits of the IBE technique in securing HWMP. Through extensive Network Simulator-3 simulations, results have shown that the IBE-HWMP outperforms the ECDSA-HWMP in terms of overhead, throughput, loss ratio and delay. Simulation results show that the use of the IBE-based HWMP provides a greater level of security with light overhead. Copyright (c) 2013 John Wiley & Sons, Ltd.

关键词： ECDSA IBE HWMP security routing protocols wireless mesh networks elliptic curve digital signature algorithm

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Efficient authentication approach for highly dynamic vehicular ad hoc networks

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INTERNATIONAL JOURNAL OF AD HOC AND UBIQUITOUS COMPUTING 2015年第3-4期19卷 193-207页

作者： Grover, Kanika Lim, Alvin Lee, Seungbae Auburn Univ Dept Comp Sci & Software Engn Auburn AL 36849 USA

Vehicular ad hoc networks (VANETs) possess an extremely dynamic nature accompanying the high mobility feature. In VANETs, each vehicle sends out safety messages at regular intervals. IEEE 1609.2 security standard for VANETs recommend the use of secure elliptic curve digital signature algorithm (ECDSA) signatures for authenticating broadcast messages. ECDSA provides source authentication, message integrity and non-repudiation;with the drawback of signature verification overhead. Due to this, a large number of messages expire in the verification queue. Considering time-bound VANET broadcast messages authenticated using complex ECDSA verification, we propose a probabilistic verification for highly dynamic and mobile vehicles to reduce packet loss ratio. Along with our intelligent authentication strategy, we maintain conditional privacy of the vehicles through a lightweight vehicle registration process. We implement the complete solution in a realistic VANET scenario. With ns-2 simulations, we show that our algorithm decreases message loss by an overall average of 68% compared to other broadcast authentication algorithms.

关键词： VANET vehicular ad hoc network broadcast authentication privacy ECDSA elliptic curve digital signature algorithm wireless

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Enhancing user and transaction privacy in bitcoin with unlinkable coin mixing scheme

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INTERNATIONAL JOURNAL OF COMPUTATIONAL SCIENCE AND ENGINEERING 2020年第4期23卷 381-395页

作者： Ansah, Albert Kofi Kwansah Adu-Gyamfi, Daniel Univ Elect Sci & Technol China Sch Comp Sci & Engn 2006 Xiyuan Chengdu 611731 Peoples R China Univ Mines & Technol Dept Comp Sci & Engn TK 237 Tarkwa Ghana Univ Energy & Nat Resources Dept Comp Sci & Informat Sunyani Ghana

The concept of coin mixing is significant in blockchain and achieves anonymity and has merited application in bitcoin. Albeit, several coin mixing schemes have been proposed, we point out that they either hoard input transactions and address mapping or not fully satisfy all requirements of practical anonymity. This paper proposes a coin mixing scheme (mixing countersignature scheme, ring signature, and coin mixing approach) that allows users to transact business untraceably and unlinkably without having to trust a third party to ensure coins are safe. Our proposed novel countersignature scheme simulation results prove the countersignature scheme's correctness with an average running time of 4 mu s using PBC type A.80. The scheme's security and privacy are met with standard ring signature, ECDSA unforgeability and our countersignature. We demonstrated the efficiency of the mixing scheme using bitcoin's core regtest mode to set up a private bitcoin network. The mix takes 80, 160, 320, 640, 800 secs to service 500, 1,000, 2,000, 4,000, 5,000 users respectively. It was observed that the number of users scales linearly with average running time.

关键词： bitcoin blockchain user privacy transaction privacy coin mixing bilinear pairing elliptic curve digital signature algorithm ECDSA ring signature countersignature anonymity

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An identity-based authentication scheme for safety messages in WAVE-enabled VANETs

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INTERNATIONAL JOURNAL OF PARALLEL EMERGENT AND DISTRIBUTED SYSTEMS 2012年第6期27卷 541-562页

作者： Biswas, Subir Misic, Jelena Misic, Vojislav Univ Manitoba Dept Comp Sci Winnipeg MB R3T 2N2 Canada Ryerson Univ Dept Comp Sci Toronto ON M5B 2K3 Canada

In a vehicular ad hoc network (VANET), a road-side infrastructure or road-side unit (RSU) is anticipated to be installed at some road-side location. This exposes the VANET to several different adversaries. In this paper, we present an authentication scheme for infrastructure-generated safety messages using an identity (ID)-based proxy signature and verification mechanism. An ID-based technique offers a certificate-less public key verification, while a proxy signature provides flexibility in message authentication and trust management. We incorporate an ID-based proxy signature framework with the standard elliptic curve digital signature algorithm for safety application messages from RSU. We also provide forwarding of safety message components ensuring the accountable authentication of RSU's application messages. Security analysis and network simulation prove that our scheme is resilient to all major security threats, compatible to standards and efficient in terms of computation complexity. We also conduct simulation experiments to determine the most suitable access classes for on-board unit and RSU.

关键词： identity-based system proxy signature authentication elliptic curve digital signature algorithm safety messages

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A Novel elliptic curve Cryptography Based Approach of Re-watermarking for Cheque Truncation System

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JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY 2015年第3期18卷 219-235页

作者： Mehan, Vineet Dhir, Renu Brar, Yadwinder Singh Natl Inst Technol Dept Comp Sci & Engn Jalandhar India GNDEC Ludhiana Punjab India

Cheque Truncation System (CTS) is a technique of preventing tangible movement of cheque by substituting it with a digital image, with an aim for secure and faster clearance. For the first time re-watermarking is applied for authenticating transactions in CTS. Methodology for the proposed approach splits the host image (I-h) into two layers (L). In L-1 cheque details are fused with two image color channels to form a composite message (C-m). Secure hash algorithm (SHA-512) is applied to C-m to generate a unique message digest (M-d). elliptic curve digital signature algorithm (ECDSA) is applied to M-d to create a digital signature. The signature is embedded by exploiting Human Visual System (HVS) color channel sensitivity in equally parted mode. In L-2, joint secret is established to form key using elliptic curve Diffie Hellman Protocol (ECDHP). Advanced Encryption Standard (AES) is applied to user details intricate in the transaction. Encrypted contents are then inserted in L-2 by applying Discrete Cosine Transform (DCT). Experimental results state solution to integrity concerns by using ECDSA with SHA-512, reaction to security issues by AES and the response to key distribution problem by ECDHP. An effective semi-blind CTS is perceived with PSNR between 59-60 dB.

关键词： Advanced Encryption Standard Cheque Truncation System Discrete Cosine Transform elliptic curve Diffie Hellman Protocol elliptic curve digital signature algorithm Re-watermarking

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