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Threshold Signature Scheme Based on Discrete Logarithm and Quadratic Residue 认领 引用
1
作者 FEI Ru-chun 1,2 , WANG Li-na 1 1.School of Computer, Wuhan University, Wuhan 430072, Hubei, China 2.Department of Information Engineering, Benxi College of Metallurgy, Benxi 117022,Liaoning,China 《Wuhan University Journal of Natural Sciences》 EI CAS 2004年第5期770-774,共5页
Digital signature scheme is a very important research field in computer security and modern cryptography. A (k, n) threshold digital signature scheme is proposed by integrating digital signature scheme with Shamir sec... Digital signature scheme is a very important research field in computer security and modern cryptography. A (k, n) threshold digital signature scheme is proposed by integrating digital signature scheme with Shamir secret sharing scheme. It can realize group-oriented digital signature, and its security is based on the difficulty in computing discrete logarithm and quadratic residue on some special conditions. In this scheme, effective digital signature can not be generated by anyk?1 or fewer legal users, or only by signature executive. In addition, this scheme can identify any legal user who presents incorrect partial digital signature to disrupt correct signature, or any illegal user who forges digital signature. A method of extending this scheme to an Abelian group such as elliptical curve group is also discussed. The extended scheme can provide rapider computing speed and stronger security in the case of using shorter key. Key words threshold scheme - digital signature - discrete logarithm - quadratic residuc - threshold digital signature CLC number TP 309. 7 Foundation item: Supported the National Nature Science Foundation of China, Hubei Province (90104005, 2002 AB0039)Biography: FEI Ru-chun (1964-), male, Ph. D candidate, Associated professor, research direction: information security and cryptography. 展开更多
关键词 threshold scheme digital signature discrete logarithm quadratic residuc threshold digital signature
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Fault Attacks on Hyperelliptic Curve Discrete Logarithm Problem over Finite Fields 认领 引用 被引量：2
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作者 Wang Mingqiang Xue Haiyang Zhan Tao 《China Communications》 SCIE CSCD 2012年第11期150-161,共12页
In this paper, we present two explicit invalid-curve attacks on the genus 2 hyperelliptic curve over a finite field. First, we propose two explicit attack models by injecting a one-bit fault in a given divisor. Then, ... In this paper, we present two explicit invalid-curve attacks on the genus 2 hyperelliptic curve over a finite field. First, we propose two explicit attack models by injecting a one-bit fault in a given divisor. Then, we discuss the construction of an invalid curve based on the faulted divisor. Our attacks are based on the fact that the Hyperelliptic Curve Scalar Multiplication (HECSM) algorithm does not utilize the curve parameters and We consider three hyperelliptic curves as the attack targets. For curve with security level 186 (in bits), our attack method can get the weakest invalid curve with security level 42 (in bits); there are 93 invalid curves with security level less than 50. We also estimate the theoretical probability of getting a weak hyperelliptic curve whose cardinality is a smooth integer. Finally, we show that the complexity of the fault attack is subexponential if the attacker can freely inject a fault in the input divisor. Cryptosystems based on the genus 2 hyperelliptic curves cannot work against our attack algorithm in practice. 展开更多
关键词 hyperelliptic curve discrete logarithm finite field genus cryptosystem
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Security Analysis of Discrete Logarithm Based Cryptosystems 认领 引用 被引量：1
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作者 WANG Yuzhu LIAO Xiaofeng 《Wuhan University Journal of Natural Sciences》 EI CAS 2006年第6期1715-1717,共3页
Discrete logarithm based cryptosysterns have subtle problems that make the schemes vulnerable. This paper gives a comprehensive listing of security issues in the systems and analyzes three classes of attacks which are... Discrete logarithm based cryptosysterns have subtle problems that make the schemes vulnerable. This paper gives a comprehensive listing of security issues in the systems and analyzes three classes of attacks which are based on mathematical structure of the group which is used in the schemes, the disclosed information of the subgroup and implementation details respectively. The analysis will, in turn, allow us to motivate protocol design and implementation decisions. 展开更多
关键词 discrete logarithm security analysis prime order subgroup secure implementation
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The discrete logarithm problem from a local duality perspective 认领 引用
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作者 HUANG MingDeh 《Science China Mathematics》 SCIE EI 2013年第7期1421-1427,共7页
The discrete logarithm problem is analyzed from the perspective of Tate local duality. Local duality in the multiplicative case and the case of Jacobians of curves over p-adic local fields are considered. When the loc... The discrete logarithm problem is analyzed from the perspective of Tate local duality. Local duality in the multiplicative case and the case of Jacobians of curves over p-adic local fields are considered. When the local field contains the necessary roots of unity, the case of curves over local fields is polynomial time reducible to the multiplicative case, and the multiplicative case is polynomial time equivalent to computing discrete logarithm in finite fields. When the local field does not contains the necessary roots of unity, similar results can be obtained at the cost of going to an extension that contains these roots of unity. There was evidence in the analysis that suggests that the minimal extension where the local duality can be rationally and algorithmically defined must contain the roots of unity. Therefore, the discrete logarithm problem appears to be well protected against an attack using local duality. These results are also of independent interest for algorithmic study of arithmetic duality as they explicitly relate local duality in the case of curves over local fields to the multiplicative case and Tate-Lichtenbaum pairing (over finite fields). 展开更多
关键词 discrete logarithm local duality
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Weak-Keys in Public Key Cryptosystems Based on Discrete Logarithms 认领 引用 被引量：1
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作者 戴瑞恩 罗平 +1 位作者 彭小宁 王道顺 《Tsinghua Science and Technology》 EI CAS 2005年第5期579-581,共3页
The discrete logarithm method is the foundation of many public key algorithms. However, one type of key, defined as a weak-key, reduces the security of public key cryptosystems based on the discrete logarithm method. ... The discrete logarithm method is the foundation of many public key algorithms. However, one type of key, defined as a weak-key, reduces the security of public key cryptosystems based on the discrete logarithm method. The weak-key occurs if the public key is a factor or multiple of the primitive element, in which case the user＇s private key is not needed but can be obtained based on the character of the public key. An algorithm is presented that can easily test whether there is a weak-key in the cryptosystem. An example is given to show that an attack can be completed for the Elgamal digital signature if a weak-key exists, therefore validating the danger of weak-keys. Methods are given to prevent the generation of these weak-keys. 展开更多
关键词 discrete logarithm public key cryptography weak-key Elgamal digital signature
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Solving the Multi-discrete Logarithm Problems over a Group of Elliptic Curves with Prime Order 认领 引用
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作者 Jun Quan LI Mu Lan LIU Liang Liang XIAO 《Acta Mathematica Sinica,English Series》 SCIE 2005年第6期1443-1450,共8页
In this paper, we discuss the expected number of steps in solving multi-discrete logarithm problems over a group of elliptic curves with prime order by using Pollard＇s rho method and parallel collision search algorit... In this paper, we discuss the expected number of steps in solving multi-discrete logarithm problems over a group of elliptic curves with prime order by using Pollard＇s rho method and parallel collision search algorithm. We prove that when using these algorithms to compute discrete logarithms, the knowledge gained through computing many logarithms does not make it easier for finding other logarithms. Hence in an elliptic cryptosystem, it is safe for many users to share the same curve, with different private keys. 展开更多
关键词 Pollard＇s rho method Parallel collision search algorithm Elliptic curve Discrete logarithm Distinguished point
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Forgery Attacks on Wang's Signature Schemes Based on Factoring and Discrete Logarithm 认领 引用
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作者 Dezhi Gao Xiangqian Liang 《Journal of Systems Science and Information》 2009年第1期43-48,共6页
To enhance the security of signature schemes, Wang proposed two signature schemes based on the difficulties of simultaneously solving the factoring and discrete logarithm＇ problems with almost the same sizes of arith... To enhance the security of signature schemes, Wang proposed two signature schemes based on the difficulties of simultaneously solving the factoring and discrete logarithm＇ problems with almost the same sizes of arithmetic modulus. This paper, firstly, shows that Wang＇s signature scheme 1 do not satisfy the claimed properties. Moreover, we will point out that the all variants of Wang＇s scheme 2 are not secure if attackers can solve discrete logarithm problems. 展开更多
关键词 cryptography security digital signature factoring discrete logarithm
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Certificateless Proxy Identity-Based Signcryption Scheme Without Bilinear Pairings 认领 引用 被引量：10
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作者 亓延峰 唐春明 +2 位作者 娄裕 徐茂智 郭宝安 《China Communications》 SCIE CSCD 2013年第11期37-41,共5页
Signcryption, which was introduced by ZHEN~ is a cryptographic primitive that fulfils the functions of both digital signature and encryption and guarantees confidentiality, integrity and non-repudiation in a more effi... Signcryption, which was introduced by ZHEN~ is a cryptographic primitive that fulfils the functions of both digital signature and encryption and guarantees confidentiality, integrity and non-repudiation in a more effi- cient way. Certificateless signcryption and pro- xy signcryption in identity-based cryptography were proposed for different applications. Most of these schemes are constructed by bilinear pairings from elliptic curves. However, some schemes were recently presented without pai- rings. In this paper, we present a certificateless proxy identity-based signcryption scheme with- out bilinear pairings, which is efficient and secure. 展开更多
关键词 certificateless signcryption iden-tity-based cryptography proxy signcryption elliptic curve discrete logarithm problem
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Self-certified multi-proxy signature schemes with message recovery 认领 引用 被引量：5
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作者 Tzong-sun WU Chien-lung HSU Han-yu LIN 《Journal of Zhejiang University-SCIENCE A》 SCIE EI CAS 2009年第2期290-300,共11页
Multi-proxy signature schemes allow the original signer to delegate his/her signing power to n proxy signers such that all proxy signers must corporately generate a valid proxy signature on behalf of the original sign... Multi-proxy signature schemes allow the original signer to delegate his/her signing power to n proxy signers such that all proxy signers must corporately generate a valid proxy signature on behalf of the original signer. We first propose a multi-proxy signature scheme based on discrete logarithms and then adapt it to the elliptic curve cryptosystem. With the integration of self-certified public-key systems and the message recovery signature schemes,our proposed schemes have the following advan-tages:(1) They do not require the signing message to be transmitted,since the verifier can recover it from the signature;(2) The authentication of the public keys,verification of the signature,and recovery of the message can be simultaneously carried out in a single logical step;(3) No certificate is needed for validating the public keys. Further,the elliptic curve variant with short key lengths especially suits the cryptographic applications with limited computing power and storage space,e.g.,smart cards. As compared with the previous work that was implemented with the certificate-based public-key systems,the proposed schemes give better performance in terms of communication bandwidth and computation efforts. 展开更多
关键词 Self-certified Multi-proxy signature Message recovery Smart cards Discrete logarithms Elliptic curve
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Applying two channels to vector space secret sharing based multi-signature scheme 认领 引用 被引量：2
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作者 肖清华 平玲娣 +1 位作者 陈小平 潘雪增 《Journal of Zhejiang University-SCIENCE A》 CAS 2005年第1期56-62,共7页
Secret sharing and digital signature is an important research area in information security and has wide applications in such fields as safeguarding and legal use of confidential information, secure multiparty computat... Secret sharing and digital signature is an important research area in information security and has wide applications in such fields as safeguarding and legal use of confidential information, secure multiparty computation and electronic commerce. But up to now, study of signature based on general vector space secret sharing is very weak. Aiming at this drawback, the authors did some research on vector space secret sharing against cheaters, and proposed an efficient but secure vector space secret sharing based multi-signature scheme, which is implemented in two channels. In this scheme, the group signature can be easily produced if an authorized subset of participants pool their secret shadows and it is impossible for them to generate a group signature if an unauthorized subset of participants pool their secret shadows. The validity of the group signature can be verified by means of verification equations. A group signature of authorized subset of participants cannot be impersonated by any other set of partici- pants. Moreover, the suspected forgery can be traced, and the malicious participants can be detected in the scheme. None of several possible attacks can successfully break this scheme. 展开更多
关键词 Vector space secret sharing Multi-signature Discrete logarithm Chinese remainder theorem
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New signature scheme based on two cryptographic assumptions 认领 引用 被引量：4
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作者 郑明辉 崔国华 《Journal of Southeast University(English Edition)》 EI CAS 2007年第3期461-464,共4页
In order to improve the security of the signature scheme, a digital signature based on two hard-solved problems is proposed. The discrete logarithm problem and the factoring problem are two well known hard- solved mat... In order to improve the security of the signature scheme, a digital signature based on two hard-solved problems is proposed. The discrete logarithm problem and the factoring problem are two well known hard- solved mathematical problems. Combining the E1Gamal scheme based on the discrete logarithm problem and the OSS scheme based on the factoring problem, a digital signature scheme based on these two cryptographic assumptions is proposed. The security of the proposed scheme is based on the difficulties of simultaneously solving the factoring problem and the discrete logarithm problem. So the signature scheme will be still secure under the situation that any one of the two hard-problems is solved. Compared with previous schemes, the proposed scheme is more efficient in terms of space storage, signature length and computation complexities. 展开更多
关键词 digital signature security factoring problem discrete logarithm problem
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Attack on an Efficient Certificateless Aggregate Signature without Pairing 认领 引用 被引量：1
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作者 LI Huimin LIANG Hongmei +1 位作者 WANG Haimin ZHANG Jinhui 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2020年第2期139-145,共7页
A Certificateless Aggregate Signature(CLAS) scheme was proposed by Qu and Mu recently, which was published in "Int J. Electronic Security and Digital Forensics, 2018, 10(2)". They used discrete logarithm to ... A Certificateless Aggregate Signature(CLAS) scheme was proposed by Qu and Mu recently, which was published in "Int J. Electronic Security and Digital Forensics, 2018, 10(2)". They used discrete logarithm to ensure the scheme's security. However,we show by formulating an attack that their CLAS scheme cannot defend against Type I adversary. Furthermore, we point out an error that exists in the signature simulation of their security proof.After that we give a correct signature simulation for the security proof. Finally, to resist the Type I attack, we present two methods for improving Qu et al's CLAS scheme. Moreover, the second improving method can elevate the trust level of Qu et al's CLAS scheme to the highest trust level: Level 3. 展开更多
关键词 certificateless aggregate signature attack security random oracle model discrete logarithm problem
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A kind of signature scheme based on class groups of quadratic fields 认领 引用 被引量：2
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作者 董晓蕾 曹珍富 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2004年第6期583-587,共5页
Quadratic-field cryptosystem is a cryptosystem built from discrete logarithm problem in ideal class groups of quadratic fields(CL-DLP). The problem on digital signature scheme based on ideal class groups of quadratic ... Quadratic-field cryptosystem is a cryptosystem built from discrete logarithm problem in ideal class groups of quadratic fields(CL-DLP). The problem on digital signature scheme based on ideal class groups of quadratic fields remained open, because of the difficulty of computing class numbers of quadratic fields. In this paper, according to our researches on quadratic fields, we construct the first digital signature scheme in ideal class groups of quadratic fields, using q as modulus, which denotes the prime divisors of ideal class numbers of quadratic fields. Security of the new signature scheme is based fully on CL-DLP. This paper also investigates realization of the scheme, and proposes the concrete technique. In addition, the technique introduced in the paper can be utilized to realize signature schemes of other kinds. 展开更多
关键词 quadratic-field cryptosystem digital signature ideal class groups discrete logarithm problem
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A novel group signature with one time secret key 认领 引用 被引量：2
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作者 谢琪 于秀源 《Journal of Zhejiang University-SCIENCE A》 CAS 2005年第6期560-564,共5页
A new group signature with one time secret key is proposed. The main merits are that it only needs the trusted center issuing the partial secret key one time for each group member; and that the group member can genera... A new group signature with one time secret key is proposed. The main merits are that it only needs the trusted center issuing the partial secret key one time for each group member; and that the group member can generate his different secret key each time when he wants to sign a message. The group public key is constant and the size of the signature is independent of the number of group members. The total computation cost of signature and verification requires only 8 modular exponentiations. 展开更多
关键词 Cryptography Group signature Discrete logarithm problem Factoring problem
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Enhancing the Security of He-Kiesler Signature Schemes 认领 引用 被引量：1
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作者 李春辉 陈一宏 《Journal of Beijing Institute of Technology》 EI CAS 2003年第3期326-328,共3页
Although the He Kiesler signature is said to be proposed based on the discrete logarithm problem and the factorization problem, it has been proved that the signature is not as secure as it was stated to be. A new sign... Although the He Kiesler signature is said to be proposed based on the discrete logarithm problem and the factorization problem, it has been proved that the signature is not as secure as it was stated to be. A new signature scheme is here proposed based on the discrete logarithm problem and the factorization problem to enhance the security of the He Kiesler signature. 展开更多
关键词 digital signture scheme discrete logarithm factoring
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A Proxy Blind Signature Scheme Based on DLP 认领 引用 被引量：2
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作者 YU Baozheng XU Congwei 《Wuhan University Journal of Natural Sciences》 CAS 2007年第1期83-86,共4页
A proxy signature scheme allows an original signer to delegate his signing capability to a proxy signer who can sign on behalf of the original signer. A blind signature is the concept with a salient feature that the s... A proxy signature scheme allows an original signer to delegate his signing capability to a proxy signer who can sign on behalf of the original signer. A blind signature is the concept with a salient feature that the signer can not make a linkage between the blind signature and the identity of the requester. Proxy signature and blind signature are used widely in electronic commerce. With satisfying the security properties of both two signatures, a new proxy blind signature scheme based on discrete logarithm problem is proposed. 展开更多
关键词 discrete logarithm problem proxy signature blind signature electronic commerce
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Short Group Signatures with Efficient Concurrent Join 认领 引用
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作者 CHEN Hefeng MA Wenping +1 位作者 ZHANG Cheng SUN Changxia 《China Communications》 SCIE CSCD 2014年第11期90-99,共10页
Group signature schemes are fundamental cryptographic tools. A group signature scheme allows members of a group to anonymously sign misuse, the anonymity messages. To counter can be revoked by the group manager. The g... Group signature schemes are fundamental cryptographic tools. A group signature scheme allows members of a group to anonymously sign misuse, the anonymity messages. To counter can be revoked by the group manager. The group joining operation is a critical component of group signature scheme, the framing attack can be prevented by group joining processes. This paper presents an efficient group signature scheme with a simple joining protocol that is based on a ＂single message and signature response＂ interaction between the prospective user and the group manager. The security of our group signature is based on the Discrete Logarithm assumption and Decisional Linear Diffie- Hellman assumption. The formal security proof of our scheme is given in the random oracle model. Our scheme is also a very efficient short group signature scheme with efficient concurrent join. 展开更多
关键词 group signature scheme random oracle model discrete logarithm assumption decisional linear diffie-hellman assumption
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Construction of k-ary Pseudorandom Elliptic Curve Sequences 认领 引用
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作者 WU Chenhuang WENG Xin CHEN Zhixiong 《Wuhan University Journal of Natural Sciences》 CAS 2011年第5期452-456,共5页
We present a method for constructing k-ary sequences over elliptic curves. Using the multiplicative character of order k of finite fields, we construct a family of k-ary pseudorandom elliptic curve sequences. The pseu... We present a method for constructing k-ary sequences over elliptic curves. Using the multiplicative character of order k of finite fields, we construct a family of k-ary pseudorandom elliptic curve sequences. The pseudorandom measures, such as the well-distribution measure, the correlation measure of order e, and the linear complexity are estimated by using certain character sums. Such sequences share the same order of magnitude on the well-distribution measure, the correlation measure of order e as the ＇truly＇ random sequences. The method indicates that it is possible to construct ＇good＇ pseudorandom sequences over elliptic curves widely used in public key cryptography. 展开更多
关键词 pseudorandom sequences discrete logarithms elliptic curves character sums
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Threshold Decryption Scheme withMultiple Policies 认领 引用
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作者 FEI Ru-chun WANG Li-na 《Wuhan University Journal of Natural Sciences》 EI CAS 2005年第1期243-247,共5页
Based on the difficulty in computing discrete logarilhm and square 1001 onsome special conditions,we propose a basic threshold seeret sharing scheme for multiple secretswith multiple policies,which allows a group of u... Based on the difficulty in computing discrete logarilhm and square 1001 onsome special conditions,we propose a basic threshold seeret sharing scheme for multiple secretswith multiple policies,which allows a group of users to share multiple secrttkeys and only onesecret shadow to be ktpt by each user.An efficient threshold decryption scheme with multiplepolicies is designed on the basis of the basic threshold scheme.This decryption scheme allowsmultiple secret keys to he shared among a groupof users,and each user to ketp only one secretshadow.Different public keys can be used to encrypt documents.If and only if the number ofcooperated users who koop the secret shadows is greater than or c-qual to the threshold value of thecorresponding secret key,they can cooperate to decrypt the documents.It is proved that theproposed scheme has very strong security,unless the attackers can solve the discrete logarithmproblem and the square root problem. 展开更多
关键词 multiple secret keys threshold scheme seeret shadow discrete logarithm square root threshold deayp-tion scheme
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A New Digital Multilevel Proxy Signature Scheme Based on Elliptic Curve Cryptography 认领 引用
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作者 QIN Yanlin WU Xiaoping 《Wuhan University Journal of Natural Sciences》 EI CAS 2006年第6期1704-1706,共3页
Based on the analysis of elliptic curve digital signature algorithm（ECDSA）,aiming at multilevel proxy signature in which the original signer delegates the digital signature authority to several proxies and its secur... Based on the analysis of elliptic curve digital signature algorithm（ECDSA）,aiming at multilevel proxy signature in which the original signer delegates the digital signature authority to several proxies and its security demands, a new multilevel proxy signature scheme based on elliptic curve discrete logarithm problem （ECDLP） is presented and its security are proved. 展开更多
关键词 elliptic curve digital signature multilevel proxy signature elliptic curve discrete logarithm
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