The design and implementation of fast algorithms related to Elliptic Curve Cryptography (ECC) over the field GF(p), such as modular addition, modular subtraction, point addition, point production, choice of embedding ...The design and implementation of fast algorithms related to Elliptic Curve Cryptography (ECC) over the field GF(p), such as modular addition, modular subtraction, point addition, point production, choice of embedding plaintext to a point, etc. are given. A practical software library has been produced which supports variable length implementation of the ECCbased ElGamal cryptosystem. More importantly, this scalable architecture of the design enables the ECC being used in restricted platforms as well as high-end servers based on Intel Pentium CPU. Applications such as electronic commerce security, data encryption communication, etc.are thus made possible for real time and effective ECC.展开更多
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
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
In the study, the digital multi-signature scheme, constructed by theintegration of one-way hash function and identification scheme, are proposed based on the ellipticcurve cryptosystem (ECC). To the efficiency in perf...In the study, the digital multi-signature scheme, constructed by theintegration of one-way hash function and identification scheme, are proposed based on the ellipticcurve cryptosystem (ECC). To the efficiency in performance, the ECC has been generally regarded aspositive; and the security caused by the Elliptic Curve Discrete Logarithm Problem (ECDLP) is highlyalso taken highly important. The main characteristic of the proposed scheme is that the length ofthe multi-signature is fixed rather than changeable and it will not increase with the number ofgroup members.展开更多
A hyperelliptic curve digital signature algorithm （HECDSA） can be viewed as the hyperelliptic curve analogue of the standard digital signature algorithm （DSA）. This article discusses divisor evaluations, the basic...A hyperelliptic curve digital signature algorithm （HECDSA） can be viewed as the hyperelliptic curve analogue of the standard digital signature algorithm （DSA）. This article discusses divisor evaluations, the basic HECDSA, variants, two HECDSA equations and a 4-tuple HECDSA scheme, and puts forward a generalized equation for HECDSA. From this generalized equation, seven general HECDSA types are derived based on the efficiency requirements. Meanwhile, the securities of these general HECDSA types are analyzed in detail.展开更多
This paper improves the method of discrete logarithm on anomalous elliptic curves, and establishes an isomorphism from E(Fp) to Fp which can be more easily implemented. Fruthermore, we give an optimized algorithm for ...This paper improves the method of discrete logarithm on anomalous elliptic curves, and establishes an isomorphism from E(Fp) to Fp which can be more easily implemented. Fruthermore, we give an optimized algorithm for discrete logarithm on anomalous elliptic curves E(Fp).展开更多
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
基金the National Natural Science Foundation of China(No.60271025)
文摘The design and implementation of fast algorithms related to Elliptic Curve Cryptography (ECC) over the field GF(p), such as modular addition, modular subtraction, point addition, point production, choice of embedding plaintext to a point, etc. are given. A practical software library has been produced which supports variable length implementation of the ECCbased ElGamal cryptosystem. More importantly, this scalable architecture of the design enables the ECC being used in restricted platforms as well as high-end servers based on Intel Pentium CPU. Applications such as electronic commerce security, data encryption communication, etc.are thus made possible for real time and effective ECC.
基金Supported by the National Natural Science Foun-dation of China (70471031)
文摘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.
基金NNSF of China.No.90304012973 Project,No.2004CB318000
文摘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.
文摘In the study, the digital multi-signature scheme, constructed by theintegration of one-way hash function and identification scheme, are proposed based on the ellipticcurve cryptosystem (ECC). To the efficiency in performance, the ECC has been generally regarded aspositive; and the security caused by the Elliptic Curve Discrete Logarithm Problem (ECDLP) is highlyalso taken highly important. The main characteristic of the proposed scheme is that the length ofthe multi-signature is fixed rather than changeable and it will not increase with the number ofgroup members.
基金supported by the National Natural Science Foundation of China (60763009)the Science and Technology Key Project of the Ministry of Education of China (207089)Zhejiang Natural Science Foundation of Outstanding Youth Team Project (R1090138)
文摘A hyperelliptic curve digital signature algorithm （HECDSA） can be viewed as the hyperelliptic curve analogue of the standard digital signature algorithm （DSA）. This article discusses divisor evaluations, the basic HECDSA, variants, two HECDSA equations and a 4-tuple HECDSA scheme, and puts forward a generalized equation for HECDSA. From this generalized equation, seven general HECDSA types are derived based on the efficiency requirements. Meanwhile, the securities of these general HECDSA types are analyzed in detail.
文摘This paper improves the method of discrete logarithm on anomalous elliptic curves, and establishes an isomorphism from E(Fp) to Fp which can be more easily implemented. Fruthermore, we give an optimized algorithm for discrete logarithm on anomalous elliptic curves E(Fp).
基金Supported by the National Natural Science Foundation of China (61063041)the Program for New Century Excellent Talents in Fujian Province University (JK2010047)the Open Funds of State Key Laboratory of Information Security (01-01-1)
文摘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.
