它在1998年既已为ISO所接受,并且包含它的其他一些标准亦在ISO的考虑之中。与普通的离散对数问题(discrete logarithm problem DLP)和大数分解问题(integer factorization problem IFP)不同,椭圆曲线离散对数问题(elliptic curve discrete logarithm problem ECDLP)没有亚指数时间的解决方法。因此椭圆曲线密码的单位比特强度要...
1.3 The Elliptic Curve Discrete Logarithm Problem 椭圆曲线的两点 Q,P∈E(Fp),Q=kP,求k, 记作 k=logpQ 最快的算法是 Pohlig-Hellman attack 和 Pollard Rho Algorithm 2. Attacks on Weak Curves E(Fp) 在没有较大的素子群时,受 Pohlig-Hellman attack 影响 #E(Fp) = p 时,受Smart's attack 影...
Elliptic Curve Cryptography (ECC) is a key-based technique for encrypting data. ECC focuses on pairs of public and private keys for decryption and encryption of web traffic. ECC is frequently discussed in the context of the Rivest–Shamir–Adleman (RSA) cryptographic algorithm. RSA achieves one-...
椭圆曲线密码 Elliptic Curve Cryptography 椭圆曲线密码( Elliptic Curve Cryptography),由Miller和Koblitz在20世纪80年代中期提出。大约在同一时间,Lenstra开发了一种使用椭圆曲线的分解算法。近年来,椭圆曲线在密码学中的应用得到了迅速的发展。其主要优点是利用椭圆曲线,我们可以用比RSA和其他现代密码系统所需要的数目小...
椭圆曲线密码（Elliptic Curve Cryptography）椭圆曲线密码在20世纪80年代中期由Miller和Koblitz提出，随后Lenstra开发了一种使用椭圆曲线的分解算法。近年来，其在密码学中的应用得到了迅速的发展，其主要优点是利用椭圆曲线，我们可以用比RSA和其他现代密码系统所需要的数目小得多的数字来实现安全性。定义1. ...
However, elliptic curve cryptography helps to solve that problem. How does elliptic curve cryptography work?# An elliptical curve can simply illustrated as a set of points defined by the following equation: y2 = x3 + ax + b, where a and b are constants....
Elliptic curve cryptographic schemes were proposed independently in 1985 by Neal Koblitz [ 3 ] and Victor Miller [ 5 ]. They are the elliptic curve analogues of schemes based on the discrete logarithm problem where the underlying group is the group of points on an elliptic curve defined over ...
Thesizeoftheellipticcurvedeterminesthedifficultyoftheproblem.ItisbelievedthatthesamelevelofsecurityaffordedbyanRSAbasedsystemwithalargemoduluscanbeachievedwithamuchsmallerellipticcurvegroup.Usingasmallgroupreducesstorageandtransmissionrequirements.Forcurrentcryptographicpurposes,anellipticcurveisaplanecurvewhichconsistsofthe...
cryptography systems are based on sound mathematical foundations that are designed to make the problem hard for an intruder to break into the system. The major approaches that since 1976 have withstood intruder attacks, are the discrete logarithm Page 1 of 25 The University of Adelaide problem (...
In this paper, we focus on FNNs for the computation of the Boolean function derived by elliptic curve cryptography defined in Eq. (1). For the general problem of the computation of a Boolean function by FNNs, the following theorem proved in [21], supports the effectiveness of the proposed...