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…
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(F_p) 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...
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...
The security of these systems is based on the relative complexity of the underlying mathematical problem. Of all these systems, for a given key size, ECC is the most secure public key cryptosystem . A survey of various protocols based on ECC has been done in the paper. The protocols have ...
to expand, meaning the size of encrypted keys must continue to grow in order to remain secure. This can prove to be a burden to certain devices, particularly mobile, that do not have as much available computational power. However, elliptic curve cryptography helps to solve that problem. ...
Only three classes of public-key cryptosystems are today considered both secure and efficient: Integer Factorization Systems, Discrete Logarithm Systems, and the Elliptic Curve Cryptosystem (ECC). While the security of all three is based on the difficulty of an underlying mathematical problem, ...
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 (...
Going back to the basics, this problem must be easy to do and hard to undo. For example, imagine one person hitting a ball from point A towards point B, and when it hits the curve, the ball bounces either straight up or straight down to the other side of the curve. If some...
Thesizeoftheellipticcurvedeterminesthedifficultyoftheproblem.ItisbelievedthatthesamelevelofsecurityaffordedbyanRSAbasedsystemwithalargemoduluscanbeachievedwithamuchsmallerellipticcurvegroup.Usingasmallgroupreducesstorageandtransmissionrequirements.Forcurrentcryptographicpurposes,anellipticcurveisaplanecurvewhichconsistsofthe...