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Elliptic-curve cryptography Verilog code
4.0
Elliptic encryption algorithm (ECC) is a kind of public key encryption system, which was first proposed by Koblitz and Miller in 1985. Its mathematical basis is the computational difficulty of elliptic discrete logarithm on Abel addition group constructed by rational points on elliptic curve. Elliptic curve cryptosystem comes from the study of elliptic curve. The so-called elliptic curve refers to the plane curve determined by Weierstrass equation: Y2 + a1xy + a3y = X3 + a2x2 + a4x + A6 (1). Where the coefficient AI (I = 1,2 , 6) defined in a field, can be rational number field, real number field, complex number field, can also be finite field GF (PR), elliptic curve cryptosystem used in the elliptic curve are defined in the finite field. All the points on the elliptic curve plus a special point called infinity constitute an Abelian group together with a defined addition operation. In the equation MP = P + P + +In P = q (2), it is easier to find point Q when m and P are known. On the contrary, it is rather difficult to find m when Q and P are known. This problem is called the discrete logarithm problem of point groups on elliptic curves. Elliptic curve cryptosystem is designed based on this difficult problem. The application of elliptic curve to cryptography was first proposed by Neal Koblitz and Victor Miller in 1985. Elliptic curve cryptosystem (ECC) is one of the most powerful public key cryptosystems. The best algorithm for solving the discrete logarithm problem on elliptic curve is Pollard Rho method, which has a time complexity of, and is of completely exponential order. Where n is the number of bits of binary representation of m in equation (2). When n = 234, about 2117, it takes 1.6x1023 MIPS years. RSA, as we all know, uses the difficult problem of large integer decomposition. At present, the time complexity of the best algorithm for factorization is sub exponential order. When n = 2048, it takes 2x1020mips years. That is to say, when RSA's key uses 2048 bits, ECC's key uses 234 bits, and the security strength is much higher. The difference of key length between them is 9 times. When ECC's key is bigger, the difference between them will be bigger. Moreover, the advantage of ECC key is very obvious. With the increase of encryption strength, the key length does not change much. Many cryptography research groups and some companies in Germany, Japan, France, the United States, Canada and other countries have implemented ECC, and some cryptographers in China have also done this work. Many standardization organizations have developed or are developing standards for elliptic curve, and many manufacturers have developed or are developing standards based on elliptic curve
qinzhen1212
2016-08-23
0
1
DES encryption algorithm c language code
no vote
Since the 50 's, cryptography research area most representative of the two major achievements. One is the 1971 United States scholar Barbara w. Tuchman (Tuchman) and Mayer (Meyer), founder of information theory, Shannon (Shannon), "multiple encryption theory" founded, in 1977, after the United States issued national standards for the data encryption standard. DES password is in fact Lucifer in the further development. It is a tradition of using the block cipher encryption method. Its algorithm is symmetric, and can be used for both encryption and decryption. United States National Bureau of standards in 1973 began to study other sectors in addition to the Department of Defense's computer systems for the data encryption standard, on May 15, 1973 and August 27, 1974, two sent asking for an encryption algorithm to the public announcement. Encryption algorithm to achieve commonly known as why DES cryptographic algorithm requires mainly into the following fou
qinzhen1212
2014-04-15
0
1
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