Elliptic curve password algorithm introduction
A relatively new technique-elliptic curve encryption system has gradually been used to do basic digital signature systems. The elliptic curve is the basic principle of digital signatures. The RSA is the same as the DSA, and the generation of digital signatures and the speed of the certification are faster than RSA and DSA. Below we briefly introduce the cryptographic algorithm on the elliptic curve and elliptic curve.
1. Elliptic curve set in a limited domain represents a limited domain, e is an elliptic curve on the domain K, then E is a collection of points: E / K = {(x, y) | Y2 A1xy a3y = x3 A2X2 A4X A6, A1, A3, A2, A4, A6 X, Y K} {O} where o represents an infinite point. Define ' ' calculation on E, P Q = R, R is a symmetry point of the straight line and the curve of the straight line of the p, Q, R is the tangent and curve of the P point when P = Q Another intersection point on the X-axis symmetry. Thus, (e, ) constitutes a charter (ABEL group), O is an addition unit element (zero). The elliptic curve discrete logarithm problem (ECDLP) is defined as follows: given the elliptic curve E of the K, a n-order point PE / K, and points QE / K, if there is L, determine an integer L, 0 ln - 1 , Q = LP. We know that RSA is based on factorial decomposition. The core of its algorithm is how to find uncle's factor decomposition, but ECDLP is a rare problem with factors. Addition on an elliptic curve: p q = r
Two times the elliptic curve: P P = R. 2. The cryptographic algorithm on the elliptic curve is based on the problem. In 1985, N.Koblitz and Miller proposed to use the elliptic curve for the cryptographic algorithm, using a limited domain elliptical curve. The group consisting of points realizes the discrete log number of cryptographic algorithms. The DSA algorithm introduced in detail in "Digital Signature Analysis and Implementation" is widely used in the elliptic curve, called the elliptic curve digital signature algorithm ECDSA, by the IEEE Working Group and AMERCIAN National Standards Institute X9. Development. The elliptic curve cryptography is then expanded. In addition to the elliptical curve, it is proposed to achieve public key cryptographic algorithm on other types of curves such as hyperseim curves. It is based on the discrete logarithmic problem ECDLP in the dot group on the oval curve on a limited domain. ECDLP is a more difficult problem than factor breakdown, and many password experts believe that it is the difficulty of the index level. From the currently known best solving algorithm, the 160-bit elliptic curve cryptographic algorithm is equivalent to the 1024-bit RSA algorithm. Thereafter, some people have realized an encryption algorithm similar to Elgamal on an elliptic curve, and a digital signature scheme that can restore clear text. In addition to the Elliptic Curve Cipration Algorithm in a finite domain, people also explored the RSA algorithm on the elliptic curve, such as Kmov, etc. 3. The development of the elliptic curve cryptographic algorithm is the familiar public key cryptographic algorithm, which can be used to implement digital signatures. The PGP software is used by the RSA algorithm. The RSA algorithm is based on large number of factor decomposition problems. Due to the improvement of the calculation level, people can gradually decompose a larger number of computers. Therefore, the key to the RSA algorithm is longer. In the SET protocol of e-commerce, specify that the user uses 10 24-bit RSA keys, the authentication center CA uses 2048 bit of RSA key. The long key brings two questions, one is slower, the other is key storage and management issues. If the electronic wallet is implemented with a 16-bit IC card, the RSA algorithm with a 1024 bit is very slow, and it is calculated in seconds. The IC card or 32-bit IC card price of the curing RSA algorithm is more expensive.
Elliptic curve encryption system consists of many encryption systems that depend on discrete algorithm, and DSA is a good example. DSA is a good example, and DSA is a discrete log-based algorithm. The elliptic curve digital signature system has been studied for many years and has created a lot of business value. Due to its own advantages, the elliptical curve cryptography has received attention. The cryptography now generally believes that it will replace RS A to become a common public key cryptographic algorithm, the SET (Secure Electronic Transactions) protocol has put it as the default public key cryptographic algorithm in the next generation set protocol, and has become research Hotspots are very promising research directions. The digital signature of the elliptic curve can be used to easily use a small limited resource device, for example: small card (the size of the credit card size contains a tiny process chip). The cryptographic algorithm on the elliptic curve is very fast, and a fast elliptic curve cryptographic algorithm is implemented on the 32-bit PC and the 16-bit microprocessor, where the EDSA digital signature on the 16-bit microprocessor is less than 500ms. Note: This article is not detailed, and there is a chance after the app
