Implementing Elliptic Curve Cryptosystems
نویسنده
چکیده
In 1987 Neil Koblitz first suggested the use of Elliptic curves for Public Key Cryptosystems. This has triggered publications about ECC (Elliptic Curve Cryptography) in recent years as well as the appearance of first University textbooks about that topic. Some Mathematicians and Computer Scientists have focused their studies of Elliptic curves on efficiency and security of ECC. Questions arise about how to adapt existing algorithms to ECC, which curves are suitable, how to choose the underlying field structure, how to determine the group order efficiently, how to represent messages as points on a curve, etc... I will try to address some of these issues from a practical point of view using known result from the Mathematical theory, referring to other sources for most of the details and proofs.
منابع مشابه
Efficient elliptic curve cryptosystems
Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...
متن کاملAn efficient blind signature scheme based on the elliptic curve discrete logarithm problem
Elliptic Curve Cryptosystems (ECC) have recently received significant attention by researchers due to their high performance such as low computational cost and small key size. In this paper a novel untraceable blind signature scheme is presented. Since the security of proposed method is based on difficulty of solving discrete logarithm over an elliptic curve, performance of the proposed scheme ...
متن کاملDiffie-Hellman type key exchange protocols based on isogenies
In this paper, we propose some Diffie-Hellman type key exchange protocols using isogenies of elliptic curves. The first method which uses the endomorphism ring of an ordinary elliptic curve $ E $, is a straightforward generalization of elliptic curve Diffie-Hellman key exchange. The method uses commutativity of the endomorphism ring $ End(E) $. Then using dual isogenies, we propose...
متن کاملEfficient elliptic curve exponentiation
Elliptic curve cryptosystems, proposed by Koblitz([8]) and Miller([11]), can be constructed over a smaller definition field than the ElGamal cryptosystems([5]) or the RSA cryptosystems([16]). This is why elliptic curve cryptosystems have begun to attract notice. There are mainly two types in elliptic curve cryptosystems, elliptic curves E over IF2r and E over IFp. Some current systems based on ...
متن کاملEecient Elliptic Curve Exponentiation Using Mixed Coordinates
Elliptic curve cryptosystems, proposed by Koblitz ((12]) and Miller ((16]), can be constructed over a smaller eld of deenition than the ElGamal cryptosystems ((6]) or the RSA cryptosystems ((20]). This is why elliptic curve cryptosystems have begun to attract notice. In this paper, we investigate eecient elliptic curve exponentiation. We propose a new coordinate system and a new mixed coordinat...
متن کامل