This paper further develops the theory of arbitrary semigroups acting on trees via elliptic mappings. A key tool is the Lyndon-Chiswell length function L for the semigroup S which allows one to construct a tree T and an action of S on T via elliptic maps. Improving on previous results, the length function of the action will also be L.

This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a wide range of applications. Notably, the new addition algorithm uses 8M for suitably selected curve constants. In comparison, the fastest point addition algorithms for (twisted) Edwards curves stated in the literature ...

1. ABSTRACT-The problem undertaken for this paper is “An Elliptic Curve Cryptography approach for Digital Signature in PDA devices”. Digital transaction have become common place and in some cases inextricably linked to modern life. This technological dependency requires that information be unaltered and confidential. So in this paper, problem is to search a good secure technique, which ensures ...

This paper describes synthesizable VDHL implementation of elliptic curve Point Multiplication. Elliptic curves used for ECC are defined over mathematical structures called Galois fields. Based on the theory of ECC, this paper has carried out Modular addition/subtraction, EC Point doubling/addition, Modular multiplicative inversion, EC point multiplier, projective to affine coordinates conversio...

Elliptic curve cryptography is known for its complexity due to its discrete logarithm problem, and this gives advantage to the system used since the formula developed using this concept is hard to break, therefore this criteria has given mathematicians a courage to explore this area of research. Earlier in [10], we have showed a new method for imbedding plaintexts using complementary elliptic c...

Randomization techniques play an important role in the protection of cryptosystems against implementation attacks. This paper studies the case of elliptic curve cryptography and propose three novel randomization methods, for the elliptic curve point multiplication, which do not impact the overall performance. Our first method, dedicated to elliptic curves over prime fields, combines the advanta...

This paper will examine the role of elliptic curves in the field of cryptography. The applicability of an analogous discrete logarithm problem to elliptic curve groups provides a basis for the security of elliptic curves. Two cryptographic protocols which implement elliptic curves are examined as well as two popular methods to solve the elliptic curve discrete logarithm problem. Finally, a comp...

Efficient computation of elliptic curve scalar multiplication has been a significant problem since Koblitz [13] and Miller [14] independently proposed elliptic curve cryptography, and several efficient methods of scalar multiplication have been proposed (e.g., [8], [9], [12]). A standard approach for computing scalar multiplication is to use the Frobenius endomorphism. If we compute the s-multi...

Public key cryptography is the famous cryptography technique used in many corporate sectors for developing software to provide security services. Hyperelliptic Curve Cryptosystem (HECC) is one of the public key cryptographic technique, an expansion of Elliptic Curve Cryptography which offers the similar level of security compared with other cryptosystems such as RSA, ECC and DSA. HECC supervise...

This paper presents a processor architecture for elliptic curve cryptography computations over GF(p). The speed to compute the Elliptic-curve point multiplication over the prime fields GF(p) is increased by using the maximum degree of parallelism, and by carefully selecting the most appropriate coordinates system. The proposed Elliptic Curve processor is implemented using FPGAs. The time, area ...