Difficulty Of Discrete Logarithm Problem Research Articles

A public key cryptosystem and signature scheme based on numerical series

A public key cryptosystem and signature scheme based on a proposed key exchange algorithm are introduced. The key exchange algorithm is based on the difficulty of calculating the nth partial sum of infinite numerical series where no exponentiation computation is required to share a secret key between two parties as in the Diffie–Hellman algorithm. With the proposed public key cryptosystem ciphering and deciphering of messages, online signing documents and verifying signatures do not require exponentiation computation while providing higher security level than the state-of-the-art cryptosystems that depend on the difficulty of discrete logarithmic problem or factorizing large prime numbers. The proposed cryptosystem and signature scheme do not depend on elliptic curve cryptography or RSA cryptography that are computationally too slow, this makes the proposed cryptosystem and signature scheme computationally faster, easier to implement and more practical to be used in online transactions. It also provides a higher level of security as it provides forward secrecy and using large size symmetric keys to encrypt and decrypt messages in a significantly short time. Moreover, the proposed signature scheme can be used as a cryptographic hash function as the hash value significantly changes when a single letter in the document is changed. In comparison with the state-of-the art the experimental results show the superiority of the proposed key exchange algorithm and public key cryptosystem.

Operations of Points on Elliptic Curve in Affine Coordinates

Summary In this article, we formalize in Mizar [1], [2] a binary operation of points on an elliptic curve over GF(p) in affine coordinates. We show that the operation is unital, complementable and commutative. Elliptic curve cryptography [3], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security.

Bipartite Threshold Multi-Secret Sharing Scheme Based on Hypersphere

To address the problem that existing bipartite secret sharing scheme is short of dynamic characteristic, and to solve the problem that each participant can only use secret share once, this paper proposed a bipartite (n1+n2, m1+m2)-threshold multi-secret sharing scheme which combined cryptography and hypersphere geometry. In this scheme, we introduced a bivariate function and a coordinate function over finite field Zp to calculate the derived points of secret share, which can reconstruct the shared secrets by producing the intersection point of hypernormal plane and normal line on the hypertangent plane. At the initial stage the secret dealer distributes to each participant a secret share that can be kept secret based on the intractability of discrete logarithm problem and need not be changed with updating the shared secrets.Each cooperative participant only needs to submit a derived point calculated from the secret share without exposing this secret share during the process of reconstructing the shared secret. Analyses indicate that the proposed scheme is not only sound and secure because of hypersphere geometric properties and the difficulty of discrete logarithm problem, but also efficient because of its well dynamic behavior and the invariant secret share. Therefore, this bipartite threshold multi-secret sharing scheme is easy to implement and is applicable in practical settings.

ANALISIS ATRIBUT KEAMANAN TERHADAP PERBAIKAN PROTOKOL GROUP KEY TRANSFER : PROTOKOL HSU

Protocol Hsu et.al first introduced in 2012 and is the protocol type Group Key Transfer based Linear Shamir's Secret Sharing Scheme (LSSS). The main idea of this protocol is to use m-secret sharing perspective. This protocol assumes that the difficulty of discrete logarithm problem (DLP) (ie given is computationally very difficult/not feasible to count ) and Cryptographyc Diffie Hellman (CDH) (ie given and it is computationally very difficult/not feasible to count ) in . Thus, it needs to analyze the security attributes to this mechanism Protocol Hsu. Good cryptographic protocols should meet the security attributes Known Security Key, Key-Compromise Impersonation Resillience, Unknown Key-Share Resillience, Key Control and Key Confirmation.

Operations of Points on Elliptic Curve in Projective Coordinates

Operations of Points on Elliptic Curve in Projective Coordinates In this article, we formalize operations of points on an elliptic curve over GF(p). Elliptic curve cryptography [7], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security. We prove that the two operations of points: compellProjCo and addellProjCo are unary and binary operations of a point over the elliptic curve.