Sang Geun Hahn

Abstract. In this paper, we present two forward secure signature schemes based on gap Diffie-Hellman groups and prove these schemes to be secure in the sense of slightly stronger security notion than that by Bellare and Miner in the random oracle model. Both schemes use the same key update strategy as the encryption scheme presented by Canetti, Halevi and Katz. Hence, our schemes outperform the previous tree-based forward secure signature scheme by Bellare and Miner in the key generation and key

A concept of bypass rewiring is introduced, and random bypass rewiring is analytically and numerically investigated with simulations. Our results show that bypass rewiring makes networks robust against removal of nodes including random failures and attacks. In particular, random bypass rewiring connects all nodes except the removed nodes on an even degree infinite network and makes the percolation threshold 0 for arbitrary occupation probabilities. In our example, the even degree network is more

Recently, a new method, called by Xedni calculus, to solve ECDLP was proposed by Silverman and Kim et. al. [11, 5]. The Xedni addresses a novel idea, but has two di#culties. One is to find good liftings and the other is to compute the dependence relation among lifted rational points. In this paper, we propose a fast algorithm to compute the dependence relation modulo the order, n P , of P for given two dependent rational points of elliptic curve over Q.

Let $t \equiv 3 \mod 4$ ($t > 3$) be a prime and $\sigma_r\colon \zeta_t \rightarrow \zeta_t^r$ be a generator of $\operatorname{Gal}(\mathbf{Q}(\zeta_t) / \mathbf{Q}(\sqrt{-t}))$ for $r \in \{1,\dots,t-1\}$. If $p = tn + r$ is a prime, then $4p^h$ can be expressed as the form $4p^h = a^2 + tb^2$ where $h$ is the class number of $\mathbf{Q}(\sqrt{-t})$. Let $\alpha t$ be the sum of representatives of $\langle r \rangle $ in $(\mathbf{Z}/t\mathbf{Z})^{\times}$ and $\beta = \phi(t)/2 - \alpha$. If

Koblitz has suggested to use “anomalous” elliptic curves defined over F2, which are non-supersingular and allow for efficient multiplication of a point by an integer. For these curves, Meier and Staffelbach gave a method to find a polynomial of the Frobenius map corresponding to a given multiplier. Muller generalized their method to arbitrary non-supersingular elliptic curves defined over a small field of characteristic 2. In this paper, we propose an algorithm to speed up scalar multiplication

In this paper, we introduce a new method to solve the elliptic curve discrete logarithm probelm (ECDLP) over a finite field by using the elliptic curve lifting problem. Moreover, we propose to find a non-trivial point in E1(Q) in order to get a lifted elliptic curve with rank smaller than the number of lifted points. By this method, we conclude that finding a non-trivial point in E1(Q) implies solving the ECDLP, the discrete logarithm problem (DLP) and the integer factorization problem (IFP). Fi