An Authenticated Key Agreement Scheme using Vector Decomposition

Encryption using vector decomposition problem (VDP) on higher dimensional vector spaces is a novel method in cryptography. Yoshida has shown that the VDP on a two-dimensional vector space is at least as hard as the computational Diffie-Hellman problem on a one-dimensional subspace under certain conditions. Steven Galbraith has shown that for certain curves, the VDP is at most as hard as the discrete logarithm problem on a one-dimensional subspace. Okomoto and Takashima proposed encryption scheme and signature schemes using VDP. An authenticated key agreement scheme using vector decomposition problem is proposed in this pape

Self-pairings on Hyperelliptic Curves

A self-pairing is a pairing computation where both inputs are the same group element. Self-pairings are used in some cryptographic schemes and protocols. In this paper, we show how to compute the Tate-Lichtenbaum pairing (D,\phi(D)) on a curve more efficiently than the general case. The speedup is obtained by requiring a simpler final exponentiation. We also discuss how to use this pairing in cryptographic applications