So far, the Elliptic Curve Cryptosystem(ECC) provides the highest strength-per-bit of any cryptosystem. The fast implementation of elliptic curve cryptosystem key algorithms, namely, Scalar Multiplication, is studied in this paper. The limitation of the traditional fixed point comb method is analyzed, and on the basis of the study improvement strategy of fixed-base comb algorithm of this propos...

In this paper, we first establish a new fixed point theorem for a Meir-Keeler type condition. As an application, we derive a simultaneous generalization of Banach contraction principle, Kannan's fixed point theorem, Chatterjea's fixed point theorem and other fixed point theorems. Some new fixed point theorems are also obtained.

in this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-laplacian fractional order differential equations. we use schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. we include some examples to show the applicability of our results.

We present a second pre-image attack on ECOH. Our attack requires 2143 time for ECOH-224 and ECOH-256, 2206 time for ECOH-384, and 2287 time for ECOH-512. The attack sets the checksum block to a fixed value and uses a collision search on the elliptic curve points. 1 An outline of ECOH We first give a description of the essential elements of ECOH. We restrict ourselves to messages that are an in...