Presence of quantum computers is a real threat against the security of currently used public key cryptographic algorithms such as RSA and Elliptic curve cryptography. Isogeny computation on elliptic curves is believed to be difficult even on a quantum computer, and hence isogeny-based protocols represent one of the few truly practical approaches to constructing quantum-resistant cryptosystems. ...

The aim of this work is to show the feasibility of the primitives of the identity based cryptosystems for applications in Smart-Cards. Several observations are applied to easily choose many supersingular elliptic curves over a prime field Fp; p > 3; p 3 mod 4, in such a way that the size of the torsion subgroup, the curve order and the finite field characteristic are of minimal Hamming weight. ...

We present a variant of the complex multiplication method that generates elliptic curves of cryptographically strong order. Our variant is based on the computation of Weber polynomials that require significantly less time and space resources than their Hilbert counterparts. We investigate the time efficiency and precision requirements for generating off-line Weber polynomials and its comparison...

Scalar multiplication is an important operation in elliptic curve cryptosystems(ECC). The algorithms for computing scalar multiplication are mostly based on the binary expansions of scalars, such as the non-adjacent form (NAF) and wNAF(sliding window method). Representing scalars using more bases can speed up the scalar multiplication, such as mbNAF, wmbNAF and extended wmbNAF, which was propos...

In most algorithms involving elliptic curves, the most expensive part consists in computing multiples of points. This paper investigates how to extend the τ -adic expansion from Koblitz curves to a larger class of curves defined over a prime field having an efficiently-computable endomorphism φ in order to perform an efficient point multiplication with efficiency similar to Solinas’ approach pr...

This contribution describes a methodology used to efficiently implement elliptic curves (EC) over GF (p) on the 16-bit TI MSP430x33x family of low-cost microcontrollers. We show that it is possible to implement EC cryptosystems in highly constrained embedded systems and still obtain acceptable performance at low cost. We modified the EC point addition and doubling formulae to reduce the number ...

We study elliptic curve cryptosystems by first investigating the schemes defined over Zp and show that the scheme is provably secure against adaptive chosen cipher-text attack under the decisional DiffieHellman assumption. Then we derive a practical elliptic curve cryptosystem by making use of some nice elliptic curve where the decisional DiffieHellman assumption is reserved.

Public-key cryptography is a fundamental component of modern electronic communication that can be constructed with many different mathematical processes. Presently, cryptosystems based on elliptic curves are becoming popular due to strong cryptographic strength per small key size. At the heart of these schemes is the complexity of the elliptic curve discrete logarithm problem (ECDLP). Pollard’s...

Since sensor nodes in wireless networks or Internet of things have limited resources, achieving secure data transmissions among is a challenge. Hence, efficient key management schemes with lightweight ciphers are essential. Many asymmetric keys public mechanisms been developed. However, they unsuitable for group communications networks, because usually devoid sufficient memory, CPU and bandwidt...