We give an algorithm that constructs, on input of a prime power q and an integer t, a
supersingular elliptic curve over Fq with trace of Frobenius t in case such a curve exists. If …

For pairing based cryptography we need elliptic curves defined over finite fields F _ q whose
group order is divisible by some prime ℓ with ℓ| q^ k-1 where k is relatively small. In Barreto …

We present an algorithm for counting points on superelliptic curves yr= f (x) over a finite field
F q of small characteristic different from r. This is an extension of an algorithm for …

Abstract Let p> 3 p> 3 be a prime and let EE, E'E′ be supersingular elliptic curves over F _p
F p. We want to construct an isogeny ϕ: E → E'ϕ: E→ E′. The currently fastest algorithm for …

Constructing a supersingular elliptic curve whose endomorphism ring is isomorphic to a
given quaternion maximal order (one direction of the Deuring correspondence) is known to …

This paper discusses representations for computation on non-supersingular elliptic curves
over binary fields, where computations are performed on the x-coordinates only. We discuss …

The subject of the thesis at hand is the description of an efficient algorithm for finding an
elliptic curve over a finite prime field of large characteristic suitable for use in cryptography …

Previously known techniques to construct pairing-friendly curves of prime or near-prime
order are restricted to embedding degree k\leqslant6. More general methods produce …

For public key cryptosystems multiplication on elliptic curves can be used instead of
exponentiation in finite fields. One attack to such a system is: embedding the elliptic curve …

The most significant pairing-based cryptographic protocol to be proposed so far is
undoubtedly the Identity-Based Encryption (IBE) protocol of Boneh and Franklin. In their …