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2016

2016

We give explicit parametrizations of the algebraic tori $$\mathbb {T}_{n}$$Tn over any finite field $$\mathbb {F}_{q}$$Fq for any…

2015

2015

A bstractThe geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop…

2011

2011

We introduce cryptography based on algebraic tori, give a new public key system called CEILIDH, and compare it to other discrete…

2009

2009

We consider representations of algebraic tori $T_n(F_q)$ over finite fields. We make use of normal elliptic bases to show that…

2008

2008

In this paper we provide explicit formulae to compute bilinear pairings in compressed form. We indicate families of curves where…

2008

2008

We present efficient compression algorithms for subgroups of multiplicative groups of finite fields, we use our compression…

2006

2006

We use the Bateman-Horn conjecture to study the order of the set of Fq-rational points of primitive subgroups that arise in torus…

2004

2004

We introduce a compact and efficient representation of elements of the algebraic torus. This allows us to design a new discrete…

Highly Cited

2003

Highly Cited

2003

We introduce the concept of torus-based cryptography, give a new public key system called CEILIDH, and compare it to other…

Highly Cited

1985

Highly Cited

1985

Let X be a semisimple algebraic monoid with unit group G. Associated with E is its polyhedral root system ( X , @, C), where X…