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2016

2016

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

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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… Expand

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2012

2012

We introduce a constructive model for algebraic tori based on reduced divisors on singular curves. By using a singular… Expand

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2011

2011

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

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2008

2008

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

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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… Expand

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2004

2004

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

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Highly Cited

2004

Highly Cited

2004

The value of the Tate pairing on an elliptic curve over a finite field may be viewed as an element of an algebraic torus. Using… Expand

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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… Expand

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1985

1985

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

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