Torus-based cryptography involves using algebraic tori to construct a group for use in ciphers based on the discrete logarithm problem. This idea wasâ€¦Â (More)

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2012

2012

- David R. Kohel
- 2012

We introduce a constructive model for algebraic tori based on reduced divisors on singular curves. By using a singularâ€¦Â (More)

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2011

2011

- Elisa Gorla
- Encyclopedia of Cryptography and Security
- 2011

In a series of three lectures, we will introduce the main concepts behind torus-based cryptography. Algebraic tori were suggestedâ€¦Â (More)

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2009

2009

- Clement Dunand, Reynald Lercier
- ArXiv
- 2009

We consider representations of algebraic tori Tn(Fq) over finite fields. We make use of normal elliptic bases to show that, forâ€¦Â (More)

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2008

2008

- Karl Rubin, Alice Silverberg
- SIAM J. Comput.
- 2008

We present efficient compression algorithms for subgroups of multiplicative groups of finite fields, we use our compressionâ€¦Â (More)

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2008

2008

- Burt A. Ovrut, T. P. Pantev, RenÃ© Reinbacher
- 2008

We construct smooth Calabi-Yau threefolds Z, torus-fibered over a dP9 base, with fundamental group Ï€1 = Z2 Ã—Z2. To do this, theâ€¦Â (More)

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2006

2006

- Jason E. Gower
- IACR Cryptology ePrint Archive
- 2006

We use the Bateman-Horn conjecture to study the order of the set of Fq-rational points of primitive subgroups that arise in torusâ€¦Â (More)

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2004

2004

- Marten van Dijk, David P. Woodruff
- CRYPTO
- 2004

We introduce a compact and efficient representation of elements of the algebraic torus. This allows us to design a newâ€¦Â (More)

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Highly Cited

2003

Highly Cited

2003

- Karl Rubin, Alice Silverberg
- CRYPTO
- 2003

We introduce the concept of torus-based cryptography, give a new public key system called CEILIDH, and compare it to otherâ€¦Â (More)

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2003

2003

- Boris A. Khesin
- 2003

We demonstrate the common bihamiltonian nature of several integrable systems. The first one is an elliptic rotator that is anâ€¦Â (More)

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2000

2000

- Ahmad El Soufi
- 2000

Given a compact manifold M, we prove that every critical Riemannian metric g for the functional â€œfirst eigenvalue of theâ€¦Â (More)

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