Projects are due January 29, 2010. You can get feedback if you 
submit a pre-version before January 11, 2010.

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Torus-based cryptography
XTR http://en.wikipedia.org/wiki/XTR
CEILIDH has separate page, but can do more torus-based crypto, too.

Coding-based cryptography
Niederreiter http://en.wikipedia.org/wiki/Niederreiter_cryptosystem
McEliece http://en.wikipedia.org/wiki/McEliece_cryptosystem
(expansion, clean up, more parameters; Niederreiter scheme)

Arithmetic on elliptic curves (different coordinate systems)
Elliptic curve cryptography http://en.wikipedia.org/wiki/Elliptic_curve_cryptography
Elliptic curve http://en.wikipedia.org/wiki/Elliptic_curve
Should split into smaller pages
Rashim, Oihana, Francesca

Primality proving, in particular:
Pocklington-Test: missing entiely
Elliptic curve primality proving http://en.wikipedia.org/wiki/Elliptic_curve_primality_proving could use some improvements
Geoff Bowes, Lavinia Opris

Hyperelliptic curves
http://en.wikipedia.org/wiki/Hyperelliptic_curve
quite a bit of stuff in http://en.wikipedia.org/wiki/Imaginary_hyperelliptic_curve

Hyperelliptic curve primality proving

Number theoretic pseudorandom number generators
Pages
http://en.wikipedia.org/wiki/Pseudorandom_number_generator  
http://en.wikipedia.org/wiki/List_of_pseudorandom_number_generators
do not cover the number theoretic constructions; only ones mentioned are
http://en.wikipedia.org/wiki/Linear_congruential_generator
http://en.wikipedia.org/wiki/Inversive_congruential_generator
but power generator, Naor-Reingold, and elliptic curve versions coul be added

Mathematical hash functions: 
VSH (very smooth hash)
ECOH (elliptic curve only hash)
FSB 
SWIFT
see http://ehash.iaik.tugraz.at/wiki/The_SHA-3_Zoo for the newer ones
Vojtech,  Timo


Message authentication codes based on number theory
http://en.wikipedia.org/wiki/Message_authentication_code
VMAC, Badger, MMH, Gilbert-McWilliams-Sloane 


Factorization:
Coppersmith method
Dutch page: Meike Rouwenhorst and Zoebaida Fiamingo
English page: Agis Christopoulos, Alina Anisimova

separte topic:
H.W. Lenstra & C. Pomerance :A rigorous time bound for factoring 
integers and related algorithms (Schnorr, Seysen)
Joux et al paper at Asiacrypt'09

Methods to compute square-roots mod p
Shanks–Tonelli algorithm http://en.wikipedia.org/wiki/Shanks%E2%80%93Tonelli_algorithm exists, can be expanded
Cipolla: missing
Legendre: missing
Pocklington: missing
Marc & Gert Jan


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Lots of Dutch pages:

All of the above + NTRU, point counting on elliptic curves, 
exponentiation, secret sharing

McEliece: Matthijs van Staalduine, Arend Jan Gerrits, Willard van de Sar

hash trees: emily 

QS, NFS
Frederique, Tom

Planetmath