Improved Area-Time Trade-offs for Field Multiplication using Optimal Normal Bases

Jithra Adikari (1, 2) , Ayad Barsoum (1) , Anwar Hasan (1) , Ashkan Hosseinzadeh Namin (1) , Christophe Negre (3, 4)

1 ECE - Department of Electrical and Computer Engineering [Waterloo]
2 ECE-Calgary - Dept. of Electr. and Comp. Eng.
3 DALI - Digits, Architectures et Logiciels Informatiques
4 UPVD - Université de Perpignan Via Domitia

In this article, we propose new schemes for subquadratic arithmetic complexity multiplication in binary fields using optimal normal bases. The schemes are based on a recently proposed method known as block recombination, which efficiently computes the sum of two products of Toeplitz matrices and vectors. Specifically, here we take advantage of some structural properties of the matrices and vectors involved in the formulation of field multiplication using optimal normal bases. This yields new space and time complexity results for corresponding bit parallel multipliers.

Mots clés: block recombination; Binary field; optimal normal basis; Toeplitz matrix; block recombination.

Domaines: Cryptographie et sécurité [cs.CR]

Jithra Adikari, Ayad Barsoum, Anwar Hasan, Ashkan Hosseinzadeh Namin, Christophe Negre. Improved Area-Time Trade-offs for Field Multiplication using Optimal Normal Bases. IEEE Transactions on Computers, 2013, 62 (1), pp.193-199. ⟨10.1109/TC.2011.198⟩. ⟨hal-00813784⟩