A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases
Information and Computation
Finite fields
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Modern Computer Algebra
Five, Six, and Seven-Term Karatsuba-Like Formulae
IEEE Transactions on Computers
IEEE Transactions on Computers
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
A Taxonomy of Pairing-Friendly Elliptic Curves
Journal of Cryptology
On compressible pairings and their computation
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
Constructing pairing-friendly elliptic curves with embedding degree 10
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Practical cryptography in high dimensional tori
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Pairing-Based cryptography at high security levels
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Efficient multiplication over extension fields
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
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Small degree extensions of finite fields are commonly used for cryptographic purposes. For extension fields of degree 2 and 3, the Karatsuba and Toom Cook formulæ perform a multiplication in the extension field using 3 and 5 multiplications in the base field, respectively. For degree 5 extensions, Montgomery has given a method to multiply two elements in the extension field with 13 base field multiplications. We propose a faster algorithm, which requires only 9 base field multiplications. Our method, based on Newton's interpolation, uses a larger number of additions than Montgomery's one but our implementation of the two methods shows that for cryptographic sizes, our algorithm is much faster.