Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Montgomery Multiplication in GF(2^k
Designs, Codes and Cryptography
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
Number Theory in Digital Signal Processing
Number Theory in Digital Signal Processing
Modular Multiplication in GF(pk) Using Lagrange Representation
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
Multithreaded parallel implementation of arithmetic operations modulo a triangular set
Proceedings of the 2007 international workshop on Parallel symbolic computation
Montgomery multiplication and squaring algorithms in GF(2k)
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
An alternative class of irreducible polynomials for optimal extension fields
Designs, Codes and Cryptography
Error detecting AES using polynomial residue number systems
Microprocessors & Microsystems
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We present a novel methodof parallelization of the multiplication operation in \GF(2^k)for an arbitrary value of k and arbitrary irreduciblepolynomial n(x) generating the field. The parallelalgorithm is based on polynomial residue arithmetic, and requiresthat we find L pairwise relatively prime modulim_i(x) such that the degree of the product polynomialM(x)=m_1(x)m_2(x)\cdots m_L(x) is at least 2k.The parallel algorithm receives the residue representations ofthe input operands (elements of the field) and produces the resultin its residue form, however, it is guaranteed that the degreeof this polynomial is less than k and it is properlyreduced by the generating polynomial n(x), i.e.,it is an element of the field. In order to perform the reductions,we also describe a new table lookup based polynomial reductionmethod.