Subquadratic Space Complexity Multiplication over Binary Fields with Dickson Polynomial Representation
نویسندگان
چکیده
We study Dickson bases for binary field representation. Such representation seems interesting when no optimal normal basis exists for the field. We express the product of two elements as Toeplitz or Hankel matrix vector product. This provides a parallel multiplier which is subquadratic in space and logarithmic in time.
منابع مشابه
Scalable Systolic Multiplier over Binary Extension Fields Based on Two-Level Karatsuba Decomposition
Shifted polynomial basis (SPB) is a variation of polynomial basis representation. SPB has potential for efficient bit level and digi -level implementations of multiplication over binary extension fields with subquadratic space complexity. For efficient implementation of pairing computation with large finite fields, this paper presents a new SPB multiplication algorithm based on Karatsuba scheme...
متن کاملEfficient implementation of low time complexity and pipelined bit-parallel polynomial basis multiplier over binary finite fields
This paper presents two efficient implementations of fast and pipelined bit-parallel polynomial basis multipliers over GF (2m) by irreducible pentanomials and trinomials. The architecture of the first multiplier is based on a parallel and independent computation of powers of the polynomial variable. In the second structure only even powers of the polynomial variable are used. The par...
متن کاملSubquadratic Binary Field Multiplier in Double Polynomial System
We propose a new space efficient operator to multiply elements lying in a binary field F2k . Our approach is based on a novel system of representation called Double Polynomial System which set elements as a bivariate polynomials over F2. Thanks to this system of representation, we are able to use a Lagrange representation of the polynomials and then get a logarithmic time multiplier with a spac...
متن کاملOverlap-free Karatsuba-Ofman Polynomial Multiplication Algorithms for Hardware Implementations
We describe how a simple way to split input operands allows for fast VLSI implementations of subquadratic GF (2)[x] Karatsuba-Ofman multipliers. The theoretical XOR gate delay of the resulting multipliers is reduced significantly. For example, it is reduced by about 33% and 25% for n = 2 and n = 3 (t > 1), respectively. To the best of our knowledge, this parameter has never been improved since ...
متن کاملSubquadratic Multiplication Using Optimal Normal Bases
Based on a recently proposed Toeplitz matrix-vector product approach, a subquadratic computational complexity scheme is presented for multiplications in binary extended finite fields using Type I and II optimal normal bases.
متن کامل