Results 1  10
of
39
Mastrovito Multiplier for All Trinomials
 IEEE Trans. Computers
, 1999
"... An e cient algorithm for the multiplication in GF (2m)was introduced by Mastrovito. The space complexity of the Mastrovito multiplier for the irreducible trinomial x m + x +1was given as m 2, 1 XOR and m 2 AND gates. In this paper, we describe an architecture based on a new formulation of the multip ..."
Abstract

Cited by 37 (3 self)
 Add to MetaCart
An e cient algorithm for the multiplication in GF (2m)was introduced by Mastrovito. The space complexity of the Mastrovito multiplier for the irreducible trinomial x m + x +1was given as m 2, 1 XOR and m 2 AND gates. In this paper, we describe an architecture based on a new formulation of the multiplication matrix, and show that the Mastrovito multiplier for the generating trinomial x m + x n +1, where m 6 = 2n, also requires m 2, 1 XOR and m 2 AND gates. However, m 2, m=2 XOR gates are su cient when the generating trinomial is of the form x m + x m=2 +1 for an even m. We also calculate the time complexity of the proposed Mastrovito multiplier, and give design examples for the irreducible trinomials x 7 + x 4 + 1 and x 6 + x 3 +1.
A generalized method for constructing subquadratic complexity GF(2 k ) multipliers
 IEEE Transactions on Computers
, 2004
"... We introduce a generalized method for constructing subquadratic complexity multipliers for even characteristic field extensions. The construction is obtained by recursively extending short convolution algorithms and nesting them. To obtain the short convolution algorithms the Winograd short convolu ..."
Abstract

Cited by 22 (0 self)
 Add to MetaCart
We introduce a generalized method for constructing subquadratic complexity multipliers for even characteristic field extensions. The construction is obtained by recursively extending short convolution algorithms and nesting them. To obtain the short convolution algorithms the Winograd short convolution algorithm is reintroduced and analyzed in the context of polynomial multiplication. We present a recursive construction technique that extends any d point multiplier into an n = d k point multiplier with area that is subquadratic and delay that is logarithmic in the bitlength n. We present a thorough analysis that establishes the exact space and time complexities of these multipliers. Using the recursive construction method we obtain six new constructions, among which one turns out to be identical to the Karatsuba multiplier. All six algorithms have subquadratic space complexities and two of the algorithms have significantly better time complexities than the Karatsuba algorithm. Keywords: Bitparallel multipliers, finite fields, Winograd convolution 1
Mastrovito multiplier for general irreducible polynomials
 IEEE Transactions on Computers
, 2000
"... ..."
Hardware and software normal basis arithmetic for pairing based cryptography in characteristic three
 IEEE Transactions on Computers
, 2005
"... Department of Computer Science, ..."
Parallel Multipliers Based on Special Irreducible Pentanomials
 IEEE Trans on Computers
, 2003
"... Abstract—The stateoftheart Galois field GFð2 m Þ multipliers offer advantageous space and time complexities when the field is generated by some special irreducible polynomial. To date, the best complexity results have been obtained when the irreducible polynomial is either a trinomial or an equal ..."
Abstract

Cited by 17 (0 self)
 Add to MetaCart
Abstract—The stateoftheart Galois field GFð2 m Þ multipliers offer advantageous space and time complexities when the field is generated by some special irreducible polynomial. To date, the best complexity results have been obtained when the irreducible polynomial is either a trinomial or an equally spaced polynomial (ESP). Unfortunately, there exist only a few irreducible ESPs in the range of interest for most of the applications, e.g., errorcorrecting codes, computer algebra, and elliptic curve cryptography. Furthermore, it is not always possible to find an irreducible trinomial of degree m in this range. For those cases where neither an irreducible trinomial nor an irreducible ESP exists, the use of irreducible pentanomials has been suggested. Irreducible pentanomials are abundant, and there are several eligible candidates for a given m. In this paper, we promote the use of two special types of irreducible pentanomials. We propose new Mastrovito and dual basis multiplier architectures based on these special irreducible pentanomials and give rigorous analyses of their space and time complexity. Index Terms—Finite fields arithmetic, parallel multipliers, pentanomials, multipliers for GFð2 m Þ. æ
Low Complexity Multiplication in a Finite Field Using Ring Representation
 IEEE Transactions on Computers
, 2003
"... ..."
Subquadratic Computational Complexity Schemes for Extended Binary Field Multiplication Using Optimal Normal Bases
, 2007
"... Based on a recently proposed Toeplitz matrixvector product approach, a subquadratic computational complexity scheme is presented for multiplications in binary extended finite fields using Type I and II optimal normal bases. basis. Index Terms Finite field, subquadratic computational complexity mult ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
Based on a recently proposed Toeplitz matrixvector product approach, a subquadratic computational complexity scheme is presented for multiplications in binary extended finite fields using Type I and II optimal normal bases. basis. Index Terms Finite field, subquadratic computational complexity multiplication, normal basis, optimal normal
Parhi, “Implementation of scalable elliptic curve cryptosystem cryptoaccelerators for GF(2 m
 Proc. 13th Asilomar Conf. on Signals, Systems and Computers
, 2004
"... This paper focuses on designing elliptic curve cryptoaccelerators in GF(2 m) that are cryptographically scalable and hold some degree of reconfigurability. Previous work in elliptic curve cryptoaccelerators focused on implementations using projective coordinate systems for specific field sizes. Th ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
This paper focuses on designing elliptic curve cryptoaccelerators in GF(2 m) that are cryptographically scalable and hold some degree of reconfigurability. Previous work in elliptic curve cryptoaccelerators focused on implementations using projective coordinate systems for specific field sizes. Their performance, scalar point multiplication per second (kP/s), was determined primarily by the underlying multiplier implementation. In addition, a multiplier only implementation and a multiplier plus divider implementation are compared in terms of critical path, area, and area time (AT) product. Our multiplier only design, designed for high performance, can achieve 6314 kP/s for GF(2 571) and requires 47876 LUTs. Meanwhile our multiplier and divider design, with a greater degree of reconfigurability, can achieve 44 kP/s for GF(2 571). However, this design requires 27355 LUTs, and has a significantly higher AT product. It is shown that reconfigurability with the reduction polynomial significantly benefits from the addition of a low latency divider unit and scalar point multiplication in affine coordinates. In both cases the performance is limited by a critical path in the control logic. 1
Efficient Cellular Automata Based Versatile Multiplier for GF(2^m)
 Journal of Information Science and Engineering
, 2002
"... this paper, a lowcomplexity Programmable Cellular Automata (PCA) based versatile modular multiplier in GF(2 ) is presented. The proposed versatile multiplier increases flexibility in using the same multiplier in different security environments, and it reduces the user's cost. Moreover, t ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
this paper, a lowcomplexity Programmable Cellular Automata (PCA) based versatile modular multiplier in GF(2 ) is presented. The proposed versatile multiplier increases flexibility in using the same multiplier in different security environments, and it reduces the user's cost. Moreover, the multiplier can be easily extended to high order of m for more security, and lowcost serial implementation is feasible in restricted computing environments, such as smart cards and wireless devices
Implementation and Analysis of Elliptic Curve Cryptosystems over Polynomial basis and ONB
"... Abstract — Polynomial bases and normal bases are both used for elliptic curve cryptosystems, but field arithmetic operations such as multiplication, inversion and doubling for each basis are implemented by different methods. In general, it is said that normal bases, especially optimal normal bases ( ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract — Polynomial bases and normal bases are both used for elliptic curve cryptosystems, but field arithmetic operations such as multiplication, inversion and doubling for each basis are implemented by different methods. In general, it is said that normal bases, especially optimal normal bases (ONB) which are special cases on normal bases, are efficient for the implementation in hardware in comparison with polynomial bases. However there seems to be more examined by implementing and analyzing these systems under similar condition. In this paper, we designed field arithmetic operators for each basis over GF(2 233), which field has a polynomial basis recommended by SEC2 and a typeII ONB both, and analyzed these implementation results. And, in addition, we predicted the efficiency of two elliptic curve cryptosystems using these field arithmetic operators.