Title :
Efficient subquadratic parallel multiplier based on modified SPB of GF(2m)
Author :
Jeng-Shyang Pan ; Meher, Pramod Kumar ; Chiou-Yng Lee ; Hong-Hai Bai
Author_Institution :
Shenzhen Grad. Sch., Harbin Inst. of Technol., Shenzhen, China
Abstract :
Toeplitz matrix-vector product (TMVP) approach is a special case of Karatsuba algorithm to design subquadratic multiplier in GF(2m). In binary extension fields, shifted polynomial basis (SPB) is a variable basis representation, and is widely studied. SPB multiplication using coordinate transformation technique can transform TMVP formulas, however, this approach is only applied for the field constructed by all trinomials or special class of pentanomials. For this reason, we present a new modified SPB multiplication for an arbitrary irreducible pentanomial, and the proposed multiplication scheme has formed a TMVP formula.
Keywords :
Galois fields; Toeplitz matrices; multiplying circuits; polynomials; GF(2m); Galois fields; Karatsuba algorithm; TMVP; Toeplitz matrix-vector product; arbitrary irreducible pentanomial; binary extension fields; coordinate transformation; modified SPB; shifted polynomial basis; subquadratic parallel multiplier; variable basis representation; Complexity theory; Computer architecture; Delays; Logic gates; Matrix converters; Matrix decomposition; Polynomials; Karatsuba algorithm; Toeplitz matrix-vector product; shifted polynomial basis;
Conference_Titel :
Circuits and Systems (ISCAS), 2015 IEEE International Symposium on
Conference_Location :
Lisbon
DOI :
10.1109/ISCAS.2015.7168912
