Low-Complexity Bit-Parallel Square Root Computation over GF(2^{m}) for All Trinomials
نویسندگان
چکیده
منابع مشابه
Low complexity bit parallel multiplier for GF(2m) generated by equally-spaced trinomials
Based on the shifted polynomial basis (SPB), a high efficient bit-parallel multiplier for the field GF(2m) defined by an equallyspaced trinomial (EST) is proposed. The use of SPB significantly reduces time delay of the proposed multiplier and at the same time Karatsuba method is combined with SPB to decrease space complexity. As a result, with the same time complexity, approximately 3/4 gates o...
متن کاملLow space complexity CRT-based bit-parallel GF(2n) polynomial basis multipliers for irreducible trinomials
By selecting the largest possible value of k ∈ (n/2, 2n/3], we further reduce the AND and XOR gate complexities of the CRT-based hybrid parallel GF (2) polynomial basis multipliers for the irreducible trinomial f = u + u + 1 over GF (2): they are always less than those of the current fastest parallel multipliers – quadratic multipliers, i.e., n AND gates and n− 1 XOR gates. Our experimental res...
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 کاملNew bit-parallel Montgomery multiplier for trinomials using squaring operation
In this paper, a new bit-parallel Montgomery multiplier for GF (2) is presented, where the field is generated with an irreducible trinomial. We first present a slightly generalized version of a newly proposed divide and conquer approach. Then, by combining this approach and a carefully chosen Montgomery factor, the Montgomery multiplication can be transformed into a composition of small polynom...
متن کاملRoot Separation for Trinomials
We give a separation bound for the complex roots of a trinomial f ∈ Z[X ]. The logarithm of the inverse of our separation bound is polynomial in the size of the sparse encoding of f ; in particular, it is polynomial in log(deg f). It is known that no such bound is possible for 4-nomials (polynomials with 4 monomials). For trinomials, the classical results (which are based on the degree of f rat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Transactions on Computers
سال: 2008
ISSN: 0018-9340
DOI: 10.1109/tc.2007.70822