Multiplication in Finite Fields and Elliptic Curves

Keywords: Binary Field Multiplication, Subquadratic Complexity, Double Polynomial System, Lagrange Representation, FFT, Montgomery reduction,.. Abstract: We propose a new

To this end, using low weight Dickson polynomials, we formulate the problem of field multiplica- tion as a product of a Toeplitz or Hankel matrix and a vector, and apply

Notice that so far, practical implementations of multiplication algorithms over finite fields have failed to simultaneously optimize the number of scalar multiplications, additions,

So far, the strategy to obtain upper bounds for bilinear complexity of multiplication in F q n over F q , has always been to apply algorithms of type Chudnovsky on infinite

Therefore, we note that so far, practical implementations of multiplication algorithms of type Chudnovsky over finite fields have failed to simultaneously optimize the number of

Beyond that, we must address the Spreadsheet Software Engineering Paradox—that computer scientists and information systems researchers have focused on spreadsheet creation aspects

Moreover they combined their notion of multiplication friendly codes with two newly introduced primitives for function fields over finite fields [11], namely the torsion limit

In this work, we derive some properties of n-universal quadratic forms, quadratic ideals and elliptic curves over finite fields F p for primes p ≥ 5.. In the first section, we give