Sep 26, 2003 · We study exponentiation in nonprime finite fields with very spe- cial exponents such as they occur, for example, in inversion, primitivity tests ...

Oct 22, 2024 · We study exponentiation in nonprime nite elds with very spe- cial exponents such as they occur, for example, in inversion, primitivity tests ...

Exponentiation in finite fields" Theory and practice. In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: AAECC-12, Toulouse, France (1997), T.

We study exponentiation in finite fields with very special exponents such as they occur, e.g., in inversion and in prim- it.ivity tests. Our algorit.hmic ...

So if we construct a finite field, we know it will have prime-power order. Another finite-field theorem tells us that all finite fields of a given size are ...

Jan 11, 2011 · Exploring prime powers in finite fields has various real-world applications, such as in error-correcting codes, cryptography, and coding theory.

Jan 14, 2010 · The first says that taking the i-th power is a homomorphism from the multiplicative group of the field to itself.

Feb 11, 2021 · There is a fine art of isolating fields in a way which provide a lot of security while keeping the computational overhead (and key size, etc.) ...

Aug 1, 2014 · One common trick, which requires O(log2m) multiplications, is to use the following algorithm: If m is even, calculate b=am/2 and then use ...

Sep 15, 2022 · Let q be a prime power, let n be a positive integer and let Fq be the finite field of cardinality q. I have some computational evidence that ...