We present and analyze two algorithms for computing the Hilbert class polynomial HD. The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < ...
— Finding low-weight multiples of a binary polynomial is a difficult problem arising in the context of stream ciphers cryptanalysis. The best algorithms to solve this problem ar...
The question of whether there is a logic that captures polynomial time was formulated by Yuri Gurevich in 1988. It is still wide open and regarded as one of the main open problems...
We consider the generation of prime order elliptic curves (ECs) over a prime field Fp using the Complex Multiplication (CM) method. A crucial step of this method is to compute the ...
Polynomial identity testing (PIT) problem is known to be challenging even for constant depth arithmetic circuits. In this work, we study the complexity of two special but natural ...