We consider the problem of deterministically factoring integers provided with oracle access to important number-theoretic functions such as Euler's Totient function - phi(.) and Carmichael's Lambda function - lambda(.).
We focus on Carmichael numbers - also known as Fermat pseudoprimes. In particular, we obtain the following results:

1. Let N ... more >>>

We introduce a variant of a polynomial family called $\TQBFfamily$ obtained from `arithmetization' of the popular $\PSPACE$-complete problem - $\TQBF$. This polynomial family has several nice characteristics such as: $\TQBFfamily \in \VPSPACE_b$, where $\VPSPACEb$ is the `bounded' algebraic version of $\PSPACE$, it is \emph{self-testable}, it captures the computational power of ... more >>>