Generating Provable Primes Efficiently on Embedded Devices

A note on efficient implementation of prime generation algorithms in small portable devices

This paper investigates existing prime generation algorithms on small portable devices, makes optimizations and compares their efficiencies. It shows by comparing the performances that the bit array algorithm is the most efficient among all the existing prime generation algorithms. The paper further optimizes the implementation of the bit array algorithm by using an optimal parameter in the pri...

On bounded arithmetic augmented by the ability to count certain sets of primes

Over 25 years ago, the first author conjectured in [15] that the existence of arbitrarily large primes is provable from the axioms IΔ0( ) + def( ), where (x) is the number of primes not exceeding x, IΔ0( ) denotes the theory of Δ0 induction for the language of arithmetic including the new function symbol , and def( ) is an axiom expressing the usual recursive definition of . We prove a modified...

Finding Primitive Roots Pseudo-Deterministically

Pseudo-deterministic algorithms are randomized search algorithms which output unique solutions (i.e., with high probability they output the same solution on each execution). We present a pseudo-deterministic algorithm that, given a prime p, finds a primitive root modulo p in time exp(O( p log p log log p)). This improves upon the previous best known provable deterministic (and pseudo-determinis...

A study of Maurer’s algorithm for finding provable primes in relation to the Miller-Rabin algorithm

SQUASH - A New MAC with Provable Security Properties for Highly Constrained Devices Such as RFID Tags

We describe a new function called SQUASH (which is short for SQU are-hASH ), which is ideally suited to challenge-response MAC applications in highly constrained devices such as RFID tags. It is exceptionally simple, requires no source of random bits, and can be efficiently implemented on processors with arbitrary word sizes. Unlike other ad-hoc proposals which have no security analysis, SQUASH...