Two Randomized Algorithms for Primality Testing

Randomness, Promise Problems, Randomized Complexity Classes

A big problem that motivates randomized algorithms is that of Primality testing: Given 0 ≤ p ≤ 2, determine if p is prime in poly(n) time. Algorithms such as Miller-Rabin and Solovay-Strassen are randomized algorithms that can solve this in polynomial time, though more recently Agrawal-Kayal-Saxena found a deterministic solution to primality testing. Remark When we say randomized, the goal is f...

Notes on Public Key Cryptography And Primality Testing Part 1: Randomized Algorithms Miller–Rabin and Solovay–Strassen Tests

.1 Error

Randomized algorithms have an additional primitive operation that deterministic algorithms do not have. We can select a number from a range [1 . . .x] uniformly at random, at a cost assumed to be linearly dependent on the size of x in binary representation. The algorithm then makes a decision based on the outcome of this random selection. We first look at some defining characteristics of random...

Random Number Generation

 AI algorithms like genetic algorithms and automated opponents.  Random game content and level generation.  Simulation of complex phenomena such as weather and fire.  Numerical methods such as Monte-Carlo integration.  Until recently primality proving used randomized algorithms.  Cryptography algorithms such as RSA use random numbers for key generation.  Weather simulation and other stat...

Derandomization and Circuit Lower Bounds

1 Introduction Primality testing is the following problem: Given a number n in binary, decide whether n is prime. In 1977, Solovay and Strassen [SS77] proposed a new type of algorithm for testing whether a given number is a prime, the celebrated randomized Solovay-Strassen primality test. This test and similar ones proved to be very useful. This fact changed the common notion of " feasible comp...