Blum-Goldwasser Cryptography

Abstract

Blum-Goldwasser cryptography is a modern incarnation of a Vernam cryptosystem (see Chap. 1) that solves the problem in the Vernam system that sender and receiver need to share a long sequence of random numbers in order to encrypt and decrypt. Encrypting and decrypting of a message is done by using a secret shared “pseudo-random” sequence k of bits. The sequence is obtained by successive squaring a secret starting number b modulo a large public modulus m that is the product of two secret primes p and q. This chapter describes how to choose p and q so that the period of the sequence k is large, what the sender sends to the receiver (who is the only person who knows the prime factors of m) to enable the receiver to reconstruct the sequence k, how the receiver can obtain the sequence efficiently using the Chinese Remainder Theorem, and, most crucially, why it is essentially necessary for a third party to factor the modulus m in order to crack the cryptosystem.