Security
The generator is not appropriate for use in simulations, only for cryptography, because it is very slow. However, there is a proof reducing its security to the computational difficulty of the Quadratic residuosity problem. Since the only known way to solve that problem requires factoring the modulus, the difficulty of Integer factorization is generally regarded as providing security. When the primes are chosen appropriately, and O(log log M) lower-order bits of each xn are output, then in the limit as M grows large, distinguishing the output bits from random should be at least as difficult as factoring M.
If integer factorization is difficult (as is suspected) then B.B.S. with large M should have an output free from any nonrandom patterns that can be discovered with any reasonable amount of calculation. Thus it appears to be as secure as other encryption technologies tied to the factorization problem, such as RSA encryption.
Read more about this topic: Blum Blum Shub
Famous quotes containing the word security:
“In the long course of history, having people who understand your thought is much greater security than another submarine.”
—J. William Fulbright (b. 1905)
“Modern children were considerably less innocent than parents and the larger society supposed, and postmodern children are less competent than their parents and the society as a whole would like to believe. . . . The perception of childhood competence has shifted much of the responsibility for child protection and security from parents and society to children themselves.”
—David Elkind (20th century)
“There is one safeguard known generally to the wise, which is an advantage and security to all, but especially to democracies as against despots. What is it? Distrust.”
—Demosthenes (c. 384–322 B.C.)