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:
“Is a Bill of Rights a security for [religious liberty]? If there were but one sect in America, a Bill of Rights would be a small protection for liberty.... Freedom derives from a multiplicity of sects, which pervade America, and which is the best and only security for religious liberty in any society. For where there is such a variety of sects, there cannot be a majority of any one sect to oppress and persecute the rest.”
—James Madison (1751–1836)
“Our security depends on the Allied Powers winning against aggressors. The Axis Powers intend to destroy democracy, it is anathema to them. We cannot provide that aid if the public are against it; therefore, it is our responsibility to persuade the public that aid to the victims of aggression is aid to American security. I expect the members of my administration to take every opportunity to speak to this issue wherever they are invited to address public forums in the weeks ahead.”
—Franklin D. Roosevelt (1882–1945)
“The three great ends which a statesman ought to propose to himself in the government of a nation, are,—1. Security to possessors; 2. Facility to acquirers; and, 3. Hope to all.”
—Samuel Taylor Coleridge (1772–1834)