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Blum Blum Shub (B.B.S.) is a pseudorandom number generator proposed in 1986 by Lenore Blum, Manuel Blum and Michael Shub[1] that is derived from Michael O. Rabin's one-way function.
Blum Blum Shub takes the form
,
where M = pq is the product of two large primes p and q. At each step of the algorithm, some output is derived from xn+1; the output is commonly either the bit parity of xn+1 or one or more of the least significant bits of xn+1.
The seed x0 should be an integer that is co-prime to M (i.e. p and q are not factors of x0) and not 1 or 0.
The two primes, p and q, should both be congruent to 3 (mod 4) (this guarantees that each quadratic residue has one square root which is also a quadratic residue), and should be safe primes with a small gcd((p-3)/2, (q-3)/2) (this makes the cycle length large).
An interesting characteristic of the Blum Blum Shub generator is the possibility to calculate any xi value directly (via Euler's theorem):
,
where is the Carmichael function. (Here we have ).
BlumBlumShub (B.B.S.) is a pseudorandom number generator proposed in 1986 by Lenore Blum, Manuel Blum and Michael Shub that is derived from Michael O...
selection algorithm), the BlumBlumShub pseudorandom number generator, the Blum–Goldwasser cryptosystem, and more recently CAPTCHAs. Blum is also known as the...
project activities. The BlumBlumShub pseudorandom number generator, published jointly by Blum, Manuel Blum, and Michael Shub, is based on the operation...
to be practical in most applications. They include: Blum–Micali algorithm (1984) BlumBlumShub (1986) Naor–Reingold pseudorandom function (1997) These...
Mathematics. Shub, along with coauthors Lenore and Manuel Blum, described a simple, unpredictable, secure random number generator (see BlumBlumShub). This...
BIOS Boot Specification, a firmware specification for the boot process BlumBlumShub, a pseudorandom number generator Kingdom Hearts Birth by Sleep, a Disney-based...
Shub may refer to: Shub (surname), people with the surname DJ Shub, Canadian music producer BlumBlumShub, pseudorandom number generator Shub-Niggurath...
security of some important cryptographic algorithms, notably RSA and the BlumBlumShub pseudorandom number generator, rests in the difficulty of factorizing...
for the BlumBlumShub algorithm. However the algorithm is very inefficient and therefore impractical unless extreme security is needed. The Blum–Micali...
Micali–Schnorr generator, Naor-Reingold pseudorandom function and the BlumBlumShub algorithm, which provide a strong security proof (such algorithms are...
where they are used by RSA and pseudorandom number generators such as BlumBlumShub. These methods rely on the fact that finding two large primes and multiplying...
later Blum–Shub–Smale machine. However, the real RAM is typically used for the analysis of concrete algorithms in computational geometry, while the Blum–Shub–Smale...
trees discovered by Sleator and Tarjan 1986 – BlumBlumShub proposed by L. Blum, M. Blum, and M. Shub 1986 – Push relabel maximum flow algorithm by Andrew...
with this problem.) A canonical model of computation over the reals is Blum–Shub–Smale machine (BSS). If real computation were physically realizable, one...
quadratic residuosity problem is the basis for the security of the BlumBlumShub pseudorandom number generator. It also yields the public key Goldwasser–Micali...
(WLAN) Boeing Satellite Systems, see Boeing Satellite Development Center Blum–Shub–Smale machine, a model of computation Broadcasting Satellite Service,...
computer scientist who has done research into the complexity theory of the Blum–Shub–Smale computational model and the complexity of numerical algorithms in...
studies algorithms whose inputs and outputs are real numbers, using the Blum–Shub–Smale machine as its model of computation. For instance, this theory is...
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