| L. Blum, M. Blum and M. Shub, "A simple unpredictable pseudo-random number generator, " SIAM Journal on Computing Vol. 15, No. 2, 364-383, May 1986. |
....It was the first provably secure public key encryption and signature scheme that is, the underlying problem of the scheme is provably as di#cult as some computational problem that is widely believed to be di#cult, such as FACTORING or DLP. The Blum Blum Shub (BBS) pseudorandom bit generator [BBS86] is based on the assumption that integer factorization is intractable. It works in a similar way to the RSA PRBG, using f(x) x (mod n) where n is a Blum integer. The BBS generator forms the basis for the Blum Goldwasser probabilistic public key encryption scheme [BG85] The scheme uses the ....
L. Blum, M. Blum, and M. Shub. A simple unpredictable pseudo-random number generator. SIAM Journal on Computing, 15(2):364--383, 1986.
....has three parts: a mathematical argument tracing our RNG s randomness to a formal definition of turbulence s unpredictability, a novel use of the FFT as an unbiasing algorithm, and a sanity check data analysis. I Introduction Secure PRNG design commonly rests on computational complexity [2, 5, 6, 13, 24], but none of the underlying problems has been proven to be hard. Specialized hardware can provide naturally random physical noise, but has disadvantages: dedicated devices tend to be expensive; natural noise tends to be biased and correlated; hardware failure can silently suppress randomness; and ....
L. Blum, M. Blum, and M. Shub, "A simple unpredictable pseudo-random number generator," SIAM J. Cornput., 15(2) (1986). pp. 364-83.
.... layer threats are typically countered by frequency hopping or spread spectrum communication [25] and MAC layer attacks can be alleviated by using a less susceptible protocol (Slotted Aloha [26] for example) good entropy management, and a cryptographically secure pseudo random number generator [27]. It is possible for adversaries to exploit weaknesses in these layers to mount attacks whose goals are similar to those discussed in Section VI (for example, an adversary could try to corrupt packets selectively by well timed collisions or jamming) but we will not consider attacks on the ....
M.Blum and S. Micali, "A simple unpredictable pseudo-random number generator," SIAM J. Computing, vol. 15, no. 2, pp. 364--383, May 1986.
....a Blum integer, i.e. N = p 1 p 2 , where p 1 and p 2 are distinct primes each congruent to 3 mod 4. Recall the notion of a Blum Blum Shub (BBS) sequence x 0 ; x 1 ; Delta Delta Delta ; x n , with x 0 = g (mod N) for a random g 2 ZN , and x i = x i Gamma1 (mod N ) 1 i n. It is shown in [BBS86] that the sequence defined by taking the least significant bit of the elements above is polynomial time unpredictable (unpredictable to the left and to the right) provided the quadratic residuosity assumption (QRA) holds. Recall also that these sequences are periodic (although not always purely ....
L. Blum, M. Blum, and M. Shub. A simple unpredictable pseudo-random number generator. SIAM Journal on Computing, 15(2):364--383, May 1986.
....O(log q) such as a 2 3 tree (there are tree schemes that achieve O(log log q) performance, but they are of mostly theoretical interest) The operation Extract(S, n) returns and simultaneously removes the n th smallest element in S. We generate a pseudo random sequence a1 , a2 , using BBS [4], with seed a0 = H(k, i, p0 , p1 , pq 1 ) Then, for each j = q 1, q 2, 1, 0 we set b j = Extract(S, a j mod (j 1) It is easy to prove that , b1 , bq 1 is a uniformly distributed permutation of S. We use the random permutation to re order the pointers as R = p ....
....of the message. 3. SECURITY Other than tampering with the document, Mallory may try to retrieve the secret message, the key, or both. We show that if the adversary could determine some bits of the secret message then he would be able to break a crypto secure pseudo random generator (e.g. BBS [4]) which is extremely unlikely (hence it is just as unlikely that the adversary can get the secret message bits) Suppose that the adversary knows an algorithm to retrieve the watermarks from the LZS 77 compressed text. We now describe how to design a method that correctly guesses the next bit ....
L. Blum, M. Blum, and M. Shub. A simple unpredictable pseudo-random number generator. SIAM J. Comput., 15(2):364--383, May 1986.
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L. Blum, M. Blum, and M. Shub, A simple unpredictable pseudo-random number generator, SIAM J. Computing, 15 (1986), pp. 364--383.
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L. Blum, M. Blum and M. Shub, "A simple unpredictable pseudo-random number generator, " SIAM Journal on Computing Vol. 15, No. 2, 364-383, May 1986.
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Blum L. Blum, M and M. Shub. A simple unpredictable pseudorandom number generator. SIAM J. Computing, 15(2), May 1986.
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L. Blum, M. Blum, and M. Shub. A Simple Unpredictable Pseudo-Random Number Generator. SIAM Journal on Computing, 15:364--383, 1986.
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Blum L. Blum, M. and Shub M. (1986) `A simple unpredictable pseudo random number generator', SIAM Journal of Computing, 15:364--383.
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L. Blum, M. Blum, M. Shub, A Simple Unpredictable Pseudo-Random Number Generator, SIAM J. Comput. 15(2): 364-383 (1986).
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Blum, Leonore, Blum, Manuel, and Shub, M., A Simple Unpredictable Pseudo-random Number Generator, SIAM Journal of Computing, vol. 15, no. 2, May 1986, pp 364-383
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L. Blum, M. Blum, and M. Shub. A Simple Unpredictable Pseudo-Random Number Generator. SICOMP, Vol. 15, pp. 364--383, 1986.
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L. Blum, M. Blum, and M. Shub, "A simple unpredictable pseudorandom number generator," SIAM J. Comput., vol. 15, no. 2, pp. 364--383, May 1986.
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L. Blum, M. Blum, and M. Shub. A simple unpredictable pseudo-random number generator. SIAM Journal on Computing, 15(2):364-383, May 1986.
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L. Blum, M. Blum, and M. Shub. A simple unpredictable pseudo-random number generator. SIAM Journal on Computing, 15(2):364--383, May 1986.
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L. Blum, M. Blum, and M. Shub, \A Simple Unpredictable PseudoRandom Number Generator," SIAM Journal of Computing, v. 15, n. 2, 1986, pp. 364-383.
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L. Blum, M. Blum, M. Shub, A simple unpredictable pseudo-random number generator , SIAM J. Comput. 15 (1986), 364--383.
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L. Blum, M. Blum, and M. Shub, A simple unpredictable pseudo-random number generator, SIAM J. Comput., vol. 15, 1986, pp. 364--383.
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M. Blum, M. Blum, and M. Shum. A simple unpredictable pseudorandom number generator. SIAM Jour. on computing, 15:364--383, 1986.
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L. Blum, M. Blum, and M. Shub. A simple unpredictable pseudo-random number generator. SIAM Journal on Computing, 15(2):364--383, May 1986.
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Blum, L., M. Blum and M. Schub (1986). A simple unpredictable pseudo-random number generator. SIAM Journal on Computing, Vol. 15, No. 2, pp. 364--383.
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L. Blum, M. Blum, and M. Shub. A simple unpredictable pseudo-random number generator. SIAM J. Comput. 15 (1986), 364-381.
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L. Blum, M. Blum, and M. Shub, A simple unpredictable pseudorandom number generator, SIAM J. Comp. 15 (1986), pp. 364-383.
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L. Blum, M. Blum, and M. Shub. A simple unpredictable pseudo-random number generator. SIAM Journal on Computing, 15(2):364-383, 1986.
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