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I am given $N$, which is Bob's encryption key. I was able to successfully factor $N$ into $N=p*q$.

Alice encrypts a messages for bob and sends
$a = [1,1,1,0,0,0,1,0,1,1,0,...]$
$b = 1545164156...$

where $b<N$. Given this information, how can I decrypt what the message Alice sent to Bob? I am very confused with the process for Blum-Blum-Shub Cryptosystem so any explanation as to how it works would be much appreciated.

share|improve this question
Richard Feynman once quipped "Nobody understands quantum physics". Well, nobody understands the BBS Cryptosystem either!(kidding). Actually this algorithm is very slow and there are other problems with using it ( see Ritter's Cryptoglossary for a good exposition on this). My advice is to not waste your time with it. Use something else like the Alternating Step Generator as the key generator for a stream cipher. There is no public cryptanalysis (break) for this generator as long as each shift register is 128 bits long. – William Hird Dec 11 '13 at 9:41
BBS is a pseudo-random generator, not a cryptosystem... – fkraiem Jun 5 '14 at 8:58

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