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In a recent program gallery post we introduced the Blum-Blum-Shub pseudorandom generator. A pseudorandom generator is simply an algorithm that takes as input a short random string of length and produces as output a longer string, say, of length . This output string should not be random, but rather “indistinguishable” from random in a sense we’ll make clear next time. The underlying function for this generator is the “modular squaring” function , for some cleverly chosen . The is chosen in such a way that makes this mapping a permutation. So this function is more than just a pseudorandom generator, it’s a *one-way permutation*.

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**Zero Knowledge Proofs for NP – Math ∩ Programming**

s blog’s Github page. In the follow up to this post, we’ll dive into more nitty gritty details about the proof that this works, and study different kinds of zero-knowledge. One-way permutations <span>In a recent program gallery post we introduced the Blum-Blum-Shub pseudorandom generator. A pseudorandom generator is simply an algorithm that takes as input a short random string of length and produces as output a longer string, say, of length . This output string should not be random, but rather “indistinguishable” from random in a sense we’ll make clear next time. The underlying function for this generator is the “modular squaring” function , for some cleverly chosen . The is chosen in such a way that makes this mapping a permutation. So this function is more than just a pseudorandom generator, it’s a one-way permutation. If you have a primality-checking algorithm on hand (we do), then preparing the Blum-Blum-Shub algorithm is only about 15 lines of code. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2

s blog’s Github page. In the follow up to this post, we’ll dive into more nitty gritty details about the proof that this works, and study different kinds of zero-knowledge. One-way permutations <span>In a recent program gallery post we introduced the Blum-Blum-Shub pseudorandom generator. A pseudorandom generator is simply an algorithm that takes as input a short random string of length and produces as output a longer string, say, of length . This output string should not be random, but rather “indistinguishable” from random in a sense we’ll make clear next time. The underlying function for this generator is the “modular squaring” function , for some cleverly chosen . The is chosen in such a way that makes this mapping a permutation. So this function is more than just a pseudorandom generator, it’s a one-way permutation. If you have a primality-checking algorithm on hand (we do), then preparing the Blum-Blum-Shub algorithm is only about 15 lines of code. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2

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