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5

Yes, what you have is enough to recover p in both cases. In the first case you just need to write the proper equation to be then solved thanks to Coppersmith method to find small roots of univariate polynomial. As explained by Alexander May in pages 40 and 41 of his thesis what you ask is always doable if the unknown bits are consecutive (and you have at ...

4

Adi Shamir's secret database of all primes is to cryptography venues what the Dahu is to French summer camps. For why, see the answers to this related question. The three other future work items in the quoted presentation are in the same vein (Breaking RSA-1024 with Fermat factoring; Breaking RSA-1024 using $1024 = 2*2*2*2*2*2*2*2*2*2$; Breaking RSA-1024 ...

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