Here I discuss breaking encryption keys that rely on the product of two ver= y large prime numbers. In other words, the interest here is to factor a num= ber (representing a key in some encryption system) that is the product of t= wo very large primes. Once the number is factored, the key is compromised. = Factoring such large numbers is believed to be computationally non-feasible= , thus the interest in discovering new algorithms to disprove this conjectu= re, and specifically to factor large numbers (product of two large primes -= the most difficult numbers to factor) much faster than with the current al= gorithms. As an important side note, I will discuss the randomness (or lack= of) of the byproduct time series involved, and show why they are unsuitabl= e to generate random deviates, despite satisfying several tests of randomne= ss. This feature (lack of randomness) can further be exploited to develop m= ore potent factoring algorithms. Read article (with algorithm, discussion, and examples) at: http://www.datasciencecentral.com/profiles/blogs/building-an-algorithm-to-b= reak-strong-encryption

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10/17/2016 6:22:28 PM

On Monday, October 17, 2016 at 1:22:31 PM UTC-5, Vincent Granville wrote: > Here I discuss breaking encryption keys that rely on the product of two v= ery large prime numbers. In other words, the interest here is to factor a n= umber (representing a key in some encryption system) that is the product of= two very large primes. Once the number is factored, the key is compromised= .. Factoring such large numbers is believed to be computationally non-feasib= le, thus the interest in discovering new algorithms to disprove this conjec= ture, and specifically to factor large numbers (product of two large primes= - the most difficult numbers to factor) much faster than with the current = algorithms. As an important side note, I will discuss the randomness (or la= ck of) of the byproduct time series involved, and show why they are unsuita= ble to generate random deviates, despite satisfying several tests of random= ness. This feature (lack of randomness) can further be exploited to develop= more potent factoring algorithms. >=20 > Read article (with algorithm, discussion, and examples) at: > http://www.datasciencecentral.com/profiles/blogs/building-an-algorithm-to= -break-strong-encryption Non randomness can be overcome using a hardware random number generator: = https://en.wikipedia.org/wiki/Hardware_random_number_generator

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10/19/2016 12:15:07 PM