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

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