“Craindre l’erreur et craindre la vérité est une seule et même chose.” (Fear of imprecision and fear of illumination are one and the same); Alexander Grothendieck
An appropriate quote, given that sampling of algorithmic error lies at the heart of the material presented on this site.
The ‘age of encryption’ would seem to have well & truly arrived. Never, since the advent of personal computing, has privacy been so prominently at centre stage as has been the case this year, 2014.
Encryption & decryption, the skill & science of one never lags far behind the other. From simple cyphers to today’s RSA, it’s a game of catch-up all along the way.
Computing power effectively doubles every 18 months, (Moore’s Law.)
Even the most sophisticated encryption may yet be found to be finitely ‘arithmetic’ in complexity. Despite the fact that they involve some multiplicatively difficult problem such as factoring very large prime numbers. http://research.microsoft.com/en-us/um/people/cohn/Thoughts/factoring.html
However, it is hypothesized there are mathematical problems that are exponentially hard to solve (2^n order of complexity) and this supposition is linked to a major unsolved problem in information theory, P=NP or P≠NP? http://en.wikipedia.org/wiki/P_versus_NP_problem
In consideration of the material presented on this site, I ask the reader do so with consideration of the author’s limited background in mathematical formalism.
Why then should you be bothered?
Because, I believe the construct which I am attempting to communicate is worthwhile.
In order to give assurance that all the obvious, and less obvious, aspects of computational error are allowed for and incorporated into the ‘One Way Function’ paper with necessary skill, I have attached a brief outline of the subject (see below).
I would sincerely appreciate the assistance of anyone so constructively inclined, as to communicate to me any criticism regarding clarification of procedural errors or nonsensical syntax which may have been inadvertently presented.
Notes on Numerical Error. Link: numerical.error