Comments on: Number Theory for Programmers, Part 2 http://www.jakevoytko.com/blog/2007/09/23/number-theory-for-programmers-part-2/ Ye Olde Computer Science Blogge Mon, 18 Jan 2010 23:12:49 -0500 http://wordpress.org/?v=2.9.1 hourly 1 By: Why Does RSA Work? : So Jake Says: http://www.jakevoytko.com/blog/2007/09/23/number-theory-for-programmers-part-2/comment-page-1/#comment-2024 Why Does RSA Work? : So Jake Says: Mon, 07 Jan 2008 02:06:00 +0000 http://www.jakevoytko.com/blog/2007/09/23/number-theory-for-programmers-part-2/#comment-2024 [...] an encryption exponent: Take any number, e, such that GCD(, e) = 1. This means that they are relatively prime, and share no common factors. This number is considered your public key (when combined with n), and [...] [...] an encryption exponent: Take any number, e, such that GCD(, e) = 1. This means that they are relatively prime, and share no common factors. This number is considered your public key (when combined with n), and [...]

]]> By: Jake http://www.jakevoytko.com/blog/2007/09/23/number-theory-for-programmers-part-2/comment-page-1/#comment-58 Jake Mon, 24 Sep 2007 19:37:26 +0000 http://www.jakevoytko.com/blog/2007/09/23/number-theory-for-programmers-part-2/#comment-58 @Joe: I'm in college, with a CS major // Math minor. I'm taking an Abstract Algebra course at the moment, and I may write another set of articles from the perspective of Group Theory. Thanks for the feedback! @Joe:

I’m in college, with a CS major // Math minor. I’m taking an Abstract Algebra course at the moment, and I may write another set of articles from the perspective of Group Theory. Thanks for the feedback!

]]> By: Joe Fredette http://www.jakevoytko.com/blog/2007/09/23/number-theory-for-programmers-part-2/comment-page-1/#comment-57 Joe Fredette Mon, 24 Sep 2007 17:42:00 +0000 http://www.jakevoytko.com/blog/2007/09/23/number-theory-for-programmers-part-2/#comment-57 "Linear hashing is obviously a very simple hash ... the simplest ... I believe" Theres always the Identity hash. :) Aside from that somewhat facetious note- good article, I don't know what your math background is- but if you haven't looked at Group Theory, That has lots of implications on Hashing, and cryptography in general (notably, RSA is a fairly simple bit of group theory, involving cyclic groups and some theorems about how the order of an element changes). Keep on with the math! “Linear hashing is obviously a very simple hash … the simplest … I believe”

Theres always the Identity hash. :)

Aside from that somewhat facetious note- good article, I don’t know what your math background is- but if you haven’t looked at Group Theory, That has lots of implications on Hashing, and cryptography in general (notably, RSA is a fairly simple bit of group theory, involving cyclic groups and some theorems about how the order of an element changes).

Keep on with the math!

]]> By: Lenny http://www.jakevoytko.com/blog/2007/09/23/number-theory-for-programmers-part-2/comment-page-1/#comment-48 Lenny Mon, 24 Sep 2007 07:12:15 +0000 http://www.jakevoytko.com/blog/2007/09/23/number-theory-for-programmers-part-2/#comment-48 <blockquote> a ^= b; // Swap a and b in place b ^= a; a ^= b;</blockquote> Since you used this pedantic form, I'll indulge myself as well in pointing out that on modern CPUs with out-of-order pipelines, this is actually slower than using a temp variable, because the instructions aren't parallelizable. Aside from my irrelevant nit, thanks for the interesting article. Number theorists amaze me with their knack for discovering seemingly arbitrary, and in the latest several decades so useful, properties of numbers.

a ^= b; // Swap a and b in place
b ^= a;
a ^= b;

Since you used this pedantic form, I’ll indulge myself as well in pointing out that on modern CPUs with out-of-order pipelines, this is actually slower than using a temp variable, because the instructions aren’t parallelizable.

Aside from my irrelevant nit, thanks for the interesting article. Number theorists amaze me with their knack for discovering seemingly arbitrary, and in the latest several decades so useful, properties of numbers.

]]> By: Marc http://www.jakevoytko.com/blog/2007/09/23/number-theory-for-programmers-part-2/comment-page-1/#comment-45 Marc Mon, 24 Sep 2007 00:24:58 +0000 http://www.jakevoytko.com/blog/2007/09/23/number-theory-for-programmers-part-2/#comment-45 Good post. I note that in your statement "clearly the only way that we can have a multiple of a equal a multiple of b is by multiplying it by a" the last "it" can be misinterpreted as "a", which I don't believe is what you intended to state. Maybe replacing this last "it" by "the latter" would be more explicit, and I'm sure you can think of other ways as well. A bit picky, I realize, but precision of thought and expression are so crucial in mathematics. Good post. I note that in your statement “clearly the only way that we can have a multiple of a equal a multiple of b is by multiplying it by a” the last “it” can be misinterpreted as “a”, which I don’t believe is what you intended to state. Maybe replacing this last “it” by “the latter” would be more explicit, and I’m sure you can think of other ways as well. A bit picky, I realize, but precision of thought and expression are so crucial in mathematics.

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