RSA Alogthrim

RSA encryption depends (as you well know) on the random selection of prime numbers. The range from which these prime numbers are selected is most relevant as it determines the number of processes that would be required to break the algorithm.

My guess.... and tell me if I'm wrong, is that you are testing your algorithm on small primes and coming up with the same e and d.

The aforementioned range of the randomly selected primes (and here is the brilliance of RSA) does change over time, and more importantly, processing power. Using small primes may cloud the situation as large primes (64 bit +) are commonly used in practice.

here is an example of short primes working out

p = 61 and q = 53
n=61*53=3233
(p-1)(q-1) = (61 - 1)(53 - 1) = 3120
e = 17
d = 2753

Hi you are right, I am using small prime to test it out, I try using prime number like, 7, 11, 13,17 and I always end up with the same e and d when I choose e.

So that mean I should not use small prime?

if you use the small primes 7,11
then m=6*10=60
so if e=17, d would be 53
if e=13, d would be 37

(60 has many small factors so 7*11 is not the best choice for p*q,even  for small primes)

The thing I do not understand is that there are so many e, which 1 should I choose? And is there any cnodition to choose e? I only know if this condition below

gcd(e, m) = 1

I realised some of the e does give me the same d and e , that would make my secret ket and public key same isn't it? Is it true that some e will make me into such suitation?

http://www.usna.edu/Users/math/wdj/book/node45.html

http://www.springerlink.com/content/v7t11545l7261306/