go with RSA. Choose a 128 digit prime number, and another 128 digit prime number... well here just read this.
RSA - Wikipedia, the free encyclopedia
modular arithmatic just means that once you get past the modulus it goes back to 0, so 5 mod 2 would be 3. 18 mod 3 would be 0.
RSA is what our internet security, credit cards, banks, digital encryption, government encryption, etc use. Basically there is no good way to factor very large numbers that are only divisible by 2 prime numbers. If you can think of a way then you'll destroy the world's economy.
(I really like my Crypto class in college)
This is the RSA public key and exponent for the SSL certificate on HighTechDealZ.com
Modulus (2048 bits): (in hex)
b0 36 7c 80 ce 5b 43 f4 6b b7 b2 58 b3 79 5c 91
36 14 43 5c 23 10 e4 2e c1 c6 47 1a 96 00 e6 be
47 b7 ab 79 af 54 b2 4f e1 b8 3e a0 20 d6 86 32
9d 2a 87 33 d4 a1 87 40 2f a3 b7 37 e5 8c bb c0
9a 0c f7 e4 97 8d 75 71 5b c6 d2 c7 1e d7 ac 62
93 7a a6 2c 2a dc 65 3a 15 d8 06 50 0a 9a 72 dc
f7 d0 f6 78 9f 11 04 7e ae 41 34 bf 93 61 ac ce
46 0b 0f ff 81 d3 d6 69 c2 61 b8 cd dc bf e7 19
b0 d7 db ad 5e af 23 72 c7 b6 28 0b 70 1d 06 6f
28 55 61 9b 62 f8 f2 d9 e9 a0 2c 86 7d c3 71 60
07 9e ce b5 98 04 7d f9 53 d7 73 f1 72 88 10 cf
76 7e 60 7a 49 63 56 86 41 ea 26 52 13 c0 90 ef
01 69 ed f4 25 ad d6 b6 f2 c8 3d d3 fc 98 83 20
19 72 34 55 3f e3 cd 24 2d 45 66 5e bc d5 80 fd
41 6f 1f 72 36 f1 30 16 a3 61 a6 80 48 5d 67 c6
a7 2f 5f 75 25 ad 63 e6 54 e6 c9 ca 77 76 6d a1
Exponent (24 bits):
65537
-Kendall