Prime Numbers and Encryption
Want to make $250 000 ? Find a big prime number, a really big one. It turns out there are organizations ready to dough out good cash for a really large prime number. This is because primes are used in RSA cryptography . RSA Algorithm Let's look at the algorithm: 1. Multiply two large prime numbers p and q to get the product N 2. Find two numbers e and d , such that ed = 1mod((p-1)(q-1)) , where e and N are relatively prime meaning they do not share any prime factors. 3. Let's call M the original message and C the ciphered message: a. To encrypt: C = M e mod(N) b. To decipher: M = C d mod(N) In essence, using the public key ( N,e) will transform the original message M to the ciphered message C . On the contrary, applying the private key d on the ciphered message C will result in the original message M . Security of Encryption The beauty of RSA is your public key can be published for anyone to