We begin with choosing two random large distinct primes p and q. We

also pick e, a random integer that is relatively prime to (p-1)*(q-1). The

random integer e is the encryption exponent. Let n = p*q. Using Euclid s

greatest common divisor algorithm, one can compute d, the decryption

exponent, such that:

e*d = 1 (mod (p-1)*(q-1))

Both plaintext m and ciphertext c should be in the set of nonnegative

integers. Furthermore, before encrypting a plaintext message m, we need

to make sure that 0 <= m < n. If m is greater than the modulus n, the result

c of the encryption will not be a unique one-to-one mapping m to c.

From one of the theorems of Euler s, we know that for all integers m,

med = m (mod n) -We begin with choosing two random large distinct primes p and q. We

also pick e, a random integer that is relatively prime to (p-1)*(q-1). The

random integer e is the encryption exponent. Let n = p*q. Using Euclid s

greatest common divisor algorithm, one can compute d, the decryption

exponent, such that:

e*d = 1 (mod (p-1)*(q-1))

Both plaintext m and ciphertext c should be in the set of nonnegative

integers. Furthermore, before encrypting a plaintext message m, we need

to make sure that 0 <= m < n. If m is greater than the modulus n, the result

c of the encryption will not be a unique one-to-one mapping　m to c.

From one of the theorems of Euler s, we know that for all integers m,

med = m (mod n)