Table 1 RSA procedures

1

Choose two prime numbers p and q (p ≠ q)

2

Compute “n value” such \(n=p*q\)

3

Compute φ(n):\(\varphi \left(n\right)=(p-1)(q-1)\)

where φ is Euler's totient function

4

Choose an integer (e) such that:

\(1<e<\varphi \left(n\right), \& gcd(e,\varphi \left(n\right))=1\)

e and φ(n) are co-prime

5

Determine (d):

\(d\equiv {e}^{-1}(mod\varphi \left(n\right))\)

(d) is the modular multiplicative inverse of e (modulo φ(n)). This is stated as solving the d given

\(d.e\equiv 1(mod\varphi \left(n\right))\)

(e,n) is the public key

(d,n) is the private key