上QQ阅读APP看书，第一时间看更新
RSA parameter generation
Before looking at encryption and decryption using RSA, we need to consider the RSA parameter generation process. Here are the steps involved in this process:
- Select two distinct large prime numbers, p, and q.
- Compute n = p*q and φ(n) = (p − 1)*(q − 1).
- Choose a random integer e, such that 1 < e < φ(n) and gcd (e, φ(n)) = 1, that is, integer e and φ(n), are coprime.
- Find d ≡ e-1 (mod φ(n)), where e-1 is the modular multiplicative inverse of e.
A modular multiplicative inverse of an integer a is an integer x, such that the product ax is congruent to 1 with respect to the modulus m.
More clearly, find d such that d*e ≡ 1 (mod φ(n)), meaning find a value d such that d*e has a remainder of 1 when divided by φ(n).
- The public key is denoted by (e, n) and the private key by (d, p, q). Here, e is called the public exponent, and d the private exponent.