RSA (cryptosystem) – Wikipedia

RSA is an asymmetric cryptographic method that can be used for both encryption and digital signing. It uses a key pair consisting of a private key, which is used to decrypt or sign data, and a public key, which is used to encrypt or verify the signature.

The private key is kept secret and cannot be computed from the public key with realistic effort.

The method was developed in 1977 by the mathematicians Romal L. Rivest, Adi Shamir and Leonard Max Adleman.

At the core of the method are mathematical one-way functions that are easy to compute in only one direction. For example, the decomposition of large numbers into their prime factors is very complex, while the multiplication of the prime factors is easy to calculate.

### Generating the Key

The public key is a pair of numbers (e, N), the private key is a pair of numbers (d, N), where N is the same for both keys.

- First, find two prime numbers p and q that are of approximately the same order of magnitude, but not too close together.
- N = p * q
- ϕ(N) = (p – 1) * ( q – 1)
- Find e as a divisor alien to ϕ(N).
- Calculate d such that e * d modulo ϕ(N) = 1

## What offers the GC Wizard?

The following functions are available with the GC Wizard:

- decrypt and encrypt with RSA
- check if the public key e matches two prime numbers p and q
- check if the private key d matches two prime numbers p and q
- compute N from two primes p and q
- compute ϕ(N) from two primes p and q
- compute the private key d from the public key e and the primes p and q