Definition
Asymmetric Encryption Scheme
An asymmetric encryption scheme with a public key space
, a private key space , a message space , and a ciphertext space is a triple of algorithms: where:
- The key generation algorithm
takes no input (arity 0) and returns a randomly selected key pair . - The encryption algorithm
takes a public key and a message , and produces a ciphertext :
- The decryption algorithm
takes a private key and a ciphertext , and produces a plaintext , or an error:
One-Way Function
Integer Factorisation
Definition
Link to originalInteger Factorisation
The integer factorisation problem is the problem of decomposing a positive integer into a product of prime numbers. Given a composite integer
, find primes and positive integers such that
Discrete Logarithm
Definition
Link to originalDiscrete Logarithm
Let
be a finite cyclic group of order with generator . For an element , the discrete logarithm of with respect to base is the unique integer such that The discrete logarithm problem is to find
given and .