This repository will record some codes mentioned in Book 'From Mathematics to Generic programming' and use some examples to test it.

Install rsa package

CC=Clang pip install -e . -vvv

or

python setup.py install

then for d2l

pip install -U d2l

,and finally for Pytorch(optional here for MAC with only CPU)

conda install pytorch torchvision torchaudio -c pytorch

First we generate two large prime numbers:

1. Choose two distinct prime numbers $p$ and $q$.
2. Compute $n = pq$.
3. Compute tue Eulear totient function $\phi(n)=(p-1)(q-1)$.

Now, we destroy $p_1$ and $p_2$; $n$ is published.

1. Generate a random public key $pub$, coprime with $\phi(n)$
2. Find the private key $prv$, which is multiplicative inverse of $pub$ modulo $\phi(n)$.

Finally, $pub$ is published and $prv$ is kept secret. When transferring message $m$, we are communicating:

1. the sender will encrypte message by raising $m$ to the power $pub$;
2. the accepter will decrpte message by rasising private $prv$:

The above uses a theorem: $$ (m^{pub})^{prv} = m \text{ mod } n $$

Attension: In reality, we represent each word by an intger and so in order to avoid different words $m$ and $m'$ encrypted by the same number like $m^{pub} = m^{'pub} \text{ mod } n$, we must require that the lenght of dictionary < $n = pq$