RSA (cryptosystem) Updated 2025-07-16
Based on the fact that we don't have a P algorithm for integer factorization as of 2020. But nor proof that one does not exist!
The private key is made of two randomly generated prime numbers: and . How such large primes are found: how large primes are found for RSA.
The public key is made of:
Given a plaintext message m, the encrypted ciphertext version is:
c = m^e mod n
This operation is called modular exponentiation can be calculated efficiently with the Extended Euclidean algorithm.
The inverse operation of finding the private m from the public c, e and is however believed to be a hard problem without knowing the factors of n.
However, if we know the private p and q, we can solve the problem. As follows.
First we calculate the modular multiplicative inverse. TODO continue.
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Video 1.
A very honest review of my Oxford University master's degree (theoretical physics at keble college) by alicedoesphysics (2020)
Source. Basically all her courses are from the Mathematical Institute of the University of Oxford, and therefore show up at the Moodle of the Oxford Mathematics Institute of Oxford.
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