Instead, we must specifically choose these values such that applying encryption and decryption actually yield the original message.Ĭhoosing these values is based on Fermat's little theorem. However, RSA does not work with any value for N, e and d. M = pow(c, d, N) # Decryption, d is a private value Setup RSA is based on modular exponentiation in a group N such that if we have a message m, a public key e and a private key d we can compute the ciphertext c as:Ĭ = pow(m, e, N) # Encryption, e and N are public valuesĪnd compute the original message from the ciphertext as: This is different from symmetric-key cryptosystems such as AES which use the same key for encryption and decryption. This means that encryption and decryption use different components.įor encryption, we use a public component that everybody can use to encrypt messages.įor decryption, we use a private component that only the person who wants to decrypt messages may know. RSA is a widely used public-key (also known as asymmetric-key) cryptosystem.
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