Secure Programming Cookbook for C and C++

7.10. Performing Raw Encryption with an RSA Public Key

Problem

You want to encrypt a small message using an RSA public key so that only an entity with the corresponding private key can decrypt the message.

Solution

Your cryptographic library should have a straightforward API to the RSA encryption algorithm: you should be able to give it the public key, the data to encrypt, a buffer for the results, an indication of the data’s length, and a specification as to what kind of padding to use (EME-OAEP padding is recommended).

When using OpenSSL, this can be done with the RSA_public_encrypt( ) function, defined in openssl/rsa.h.

If, for some reason, you need to implement RSA on your own (which we strongly recommend against), refer to the Public Key Cryptography Standard (PKCS) #1, Version 2.1 (the latest version).

Discussion

Tip

Be sure to read the generic considerations for public key cryptography in Recipe 7.1 and Recipe 7.2.

Conceptually, RSA encryption is very simple. A message is translated into an integer and encrypted with integer math. Given a message m written as an integer, if you want to encrypt to a public key, you take the modulus n and the exponent e from that public key. Then compute c = m ^e mod n, where c is the ciphertext, written as an integer. Given the ciphertext, you must have the private key to recover m. The private key consists of a single integer d, which can undo the encipherment with the operation m = cd mod n.

This scheme is believed to be as “hard” as factoring ...