Understanding RSA security
The security of RSA relies on the difficulty of the integer factorization problem. As a reminder, the factorization operation is breaking a positive integer number into a multiplication of prime numbers. Currently, there is no polynomial-time algorithm for integer factorization that can be run by a classical computer, and hence, this problem remains very computationally expensive. And how big are the integer numbers used in RSA? Typically, they are hundreds or thousands of decimal digits, or thousands or tens of thousands of bits. Apparently, usual integer types in C language are not large enough to perform mathematics with big numbers used in RSA. Hence, OpenSSL includes a big-number sub-library in order to deal with big numbers. Types and functions of that big-number sub-library have a BN_ prefix.
An RSA public or private key consists of several big or small integer numbers called a modulus, an exponent, and, optionally, primes and coefficients. As mentioned...
