System.Security.Cryptography.RSAParameters structure
This article provides supplementary remarks to the reference documentation for this API.
The RSAParameters structure represents the standard parameters for the RSA algorithm.
The RSA class exposes an ExportParameters method that enables you to retrieve the raw RSA key in the form of an RSAParameters structure.
To understand the contents of this structure, it helps to be familiar with how the RSA algorithm works. The next section discusses the algorithm briefly.
RSA algorithm
To generate a key pair, you start by creating two large prime numbers named p and q. These numbers are multiplied and the result is called n. Because p and q are both prime numbers, the only factors of n are 1, p, q, and n.
If we consider only numbers that are less than n, the count of numbers that are relatively prime to n, that is, have no factors in common with n, equals (p - 1)(q - 1).
Now you choose a number e, which is relatively prime to the value you calculated. The public key is now represented as {e, n}.
To create the private key, you must calculate d, which is a number such that (d)(e) mod (p - 1)(q - 1) = 1. In accordance with the Euclidean algorithm, the private key is now {d, n}.
Encryption of plaintext m to ciphertext c is defined as c = (m ^ e) mod n. Decryption would then be defined as m = (c ^ d) mod n.
Summary of fields
Section A.1.2 of the PKCS #1: RSA Cryptography Standard defines a format for RSA private keys.
The following table summarizes the fields of the RSAParameters structure. The third column provides the corresponding field in section A.1.2 of PKCS #1: RSA Cryptography Standard.
| RSAParameters field | Contains | Corresponding PKCS #1 field |
|---|---|---|
| D | d, the private exponent | privateExponent |
| DP | d mod (p - 1) | exponent1 |
| DQ | d mod (q - 1) | exponent2 |
| Exponent | e, the public exponent | publicExponent |
| InverseQ | (InverseQ)(q) = 1 mod p | coefficient |
| Modulus | n | modulus |
| P | p | prime1 |
| Q | q | prime2 |
The security of RSA derives from the fact that, given the public key { e, n }, it is computationally infeasible to calculate d, either directly or by factoring n into p and q. Therefore, any part of the key related to d, p, or q must be kept secret. If you call ExportParameters and ask for only the public key information, this is why you will receive only Exponent and Modulus. The other fields are available only if you have access to the private key, and you request it.
RSAParameters is not encrypted in any way, so you must be careful when you use it with the private key information. All members of RSAParameters are serialized. If anyone can derive or intercept the private key parameters, the key and all the information encrypted or signed with it are compromised.
