# RSAParameters Structure

July 28, 2014

Represents the standard parameters for the RSA algorithm.

**Namespace:**System.Security.Cryptography

**Assembly:**mscorlib (in mscorlib.dll)

The RSAParameters type exposes the following members.

Name | Description | |
---|---|---|

Equals | Indicates whether this instance and a specified object are equal. (Inherited from ValueType.) | |

Finalize | Allows an object to try to free resources and perform other cleanup operations before the Object is reclaimed by garbage collection. (Inherited from Object.) | |

GetHashCode | Returns the hash code for this instance. (Inherited from ValueType.) | |

GetType | Gets the Type of the current instance. (Inherited from Object.) | |

MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |

ToString | Returns the fully qualified type name of this instance. (Inherited from ValueType.) |

Name | Description | |
---|---|---|

D | Represents the D parameter for the RSA algorithm. | |

DP | Represents the DP parameter for the RSA algorithm. | |

DQ | Represents the DQ parameter for the RSA algorithm. | |

Exponent | Represents the Exponent parameter for the RSA algorithm. | |

InverseQ | Represents the InverseQ parameter for the RSA algorithm. | |

Modulus | Represents the Modulus parameter for the RSA algorithm. | |

P | Represents the P parameter for the RSA algorithm. | |

Q | Represents the Q parameter 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. Understanding the contents of this structure requires familiarity 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 on the RSA Laboratories Web site 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, the private exponent | privateExponent | |

d mod (p - 1) | exponent1 | |

d mod (q - 1) | exponent2 | |

e, the public exponent | publicExponent | |

(InverseQ)(q) = 1 mod p | coefficient | |

n | modulus | |

p | prime1 | |

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. In fact, none of the fields that contain private key information can be serialized. If you try to serialize an RSAParameters structure with a remoting call or by using one of the serializers, you will receive only public key information. If you want to pass private key information, you will have to manually send that data. In all cases, if anyone can derive the parameters, the key that you transmit becomes useless.