Generate Rsa Private Key From P And Q In C++
System.Runtime.InteropServices.ComVisible(true) System.Serializable public struct RSAParameters 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. I have a private key components p, q, Dp, Dq, and QInv. I need to calculate the public key modulus and exponent. Modulus was super simple p.q, but exponent I can't figure out. Have searched all the articles and often found how to go opposite way - generating public private key once you pick the exponenet.
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| C++ example code showing how to generate an RSA public/private key.
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-->Definition
Represents the standard parameters for the RSA algorithm.
Generate Rsa Private Key From P And Q In C B
- Attributes
Remarks
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).
P And Q Logic
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.
P And Q Ferries
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.
Mind Your P And Q
| 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. 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.
Generate Rsa Private Key From P And Q In C R
.NET Core 2.1.0 and later: The serialization restrictions have been removed and all members of RSAParameters are serialized. Care must be excercised when writing or upgrading code against .NET Core 2.1.0 or later, because if anyone can derive or intercept the private key parameters the key and all the information encrypted or signed with it are compromised.
Fields
| D | Represents the |
| DP | Represents the |
| DQ | Represents the |
| Exponent | Represents the |
| InverseQ | Represents the |
| Modulus | Represents the |
| P | Represents the |
| Q | Represents the |