====== RSA ======
 
[[/glossaire/rsa|/glossaire/rsa]]

Présentations de l'algo RSA:
  * [[http://www.di-mgt.com.au/rsa_alg.html]]
  * [[http://www.cryptosec.org/RSA.html]]

  * key generation
    * p, q are two large random primes
    * n = pq is of the required bit length
    * phi = (p-1)(q-1)
    * public exponent e: 1 < e < phi, gcd(e, phi) = 1
    * secret exponent d: 1 < d < phi, ed ≡ 1 (mod phi)
    * destroy p, q and phi
  * public key: n , e
  * private key: n, d
  * Encryption: c = m<sup>e</sup> mod n
  * Decryption: m = c<sup>d</sup> mod n
  * Signing: s = m<sup>d</sup> mod n
  * Signing verification: v = s<sup>e</sup> mod n
  * Then use advanced schemes:
    * RSAES-OAEP: (PKCS#1 version 2 and in IEEE P136) The encoding technique involves a Mask Generation Function (MGF) based on a hash function
    * RSASSA-PSS: The PSS encoding method is used to encode before creating a signature. However, there are active patents associated with this method



===== Divers =====

==== RSA en Javascript ====

Implémentations RSA (et du BigInt) en Javascript:
  * [[http://www-cs-students.stanford.edu/~tjw/jsbn/|Tom Wu]] ({{:informatique:javascript-rsa_by_tom_wu.zip|copie locale}})
    * qui utilise cette lib:
      * [[https://github.com/garfieldius/rsa-javascript-php|garfieldius/rsa-javascript-php]]
  * [[http://ohdave.com/rsa/|Dave Shapiro]] ({{:informatique:javascript-rsa_by_dave_shapiro.zip|copie locale}})
  * [[http://www9.atwiki.jp/kurushima/pub/jsrsa/|Kenji Urushima]]: signature RSA depuis certificat x509 , (utilise BigInt et RSA de TomWu).

Bench Signature RSA clé 2048 bits:
  * AMD ATHLON 64 X2 core processor 4200
    * FF: 1.872
    * **IE: 12.406**
  * Intel Core i7 M640 2.80GHz
    * FF: 2.846
    * **Chromium: 0.210**
  * Intel Core2 à 2.40GHz
    * Firefox: 3.762
    * Epiphany: 1.498
Bench Signature RSA clé 1024 bits:
  * AMD ATHLON 64 X2 core processor 4200
    * FF: 
    * IE:
  * Intel Core i7 M640 2.80GHz
    * FF: 0.247
    * Chromium: 0.038
  * Intel Core2 à 2.40GHz
    * 
    * 

==== .Net RSA Parameters ====

RSAParameters Structure ([[http://msdn.microsoft.com/en-us/library/system.security.cryptography.rsaparameters.aspx|msdn]])
^ 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 |


<code csharp>
int dwKeySize = 384 ;
bool exportPrivateKey = true ;
RSACryptoServiceProvider rsa = new RSACryptoServiceProvider( dwKeySize );
using( StreamWriter sw = new StreamWriter( "RSAParameters.xml" ) )
{
 sw.Write( rsa.ToXmlString( exportPrivateKey ) );
 sw.Close();
}
</code>

Format .Net System.Security.Cryptography.RSACryptoServiceProvider.ToXmlString() :

Private:
<code xml>
 <RSAKeyValue>
  <Modulus>3XGodAOyDWfoGGMelpKft1Wx1E15m5yot4Rj0ppWpa/wTaHcudYfl+VIq+0EaC4N</Modulus> 
  <Exponent>AQAB</Exponent> 
  <P>+dhBWqM/4f1FBB3dP2fqKfhRnsfGqgTz</P> 
  <Q>4uZIM7QCetizjB9PGLoLcLIM2f1vDcD/</Q> 
  <DP>U2mXqCMImPJtsEooK5sN2qVE2rXn5atx</DP> 
  <DQ>xblS9etJte+dFuA5txx4163w0Q2udtfV</DQ> 
  <InverseQ>3q9gba8r1cFdsp/0uAYO3aVn7gnwqCPG</InverseQ> 
  <D>W9XmAW8C6XJdG7gHmHRoTlT4sc4Lj9BwliwVb9fN0sSqbF4UlABupXlIZTyuCBS1</D> 
 </RSAKeyValue>
</code>
Public only:
<code xml>
 <RSAKeyValue>
   <Modulus>t6yVboVvHOyCpOH7/hdA2cRlmkDoMZJc3cC72PpakR2/7dbq9Lqc1a+MY09sOMDH</Modulus>
   <Exponent>AQAB</Exponent>
 </RSAKeyValue>
</code>