RSA

/glossaire/rsa

Présentations de l'algo RSA:

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^e mod n
Decryption: m = c^d mod n
Signing: s = m^d mod n
Signing verification: v = s^e 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:

Tom Wu (copie locale)
- qui utilise cette lib:
  - garfieldius/rsa-javascript-php
Dave Shapiro (copie locale)
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 (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

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();
}

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

Private:

 <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>

Public only:

 <RSAKeyValue>
   <Modulus>t6yVboVvHOyCpOH7/hdA2cRlmkDoMZJc3cC72PpakR2/7dbq9Lqc1a+MY09sOMDH</Modulus>
   <Exponent>AQAB</Exponent>
 </RSAKeyValue>