Package net.i2p.crypto.eddsa.math.ed25519

Class Ed25519ScalarOps

java.lang.Object
net.i2p.crypto.eddsa.math.ed25519.Ed25519ScalarOps
All Implemented Interfaces:
Serializable, ScalarOps
public class Ed25519ScalarOps
extends Object
implements ScalarOps
Class for reducing a huge integer modulo the group order q and doing a combined multiply plus add plus reduce operation.

$q = 2^{252} + 27742317777372353535851937790883648493$.

Reviewed/commented by Bloody Rookie (nemproject@gmx.de)

See Also:
Serialized Form

  • Constructor Details

  • Method Details

    • reduce

      public byte[] reduce​(byte[] s)
      Reduction modulo the group order $q$.

      Input: $s[0]+256*s[1]+\dots+256^{63}*s[63] = s$

      Output: $s[0]+256*s[1]+\dots+256^{31}*s[31] = s \bmod q$ where $q = 2^{252} + 27742317777372353535851937790883648493$.

      Specified by:
      reduce in interface ScalarOps
      Parameters:
      s - the scalar to reduce
      Returns:
      $s \bmod l$

    • multiplyAndAdd

      public byte[] multiplyAndAdd​(byte[] a, byte[] b, byte[] c)
      $(ab+c) \bmod q$

      Input:

      • $a[0]+256*a[1]+\dots+256^{31}*a[31] = a$
      • $b[0]+256*b[1]+\dots+256^{31}*b[31] = b$
      • $c[0]+256*c[1]+\dots+256^{31}*c[31] = c$

      Output: $result[0]+256*result[1]+\dots+256^{31}*result[31] = (ab+c) \bmod q$ where $q = 2^{252} + 27742317777372353535851937790883648493$.

      See the comments in reduce(byte[]) for an explanation of the algorithm.

      Specified by:
      multiplyAndAdd in interface ScalarOps
      Parameters:
      a - a scalar
      b - a scalar
      c - a scalar
      Returns:
      $(a*b + c) \bmod l$