Add eddsa from ref10 implementation (with some modifications).

core/crypto/ed25519/base.py

@@ -0,0 +1,65 @@
+b = 256
+q = 2**255 - 19
+l = 2**252 + 27742317777372353535851937790883648493
+
+def expmod(b,e,m):
+  if e == 0: return 1
+  t = expmod(b,e/2,m)**2 % m
+  if e & 1: t = (t*b) % m
+  return t
+
+def inv(x):
+  return expmod(x,q-2,q)
+
+d = -121665 * inv(121666)
+I = expmod(2,(q-1)/4,q)
+
+def xrecover(y):
+  xx = (y*y-1) * inv(d*y*y+1)
+  x = expmod(xx,(q+3)/8,q)
+  if (x*x - xx) % q != 0: x = (x*I) % q
+  if x % 2 != 0: x = q-x
+  return x
+
+By = 4 * inv(5)
+Bx = xrecover(By)
+B = [Bx % q,By % q]
+
+def edwards(P,Q):
+  x1 = P[0]
+  y1 = P[1]
+  x2 = Q[0]
+  y2 = Q[1]
+  x3 = (x1*y2+x2*y1) * inv(1+d*x1*x2*y1*y2)
+  y3 = (y1*y2+x1*x2) * inv(1-d*x1*x2*y1*y2)
+  return [x3 % q,y3 % q]
+
+def radix255(x):
+  x = x % q
+  if x + x > q: x -= q
+  x = [x,0,0,0,0,0,0,0,0,0]
+  bits = [26,25,26,25,26,25,26,25,26,25]
+  for i in range(9):
+    carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i]
+    x[i] -= carry * 2**bits[i]
+    x[i + 1] += carry
+  result = ""
+  for i in range(9):
+    result = result+str(x[i])+","
+  result = result+str(x[9])
+  return result
+
+Bi = B
+for i in range(32):
+  print "{"
+  Bij = Bi
+  for j in range(8):
+    print " {"
+    print "  {",radix255(Bij[1]+Bij[0]),"},"
+    print "  {",radix255(Bij[1]-Bij[0]),"},"
+    print "  {",radix255(2*d*Bij[0]*Bij[1]),"},"
+    Bij = edwards(Bij,Bi)
+    print " },"
+  print "},"
+  for k in range(8):
+    Bi = edwards(Bi,Bi)