Add the Python implementation of the ed25519 signature scheme

ed25519 is an elliptive-curve public key signature scheme.
http://ed25519.cr.yp.to/

ed25519/checkparams.py

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+from ed25519 import *
+
+assert b >= 10
+assert 8 * len(H("hash input")) == 2 * b
+assert expmod(2,q-1,q) == 1
+assert q % 4 == 1
+assert expmod(2,l-1,l) == 1
+assert l >= 2**(b-4)
+assert l <= 2**(b-3)
+assert expmod(d,(q-1)/2,q) == q-1
+assert expmod(I,2,q) == q-1
+assert isoncurve(B)
+assert scalarmult(B,l) == [0,1]

ed25519/ed25519.py

@@ -0,0 +1,104 @@
+import hashlib
+
+b = 256
+q = 2**255 - 19
+l = 2**252 + 27742317777372353535851937790883648493
+
+def H(m):
+  return hashlib.sha512(m).digest()
+
+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 scalarmult(P,e):
+  if e == 0: return [0,1]
+  Q = scalarmult(P,e/2)
+  Q = edwards(Q,Q)
+  if e & 1: Q = edwards(Q,P)
+  return Q
+
+def encodeint(y):
+  bits = [(y >> i) & 1 for i in range(b)]
+  return ''.join([chr(sum([bits[i * 8 + j] << j for j in range(8)])) for i in range(b/8)])
+
+def encodepoint(P):
+  x = P[0]
+  y = P[1]
+  bits = [(y >> i) & 1 for i in range(b - 1)] + [x & 1]
+  return ''.join([chr(sum([bits[i * 8 + j] << j for j in range(8)])) for i in range(b/8)])
+
+def bit(h,i):
+  return (ord(h[i/8]) >> (i%8)) & 1
+
+def publickey(sk):
+  h = H(sk)
+  a = 2**(b-2) + sum(2**i * bit(h,i) for i in range(3,b-2))
+  A = scalarmult(B,a)
+  return encodepoint(A)
+
+def Hint(m):
+  h = H(m)
+  return sum(2**i * bit(h,i) for i in range(2*b))
+
+def signature(m,sk,pk):
+  h = H(sk)
+  a = 2**(b-2) + sum(2**i * bit(h,i) for i in range(3,b-2))
+  r = Hint(''.join([h[i] for i in range(b/8,b/4)]) + m)
+  R = scalarmult(B,r)
+  S = (r + Hint(encodepoint(R) + pk + m) * a) % l
+  return encodepoint(R) + encodeint(S)
+
+def isoncurve(P):
+  x = P[0]
+  y = P[1]
+  return (-x*x + y*y - 1 - d*x*x*y*y) % q == 0
+
+def decodeint(s):
+  return sum(2**i * bit(s,i) for i in range(0,b))
+
+def decodepoint(s):
+  y = sum(2**i * bit(s,i) for i in range(0,b-1))
+  x = xrecover(y)
+  if x & 1 != bit(s,b-1): x = q-x
+  P = [x,y]
+  if not isoncurve(P): raise Exception("decoding point that is not on curve")
+  return P
+
+def checkvalid(s,m,pk):
+  if len(s) != b/4: raise Exception("signature length is wrong")
+  if len(pk) != b/8: raise Exception("public-key length is wrong")
+  R = decodepoint(s[0:b/8])
+  A = decodepoint(pk)
+  S = decodeint(s[b/8:b/4])
+  h = Hint(encodepoint(R) + pk + m)
+  if scalarmult(B,S) != edwards(R,scalarmult(A,h)):
+    raise Exception("signature does not pass verification")

ed25519/sign.py

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+import sys
+import binascii
+import ed25519
+
+# examples of inputs: see sign.input
+# should produce no output: python sign.py < sign.input
+
+# warning: currently 37 seconds/line on a fast machine
+
+# fields on each input line: sk, pk, m, sm
+# each field hex
+# each field colon-terminated
+# sk includes pk at end
+# sm includes m at end
+
+while 1:
+  line = sys.stdin.readline()
+  if not line: break
+  x = line.split(':')
+  sk = binascii.unhexlify(x[0][0:64])
+  pk = ed25519.publickey(sk)
+  m = binascii.unhexlify(x[2])
+  s = ed25519.signature(m,sk,pk)
+  ed25519.checkvalid(s,m,pk)
+  forgedsuccess = 0
+  try:
+    if len(m) == 0:
+      forgedm = "x"
+    else:
+      forgedmlen = len(m)
+      forgedm = ''.join([chr(ord(m[i])+(i==forgedmlen-1)) for i in range(forgedmlen)])
+    ed25519.checkvalid(s,forgedm,pk)
+    forgedsuccess = 1
+  except:
+    pass
+  assert not forgedsuccess
+  assert x[0] == binascii.hexlify(sk + pk)
+  assert x[1] == binascii.hexlify(pk)
+  assert x[3] == binascii.hexlify(s + m)