--- /dev/null
+# ed25519.py - Optimized version of the reference implementation of Ed25519
+#
+# Written in 2011? by Daniel J. Bernstein <djb@cr.yp.to>
+# 2013 by Donald Stufft <donald@stufft.io>
+# 2013 by Alex Gaynor <alex.gaynor@gmail.com>
+# 2013 by Greg Price <price@mit.edu>
+#
+# To the extent possible under law, the author(s) have dedicated all copyright
+# and related and neighboring rights to this software to the public domain
+# worldwide. This software is distributed without any warranty.
+#
+# You should have received a copy of the CC0 Public Domain Dedication along
+# with this software. If not, see
+# <http://creativecommons.org/publicdomain/zero/1.0/>.
+
+"""
+NB: This code is not safe for use with secret keys or secret data.
+The only safe use of this code is for verifying signatures on public messages.
+Functions for computing the public key of a secret key and for signing
+a message are included, namely publickey_unsafe and signature_unsafe,
+for testing purposes only.
+The root of the problem is that Python's long-integer arithmetic is
+not designed for use in cryptography. Specifically, it may take more
+or less time to execute an operation depending on the values of the
+inputs, and its memory access patterns may also depend on the inputs.
+This opens it to timing and cache side-channel attacks which can
+disclose data to an attacker. We rely on Python's long-integer
+arithmetic, so we cannot handle secrets without risking their disclosure.
+"""
+
+import hashlib
+import operator
+import sys
+
+
+# __version__ = "1.0.dev0"
+
+
+# Useful for very coarse version differentiation.
+PY3 = sys.version_info[0] == 3
+
+if PY3:
+ indexbytes = operator.getitem
+ intlist2bytes = bytes
+ int2byte = operator.methodcaller("to_bytes", 1, "big")
+else:
+ int2byte = chr
+ range = xrange
+
+ def indexbytes(buf, i):
+ return ord(buf[i])
+
+ def intlist2bytes(l):
+ return b"".join(chr(c) for c in l)
+
+
+b = 256
+q = 2 ** 255 - 19
+l = 2 ** 252 + 27742317777372353535851937790883648493
+
+
+def H(m):
+ return hashlib.sha512(m).digest()
+
+
+def pow2(x, p):
+ """== pow(x, 2**p, q)"""
+ while p > 0:
+ x = x * x % q
+ p -= 1
+ return x
+
+
+def inv(z):
+ """$= z^{-1} \mod q$, for z != 0"""
+ # Adapted from curve25519_athlon.c in djb's Curve25519.
+ z2 = z * z % q # 2
+ z9 = pow2(z2, 2) * z % q # 9
+ z11 = z9 * z2 % q # 11
+ z2_5_0 = (z11 * z11) % q * z9 % q # 31 == 2^5 - 2^0
+ z2_10_0 = pow2(z2_5_0, 5) * z2_5_0 % q # 2^10 - 2^0
+ z2_20_0 = pow2(z2_10_0, 10) * z2_10_0 % q # ...
+ z2_40_0 = pow2(z2_20_0, 20) * z2_20_0 % q
+ z2_50_0 = pow2(z2_40_0, 10) * z2_10_0 % q
+ z2_100_0 = pow2(z2_50_0, 50) * z2_50_0 % q
+ z2_200_0 = pow2(z2_100_0, 100) * z2_100_0 % q
+ z2_250_0 = pow2(z2_200_0, 50) * z2_50_0 % q # 2^250 - 2^0
+ return pow2(z2_250_0, 5) * z11 % q # 2^255 - 2^5 + 11 = q - 2
+
+
+d = -121665 * inv(121666) % q
+I = pow(2, (q - 1) // 4, q)
+
+
+def xrecover(y):
+ xx = (y * y - 1) * inv(d * y * y + 1)
+ x = pow(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, 1, (Bx * By) % q)
+ident = (0, 1, 1, 0)
+
+
+def edwards_add(P, Q):
+ # This is formula sequence 'addition-add-2008-hwcd-3' from
+ # http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
+ (x1, y1, z1, t1) = P
+ (x2, y2, z2, t2) = Q
+
+ a = (y1-x1)*(y2-x2) % q
+ b = (y1+x1)*(y2+x2) % q
+ c = t1*2*d*t2 % q
+ dd = z1*2*z2 % q
+ e = b - a
+ f = dd - c
+ g = dd + c
+ h = b + a
+ x3 = e*f
+ y3 = g*h
+ t3 = e*h
+ z3 = f*g
+
+ return (x3 % q, y3 % q, z3 % q, t3 % q)
+
+
+def edwards_double(P):
+ # This is formula sequence 'dbl-2008-hwcd' from
+ # http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
+ (x1, y1, z1, t1) = P
+
+ a = x1*x1 % q
+ b = y1*y1 % q
+ c = 2*z1*z1 % q
+ # dd = -a
+ e = ((x1+y1)*(x1+y1) - a - b) % q
+ g = -a + b # dd + b
+ f = g - c
+ h = -a - b # dd - b
+ x3 = e*f
+ y3 = g*h
+ t3 = e*h
+ z3 = f*g
+
+ return (x3 % q, y3 % q, z3 % q, t3 % q)
+
+
+def scalarmult(P, e):
+ if e == 0:
+ return ident
+ Q = scalarmult(P, e // 2)
+ Q = edwards_double(Q)
+ if e & 1:
+ Q = edwards_add(Q, P)
+ return Q
+
+
+# Bpow[i] == scalarmult(B, 2**i)
+Bpow = []
+
+
+def make_Bpow():
+ P = B
+ for i in range(253):
+ Bpow.append(P)
+ P = edwards_double(P)
+make_Bpow()
+
+def scalarmultbase(e):
+ return scalarmult_B(e)
+
+def scalarmult_B(e):
+ """
+ Implements scalarmult(B, e) more efficiently.
+ """
+ # scalarmult(B, l) is the identity
+ e = e % l
+ P = ident
+ for i in range(253):
+ if e & 1:
+ P = edwards_add(P, Bpow[i])
+ e = e // 2
+ assert e == 0, e
+ return P
+
+
+def encodeint(y):
+ bits = [(y >> i) & 1 for i in range(b)]
+ return b''.join([
+ int2byte(sum([bits[i * 8 + j] << j for j in range(8)]))
+ for i in range(b//8)
+ ])
+
+
+def encodepoint(P):
+ (x, y, z, t) = P
+ zi = inv(z)
+ x = (x * zi) % q
+ y = (y * zi) % q
+ bits = [(y >> i) & 1 for i in range(b - 1)] + [x & 1]
+ return b''.join([
+ int2byte(sum([bits[i * 8 + j] << j for j in range(8)]))
+ for i in range(b // 8)
+ ])
+
+
+def bit(h, i):
+ return (indexbytes(h, i // 8) >> (i % 8)) & 1
+
+
+def publickey_unsafe(sk):
+ """
+ Not safe to use with secret keys or secret data.
+ See module docstring. This function should be used for testing only.
+ """
+ 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_unsafe(m, sk, pk):
+ """
+ Not safe to use with secret keys or secret data.
+ See module docstring. This function should be used for testing only.
+ """
+ h = H(sk)
+ a = 2 ** (b - 2) + sum(2 ** i * bit(h, i) for i in range(3, b - 2))
+ r = Hint(
+ intlist2bytes([indexbytes(h, j) for j 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, y, z, t) = P
+ return (z % q != 0 and
+ x*y % q == z*t % q and
+ (y*y - x*x - z*z - d*t*t) % 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, 1, (x*y) % q)
+ if not isoncurve(P):
+ raise ValueError("decoding point that is not on curve")
+ return P
+
+
+class SignatureMismatch(Exception):
+ pass
+
+
+def checkvalid(s, m, pk):
+ """
+ Not safe to use when any argument is secret.
+ See module docstring. This function should be used only for
+ verifying public signatures of public messages.
+ """
+ if len(s) != b // 4:
+ raise ValueError("signature length is wrong")
+
+ if len(pk) != b // 8:
+ raise ValueError("public-key length is wrong")
+
+ R = decodepoint(s[:b // 8])
+ A = decodepoint(pk)
+ S = decodeint(s[b // 8:b // 4])
+ h = Hint(encodepoint(R) + pk + m)
+
+ (x1, y1, z1, t1) = P = scalarmult_B(S)
+ (x2, y2, z2, t2) = Q = edwards_add(R, scalarmult(A, h))
+
+ if (not isoncurve(P) or not isoncurve(Q) or
+ (x1*z2 - x2*z1) % q != 0 or (y1*z2 - y2*z1) % q != 0):
+ raise SignatureMismatch("signature does not pass verification")
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