# single-file pure-python ed25519 digital signatures, rearranged to minimize
# the namespace pollution so this can be embedded in another file. Adapted
# from https://bitbucket.org/dholth/ed25519ll


# Ed25519 digital signatures
# Based on http://ed25519.cr.yp.to/python/ed25519.py
# See also http://ed25519.cr.yp.to/software.html
# Adapted by Ron Garret
# Sped up considerably using coordinate transforms found on:
# http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
# Specifically add-2008-hwcd-4 and dbl-2008-hwcd

def Ed25519():
    # don't add many names to the file we're copied into

    try: # pragma nocover
        unicode
        PY3 = False
        def asbytes(b):
            """Convert array of integers to byte string"""
            return ''.join(chr(x) for x in b)
        def joinbytes(b):
            """Convert array of bytes to byte string"""
            return ''.join(b)
        def bit(h, i):
            """Return i'th bit of bytestring h"""
            return (ord(h[i//8]) >> (i%8)) & 1

    except NameError: # pragma nocover
        PY3 = True
        asbytes = bytes
        joinbytes = bytes
        def bit(h, i):
            return (h[i//8] >> (i%8)) & 1

    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

    # Can probably get some extra speedup here by replacing this with
    # an extended-euclidean, but performance seems OK without that
    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

    # Faster (!) version based on:
    # http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html

    def xpt_add(pt1, pt2):
        (X1, Y1, Z1, T1) = pt1
        (X2, Y2, Z2, T2) = pt2
        A = ((Y1-X1)*(Y2+X2)) % q
        B = ((Y1+X1)*(Y2-X2)) % q
        C = (Z1*2*T2) % q
        D = (T1*2*Z2) % q
        E = (D+C) % q
        F = (B-A) % q
        G = (B+A) % q
        H = (D-C) % q
        X3 = (E*F) % q
        Y3 = (G*H) % q
        Z3 = (F*G) % q
        T3 = (E*H) % q
        return (X3, Y3, Z3, T3)

    def xpt_double (pt):
        (X1, Y1, Z1, _) = pt
        A = (X1*X1)
        B = (Y1*Y1)
        C = (2*Z1*Z1)
        D = (-A) % q
        J = (X1+Y1) % q
        E = (J*J-A-B) % q
        G = (D+B) % q
        F = (G-C) % q
        H = (D-B) % q
        X3 = (E*F) % q
        Y3 = (G*H) % q
        Z3 = (F*G) % q
        T3 = (E*H) % q
        return (X3, Y3, Z3, T3)

    def pt_xform (pt):
        (x, y) = pt
        return (x, y, 1, (x*y)%q)

    def pt_unxform (pt):
        (x, y, z, _) = pt
        return ((x*inv(z))%q, (y*inv(z))%q)

    def xpt_mult (pt, n):
        if n==0: return pt_xform((0,1))
        _ = xpt_double(xpt_mult(pt, n>>1))
        return xpt_add(_, pt) if n&1 else _

    def scalarmult(pt, e):
        return pt_unxform(xpt_mult(pt_xform(pt), e))

    def encodeint(y):
        bits = [(y >> i) & 1 for i in range(b)]
        e = [(sum([bits[i * 8 + j] << j for j in range(8)]))
                                        for i in range(b//8)]
        return asbytes(e)

    def encodepoint(P):
        x = P[0]
        y = P[1]
        bits = [(y >> i) & 1 for i in range(b - 1)] + [x & 1]
        e = [(sum([bits[i * 8 + j] << j for j in range(8)]))
                                        for i in range(b//8)]
        return asbytes(e)

    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):
        sk = sk[:32]
        h = H(sk)
        a = 2**(b-2) + sum(2**i * bit(h,i) for i in range(3,b-2))
        inter = joinbytes([h[i] for i in range(b//8,b//4)])
        r = Hint(inter + 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)
        v1 = scalarmult(B,S)
    #  v2 = edwards(R,scalarmult(A,h))
        v2 = pt_unxform(xpt_add(pt_xform(R), pt_xform(scalarmult(A, h))))
        return v1==v2


    import os

    def create_signing_key():
        seed = os.urandom(32)
        return seed
    def create_verifying_key(signing_key):
        return publickey(signing_key)

    def sign(skbytes, msg):
        """Return just the signature, given the message and just the secret
        key."""
        if len(skbytes) != 32:
            raise ValueError("Bad signing key length %d" % len(skbytes))
        vkbytes = create_verifying_key(skbytes)
        sig = signature(msg, skbytes, vkbytes)
        return sig

    def verify(vkbytes, sig, msg):
        if len(vkbytes) != 32:
            raise ValueError("Bad verifying key length %d" % len(vkbytes))
        if len(sig) != 64:
            raise ValueError("Bad signature length %d" % len(sig))
        rc = checkvalid(sig, msg, vkbytes)
        if not rc:
            raise ValueError("rc != 0", rc)
        return True

    return (create_signing_key, create_verifying_key, sign, verify)

(ed25519_create_signing_key, ed25519_create_verifying_key,
 ed25519_sign, ed25519_verify) = Ed25519()

## sk = ed25519_create_signing_key()
## msg = "hello world"
## sig = ed25519_sign(sk, msg)
## assert len(sig) == 64
## vk = ed25519_create_verifying_key(sk)
## ed25519_verify(vk, sig, msg)
## print "ok"