# 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

import hashlib
import random

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

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):
    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


##########################################################
#
# Curve25519 reference implementation by Matthew Dempsky, from:
# http://cr.yp.to/highspeed/naclcrypto-20090310.pdf

# P = 2 ** 255 - 19
P = q
A = 486662


# 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, P - 2, P)


def add(n, m, d):
    (xn, zn) = n
    (xm, zm) = m
    (xd, zd) = d
    x = 4 * (xm * xn - zm * zn) ** 2 * zd
    z = 4 * (xm * zn - zm * xn) ** 2 * xd
    return (x % P, z % P)


def double(n):
    (xn, zn) = n
    x = (xn ** 2 - zn ** 2) ** 2
    z = 4 * xn * zn * (xn ** 2 + A * xn * zn + zn ** 2)
    return (x % P, z % P)


def curve25519(n, base=9):
    one = (base, 1)
    two = double(one)

    # f(m) evaluates to a tuple
    # containing the mth multiple and the
    # (m+1)th multiple of base.
    def f(m):
        if m == 1:
            return (one, two)

        (pm, pm1) = f(m // 2)
        if m & 1:
            return (add(pm, pm1, one), double(pm1))

        return (double(pm), add(pm, pm1, one))

    ((x, z), _) = f(n)
    return (x * inv(z)) % P


def genkey(n=0):
    n = n or random.randint(0, P)
    n &= ~7
    n &= ~(128 << 8 * 31)
    n |= 64 << 8 * 31
    return n


# def str2int(s):
#    return int(hexlify(s), 16)
#    # return sum(ord(s[i]) << (8 * i) for i in range(32))
#
# def int2str(n):
#    return unhexlify("%x" % n)
#    # return ''.join([chr((n >> (8 * i)) & 255) for i in range(32)])

#################################################


def dsa_test():
    import os
    msg = str(random.randint(q, q + q)).encode('utf-8')
    sk = os.urandom(32)
    pk = publickey(sk)
    sig = signature(msg, sk, pk)
    return checkvalid(sig, msg, pk)


def dh_test():
    sk1 = genkey()
    sk2 = genkey()
    return curve25519(sk1, curve25519(sk2)) == curve25519(sk2, curve25519(sk1))