Reverse Iteration Fractal Cipher (RIFC) w/ HMAC

# Chris M. Thomasson 8/11/2016
# Reverse Iteration Fractal Cipher (RIFC) w/ HMAC


import math;
import random;
import hmac;
import copy;


# Complex Absolute Value
def cabs(z):
    return math.sqrt(z.real**2 + z.imag**2);


# Complex Argument
def carg(z):
    return math.atan2(z.imag, z.real);


# Complex Argument Range [0...PI2]
def cargr(z):
    a = math.atan2(z.imag, z.real);
    if (a < 0): a += math.pi * 2;
    return a;


# Get n from a power
def npow(p):
    return int(math.ceil(math.fabs(p)));


# Complex Roots
def croots(z, p):
    l = cabs(z);
    s = l**(1.0 / p);
    a = carg(z) / p;
    n = npow(p);
    astep = (math.pi * 2.0) / p;
    result = [];

    for i in range(n):
        r = complex(math.cos(a + astep * i) * s,
                    math.sin(a + astep * i) * s);
        result.append(r);

    return result;


# Find Root
def froot(z, r):
    n = 0;
    for i in r:
        d = z - i;
        l = math.sqrt(d.real**2 + d.imag**2);
        if l < 0.000001: return n;
        n = n + 1;
    return -1;


# Secret Key
class ct_rifc_skey:
    def __init__(self, z, c_0, c_1, p_0, p_1, n, hmkey):
        self.z = z;
        self.c_0 = c_0;
        self.c_1 = c_1;
        self.p_0 = p_0;
        self.p_1 = p_1;
        self.n = n;
        self.hmack = copy.copy(hmkey);

    def __repr__(self):
        return "(%s, %s, %s, %s, %s, %s)" % (self.z, self.c_0, self.c_1, self.p_0, self.p_1, self.n);

    def __str__(self): return self.__repr__();


# Reverse Iteration Fractal Cipher (RIFC)
class ct_rifc:
    def __init__(self):
        self.foo = 1;

    def __repr__(self):
        return "(%s)" % ("ct_rifc");

    def __str__(self): return self.__repr__();

    def encrypt_ptxt(self, z, c, p, ptxt):
        n = 0;
        for i in ptxt:
            r = croots(z - c, p);
            z = r[int(i)];
            print("(encrypt_ptxt(z[%s]:(%s):%s)" % (n, i, z));
            n = n + 1;
        return z;

    def encrypt_rand(self, z, c, p, n):
        np = npow(p);
        for i in range(n):
            r = croots(z - c, p);
            z = r[random.randint(0, np - 1)];
            print("(encrypt_rand(z[%s]:%s)" % (i, z));
        return z;

    def decrypt_rand(self, z, c, p, n):
        for i in range(n):
            f = z**p + c;
            print("(decrypt_rand(z[%s]:%s)" % (n - i - 1, z));
            z = f;
        return z;

    def decrypt_ptxt(self, z, c, p, n):
        ptxt = "";
        for i in range(n):
            f = z**p + c;
            r = croots(f - c, p);
            b = froot(z, r);
            ptxt += str(b);
            print("(decrypt_ptxt(z[%s]:(%s):%s)" % (n - i - 1, b, z));
            z = f;
        ptxt = ptxt[::-1];
        return [ptxt, z];

    def encrypt(self, z, skey, ptxt):
        z = self.encrypt_ptxt(z, skey.c_0, skey.p_0, ptxt);
        print("----------------------------");
        return self.encrypt_rand(z, skey.c_1, skey.p_1, skey.n);

    def decrypt(self, z, skey, n):
        z = self.decrypt_rand(z, skey.c_1, skey.p_1, skey.n);
        print("----------------------------");
        return self.decrypt_ptxt(z, skey.c_0, skey.p_0, n);




# Main Program
skey = ct_rifc_skey((0+0j), (-.75+.09j), (.1+.8j), 2, 3, 8, "hmac_secret_key");
rifc = ct_rifc();

ptxt = "01000001";
n = len(ptxt);

# Display environment
print("secret key: %s" % (skey));
print("plaintext: %s" % (ptxt));
print("__________________________________________");

# Encrypt
cp = rifc.encrypt(skey.z, skey, ptxt);
cpassert = hmac.new(skey.hmack.encode());
cpassert.update(str(cp).encode());
cphash = cpassert.hexdigest();
print("__________________________________________");

print("\ncipherhash:%s" % (cphash));
print("cipherpoint:%s\n" % (cp));
print("__________________________________________");

# Decrypt
# Eve can try to alter the cipherpoint, but it will alert Bob!  :^)
cp += (0+0j);
d = rifc.decrypt(cp, skey, n);
print("__________________________________________\n");

dcpassert = hmac.new(skey.hmack.encode());
dcpassert.update(str(cp).encode());
dcphash = dcpassert.hexdigest();

print("cipherhash: %s" % (dcphash));
print("decrypted: %s" % (d));

if (d[0] != ptxt or not hmac.compare_digest(cphash, dcphash)):
    print("Data Corrupted!");