Reverse Fractal Iteration N-Ary Encoding with Random Offset

# Chris M. Thomasson 7/22/2016
# Reverse Fractal Iteration N-Ary Encoding with Random Offset
# Does NOT work with fractional powers yet!
# Thats coming...


import math;
import random;


# 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);


# Generate Random Complex Number
def randc(nmin, nmax):
    d = nmax - nmin;
    x = nmin + random.random() * d;
    y = nmin + random.random() * d;
    return complex(x, y);


# Complex Roots
def croots(z, p):
    l = cabs(z);
    s = l**(1.0 / p);
    a = carg(z) / p;
    n = math.ceil(math.fabs(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;


# Encrypt N-Ary Stream
def encrypt_nary(z, c, p, s, pt):
    n = 0;
    for i in pt:
        r = croots(z - c, p);
        z = r[int(i)];
        a = carg(z);
        print("z[" + str(n) + "]:(" + i + "):" + str(z) + ", a:" + str(a));
        n = n + 1;
    z += s;
    print("----------------------");
    print("Ciphertext:" + str(z));
    return z;

# Decrypt N-Ary Stream
def decrypt_nary(z, c, p, s, n):
    pt = "";
    print("Ciphertext:" + str(ct));
    print("----------------------");
    z -= s;
    for i in range(n):
        f = z**p + c;
        r = croots(f - c, p);
        b = froot(z, r);
        pt += str(b);
        a = carg(z);
        print("z[" + str(n - i - 1) + "]:(" + str(b) + "):" + str(z) + ", a:" + str(a));
        z = f;
    pt = pt[::-1]; # reverse symbols
    return pt;




# The Secret Key
c = (-.75+.09j);
z = (0+0j);
p = 5;
s = randc(-9999999, 9999999);

# The Plaintext
pt0 = "0123443210";
n = len(pt0);

# Display our environment.
print("c:" + str(c));
print("z:" + str(z));
print("p:" + str(p));
print("s:" + str(s));
print("n:" + str(n));
print("pt0:" + str(pt0));
print("");print("");



print("Encrypt " + str(p) + "-Ary Stream: " + str(n) + " Iterations");
print("_________________________________________");

# The Ciphertext
ct = encrypt_nary(z, c, p, s, pt0);

print("_________________________________________");
print("\n");


print("Decrypt " + str(p) + "-Ary Stream: " + str(n) + " Iterations");
print("_________________________________________");

# The Decrypted Plaintext
pt1 = decrypt_nary(ct, c, p, s, n);

print("_________________________________________");
print("");



# Verify Data Integrity
print("pt1:" + pt1);
if pt0 != pt1: print("DATA CORRUPTED!!! ;^o");