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ADD: Added the xor compression test files from before, while the xor …
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…compression proved to be irreversible due to the pidgeon hole principle, it still may be feasible to use it in some form.
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gnu-user committed Jun 27, 2012
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357 changes: 357 additions & 0 deletions etc/research/compression/xor-compression/inverse_test.c
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/**
* The following is a demonstration to test the compression algorithm where a recipient
* receives a single byte Z which is the compressed message that was originally 2 bytes
* (X and Y) and was compressed to a single value Z. Both the sender and recipient know
* the constant C, the recipient must be able to recover the original 2 bytes (X and Y)
* in the exact same order given the single byte, Z received and known constant C.
*/
#include <stdio.h>
#include <stdbool.h>

#define BYTETOBINARYPATTERN "%d%d%d%d%d%d%d%d"

#define BYTETOBINARY(byte) \
(byte & 0x80 ? 1 : 0), \
(byte & 0x40 ? 1 : 0), \
(byte & 0x20 ? 1 : 0), \
(byte & 0x10 ? 1 : 0), \
(byte & 0x08 ? 1 : 0), \
(byte & 0x04 ? 1 : 0), \
(byte & 0x02 ? 1 : 0), \
(byte & 0x01 ? 1 : 0)

typedef unsigned char BYTE;

BYTE calcQ(BYTE *X, BYTE *Y, const BYTE *C)
{
// (X XNOR Y) XOR C
return (~(*X ^ *Y)) ^ *C;
}

BYTE calcR(BYTE *X, BYTE *Y, const BYTE *D)
{
// (X XNOR Y) XOR D
return (~(*X ^ *Y)) ^ *D;
}

/**
* Calculate Z, R XOR C and Q XOR D are equivalent
*
* Z = R XOR C = Q XOR D
*
**/
BYTE calcZ(BYTE *R, const BYTE *C)
{
// R XOR C
return *R ^ *C;
}


/**
* Calculate Z', R XNOR C and Q XNOR D are equivalent
*
* Z' = R XNOR C = Q XNOR D
*
* NOTE: An interesting fact about Z' is that it is equal to ~Z, this is the
* unique result that makes it possible to recover the variables X and Y!
*
**/
BYTE calcZprime(BYTE *Q, const BYTE *D)
{
// Q XNOR D
return ~(*Q ^ *D);
}


/**
* Calculate X from the value Z and known constant C
*
* X = Z XNOR C = Z' XOR C
*
**/
BYTE calcX(BYTE *Z, const BYTE *C)
{
// Z XNOR C
return ~(*Z ^ *C);
}


/**
* Calculate Y from the value Zprime and calculated value Q
*
* Y = Z' XNOR Q = Z XOR Q
*
**/
BYTE calcY(BYTE *Zprime, BYTE *Q)
{
// Z' XNOR Q
return ~(*Zprime ^ *Q);
}


int main(void)
{
// C MUST BE PRIME to ensure that it is co-prime with other values
const BYTE C = 0x07;

// D MUST be assigned the same value as Y
BYTE D = 0x00;

// Variable for the X, Y, etc. values calculated by the recipient
BYTE calculated_X = 0x00;
BYTE calculated_Y = 0x00;
BYTE calculated_Q = 0x00;
BYTE calculated_R = 0x00;
BYTE calculated_Z = 0x00;
BYTE calculated_Zprime = 0x00;

bool root_found = false;

BYTE Q = 0x00;
BYTE R = 0x00;

BYTE Z1 = 0x00;
BYTE Z2 = 0x00;

BYTE sender_Z1prime = 0x00;
BYTE sender_Z2prime = 0x00;

BYTE recipient_Zprime = 0x00;

// Iterate through every possible combination of the X and Y byte values to verify
// that it is possible to recover X and Y from Z given ANY combinations of values
for (BYTE X = 0x00; X < 0x10; ++X)
{
// For each value of X iterate for each value of Y incremented by 0x01
for (BYTE Y = 0x00; Y < 0x10; ++Y)
{
/**
* Simulate the sender compressing the 2 bytes into a single byte, Z and
* then sending Z to the recipient
*/
D = Y; // D MUST be same value as Y, D is not known to recipient
Q = calcQ(&X, &Y, &C);
R = calcR(&X, &Y, &D);

// Calculate Z using both equivalent methods, Z = R XOR C = Q XOR D
Z1 = calcZ(&R, &C);
Z2 = calcZ(&Q, &D);

// Calcualte Z' using both equivalent methods, Z' = R XNOR C = Q XNOR D
sender_Z1prime = calcZprime(&R, &C);
sender_Z2prime = calcZprime(&Q, &D);

// Verify that Z using both methods is equivalent (This is an AXIOM OF THE
// COMPRESSION ALGORITHM) so if it's wrong we have a major flaw
if (Z1 != Z2)
{
printf("Z1 NOT EQUIVALENT TO Z2!\n");
printf("SENDER X, Y:\t"BYTETOBINARYPATTERN", "BYTETOBINARYPATTERN"\t: %d, %d\n", BYTETOBINARY(X), BYTETOBINARY(Y), X, Y);
printf("Q:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Q)), 0xF0 ^ Q);
printf("R:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ R)), 0xF0 ^ R);
printf("Z1:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Z1)), 0xF0 ^ Z1);
printf("Z2:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Z2)), 0xF0 ^ Z2);
}

// Verify that Z' using both methods is equivalent (This is an AXIOM OF THE
// COMPRESSION ALGORITHM) so if it's wrong we have a major flaw
if (sender_Z1prime != sender_Z2prime)
{
printf("Z1 PRIME NOT EQUIVALENT TO Z2 PRIME!\n");
printf("SENDER X, Y:\t"BYTETOBINARYPATTERN", "BYTETOBINARYPATTERN"\t: %d, %d\n", BYTETOBINARY(X), BYTETOBINARY(Y), X, Y);
printf("Q:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Q)), 0xF0 ^ Q);
printf("R:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ R)), 0xF0 ^ R);
printf("Z1 PRIME:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ sender_Z1prime)), 0xF0 ^ sender_Z1prime);
printf("Z2 PRIME:\t\t"BYTETOBINARYPATTERN", %d\n\n", BYTETOBINARY((0xF0 ^ sender_Z2prime)), 0xF0 ^ sender_Z2prime);
}


/**
* Simulate the recipient receiving a single byte, Z and getting the original
* bytes X and Y from Z, the recipient knows the constant value C, which is prime
*/
// The user can get Z' which is ~Z, this is the UNIQUE property that makes it
// possible to recover X and Y by using the equations of for Z and Z' given the
// two values Z and Z' = ~Z
recipient_Zprime = ~(Z1);

// Verify that the Zprime the recipient gets from ~Z is ACTUALLY, the same Zprime
// that the sender calculated using the equations (This is an AXIOM OF THE
// COMPRESSION ALGORITHM), so if it's wrong we have a major flaw
if (recipient_Zprime != sender_Z1prime)
{
printf("RECIPIENT'S Z PRIME NOT EQUIVALENT TO SENDER'S Z PRIME!!!\n");
printf("SENDER X, Y:\t"BYTETOBINARYPATTERN", "BYTETOBINARYPATTERN"\t: %d, %d\n", BYTETOBINARY(X), BYTETOBINARY(Y), X, Y);
printf("Q:\t\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Q)), 0xF0 ^ Q);
printf("R:\t\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ R)), 0xF0 ^ R);
printf("SENDER Z PRIME:\t\t"BYTETOBINARYPATTERN", %d\n\n", BYTETOBINARY(sender_Z1prime), sender_Z1prime);
printf("RECIPIENT Z PRIME:\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(recipient_Zprime), recipient_Zprime);
}

// Now the user can calculate X very easily given a unique property when C is prime and D == Y
// The user has RECEIVED Z and BOTH recipient and sender KNOW C, UNKNOWN is Y == D
calculated_X = calcX(&Z1, &C);

// Verify that the CALCULATED X IS ACTUALLY EQUAL to the Sender's X value the recipients'
// calculated X should ALWAYS be equivalent to the sender's X when Y == D (This is an AXIOM OF THE
// COMPRESSION ALGORITHM), so if it's wrong we have a major flaw
if (calculated_X != X)
{
printf("RECIPIENT'S CALCULATED X NOT EQUIVALENT TO SENDER'S X!!!\n");
printf("Q:\t\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Q)), 0xF0 ^ Q);
printf("R:\t\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ R)), 0xF0 ^ R);
printf("SENDER X, Y:\t"BYTETOBINARYPATTERN", "BYTETOBINARYPATTERN"\t: %d, %d\n", BYTETOBINARY(X), BYTETOBINARY(Y), X, Y);
printf("RECIPIENT X:\t"BYTETOBINARYPATTERN"\t\t: %d\n\n", BYTETOBINARY(calculated_X), calculated_X);
}

/**
calculated_Y = 0x00;
calculated_Q = 0x00;
calculated_R = 0x00;
calculated_Z = 0x00;
calculated_Zprime = 0x00;
root_found = false;
calculated_Q = calcQ(&calculated_X, &Y, &C);
calculated_R = calcR(&calculated_X, &Y, &Y);
calculated_Z = calcZ(&calculated_R, &C);
calculated_Zprime = calcZprime(&calculated_Q, &Y);
calculated_Y = calcY(&calculated_Zprime, &calculated_Q);
printf("SENDER Q:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Q)), 0xF0 ^ Q);
printf("CALCULATED Q:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ calculated_Q)), 0xF0 ^ calculated_Q);
printf("SENDER R:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ R)), 0xF0 ^ R);
printf("CALCULATED R:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ calculated_R)), 0xF0 ^ calculated_R);
printf("SENDER Z:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Z1)), 0xF0 ^ Z1);
printf("CALCULATED Z:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ calculated_Z)), 0xF0 ^ calculated_Z);
printf("SENDER Z PRIME:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(sender_Z1prime), sender_Z1prime);
printf("RECIPIENT Z PRIME:\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(recipient_Zprime), recipient_Zprime);
printf("CALCULATED Z PRIME:\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(calculated_Zprime), calculated_Zprime);
printf("SENDER X, Y:\t"BYTETOBINARYPATTERN", "BYTETOBINARYPATTERN"\t: %d, %d\n", BYTETOBINARY(X), BYTETOBINARY(Y), X, Y);
printf("RECIPIENT X, Y:\t"BYTETOBINARYPATTERN", "BYTETOBINARYPATTERN"\t: %d, %d\n\n\n", BYTETOBINARY(calculated_X),
BYTETOBINARY(calculated_Y), calculated_X, calculated_Y);
*/
// Now solve for the unknown value Y, given the Z' value, X, and C, the only way to feasibly solve
// for Y is to perform a bruteforce search given the known values and the equations for
// Z' and Q. THERE MUST ONLY BE ONE ROOT, Y, GIVEN THE ROOT X , Z' and C (This is an AXIOM OF THE
// COMPRESSION ALGORITHM), so if it's wrong we have a major flaw, in fact its IMPOSSIBLE to
// reverse the compression unless Y == D is UNIQUE!!!!
for (BYTE Y_TEST = 0x00; Y_TEST < 0x10; ++Y_TEST)
{
calculated_Q = calcQ(&calculated_X, &Y_TEST, &C);
calculated_R = calcR(&calculated_X, &Y_TEST, &Y_TEST);

calculated_Z = calcZ(&calculated_R, &C);
calculated_Zprime = calcZprime(&calculated_Q, &Y_TEST);

//printf("Calculated X: %d\n", calculated_X);
//printf("Calculated Y: %d\n", Y_TEST);
//printf("Calculated Q: %d\n", 0xF0 ^ calculated_Q);
//printf("Calculated R: %d\n", 0xF0 ^ calculated_R);
//printf("Calculated Z: %d\n", 0xF0 ^ calculated_Z);
//printf("Calculated Z PRIME: %d\n\n", calculated_Zprime);

/**
printf("SENDER Q:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Q)), 0xF0 ^ Q);
printf("CALCULATED Q:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ calculated_Q)), 0xF0 ^ calculated_Q);
printf("SENDER R:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ R)), 0xF0 ^ R);
printf("CALCULATED R:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ calculated_R)), 0xF0 ^ calculated_R);
printf("SENDER Z:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Z1)), 0xF0 ^ Z1);
printf("CALCULATED Z:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ calculated_Z)), 0xF0 ^ calculated_Z);
printf("SENDER Z PRIME:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(sender_Z1prime), sender_Z1prime);
printf("RECIPIENT Z PRIME:\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(recipient_Zprime), recipient_Zprime);
printf("CALCULATED Z PRIME:\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(calculated_Zprime), calculated_Zprime);
printf("SENDER X, Y:\t"BYTETOBINARYPATTERN", "BYTETOBINARYPATTERN"\t: %d, %d\n", BYTETOBINARY(X), BYTETOBINARY(Y), X, Y);
printf("RECIPIENT X, Y:\t"BYTETOBINARYPATTERN", "BYTETOBINARYPATTERN"\t: %d, %d\n\n\n", BYTETOBINARY(calculated_X),
BYTETOBINARY(Y_TEST), calculated_X, Y_TEST);
*/

// If the calculated Z' given the calculated root Y matches the known Z' which is
// Z' = ~Z, then the root Y satisfies the equations and IS THE ROOT. Remember that
// for the sender as well as the recipient Y == D, this is the unique property that
// makes it possible to avoid the 0000/1111 cancellations of XOR
if (calculated_X == calcX(&calculated_Z, &C))
{
if (Y_TEST == calcY(&calculated_Zprime, &calculated_Q))
{
if (Z1 == calculated_Z && recipient_Zprime == calculated_Zprime)
{
// X XOR Y SHOULD NOT BE EQUIVALENT TO Z, ONLY THE UNIQUE ROOT IS NOT A COMBINATION
// OF X XOR Y = Z
//if (Y_TEST == Y)
if ((calculated_X ^ Y_TEST) != calculated_Z)
{
calculated_Y = Y_TEST;
root_found = true;
break;
}
}
}
}
}
// If the correct root is found I will be DELIGHTED, the calculated Y MUST
// be UNIQUE and equivalent to the initial Y value of the sender, if it does
// not match we have a major flaw,
if (calculated_Y == Y)
{
printf("RECIPIENT'S CALCULATED Y EQUIVALENT TO SENDER'S Y!!!!!!!!!!!!!!!!!!!!\n");
printf("SENDER Q:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Q)), 0xF0 ^ Q);
printf("CALCULATED Q:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ calculated_Q)), 0xF0 ^ calculated_Q);
printf("SENDER R:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ R)), 0xF0 ^ R);
printf("CALCULATED R:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ calculated_R)), 0xF0 ^ calculated_R);
printf("SENDER Z:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Z1)), 0xF0 ^ Z1);
printf("CALCULATED Z:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ calculated_Z)), 0xF0 ^ calculated_Z);
printf("SENDER Z PRIME:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(sender_Z1prime), sender_Z1prime);
printf("RECIPIENT Z PRIME:\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(recipient_Zprime), recipient_Zprime);
printf("CALCULATED Z PRIME:\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(calculated_Zprime), calculated_Zprime);
printf("SENDER X, Y:\t"BYTETOBINARYPATTERN", "BYTETOBINARYPATTERN"\t: %d, %d\n", BYTETOBINARY(X), BYTETOBINARY(Y), X, Y);
printf("RECIPIENT X, Y:\t"BYTETOBINARYPATTERN", "BYTETOBINARYPATTERN"\t: %d, %d\n\n", BYTETOBINARY(calculated_X),
BYTETOBINARY(calculated_Y), calculated_X, calculated_Y);
}
// major flaw, back to the drawing board!
else
{
printf("RECIPIENT'S CALCULATED Y NOT EQUIVALENT TO SENDER'S Y!!!!!!!!!!!!!!!!!!!!\n");
printf("SENDER Q:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Q)), 0xF0 ^ Q);
printf("CALCULATED Q:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ calculated_Q)), 0xF0 ^ calculated_Q);
printf("SENDER R:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ R)), 0xF0 ^ R);
printf("CALCULATED R:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ calculated_R)), 0xF0 ^ calculated_R);
printf("SENDER Z:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Z1)), 0xF0 ^ Z1);
printf("CALCULATED Z:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ calculated_Z)), 0xF0 ^ calculated_Z);
printf("SENDER Z PRIME:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(sender_Z1prime), sender_Z1prime);
printf("RECIPIENT Z PRIME:\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(recipient_Zprime), recipient_Zprime);
printf("CALCULATED Z PRIME:\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(calculated_Zprime), calculated_Zprime);
printf("SENDER X, Y:\t"BYTETOBINARYPATTERN", "BYTETOBINARYPATTERN"\t: %d, %d\n", BYTETOBINARY(X), BYTETOBINARY(Y), X, Y);
printf("RECIPIENT X, Y:\t"BYTETOBINARYPATTERN", "BYTETOBINARYPATTERN"\t: %d, %d\n\n", BYTETOBINARY(calculated_X),
BYTETOBINARY(calculated_Y), calculated_X, calculated_Y);
}
}
/**
Zprime = calcZprime(&Q, &D);
calculated_Y = calcY(&Zprime, &Q);
if ( X == calculated_X && Y == calculated_Y)
{
printf("Q:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Q)), 0xF0 ^ Q);
printf("R:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ R)), 0xF0 ^ R);
printf("Z1:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Z1)), 0xF0 ^ Z1);
printf("Z2:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY((0xF0 ^ Z2)), 0xF0 ^ Z2);
);
//printf("Z':\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(Zprime), Zprime);
printf("Q:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(Q), Q);
printf("R:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(R), R);
printf("Z:\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(Z), Z);
printf("Z':\t\t"BYTETOBINARYPATTERN", %d\n", BYTETOBINARY(Zprime), Zprime);
printf("INITIAL X, Y:\t"BYTETOBINARYPATTERN", "BYTETOBINARYPATTERN"\t: %d, %d\n", BYTETOBINARY(X), BYTETOBINARY(Y), X, Y);
printf("SOLVED X, Y:\t"BYTETOBINARYPATTERN", "BYTETOBINARYPATTERN"\t: %d, %d\n\n",
BYTETOBINARY(calculated_X), BYTETOBINARY(calculated_Y), calculated_X, calculated_Y);
}*/
}
return 0;
}
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