[0CTF/TCTF 2019] zer0lfsr

Equation is given by $ X_i = X_{i-48} \oplus X_{i-23}$, $ Y_i = Y_{i-48} \oplus Y_{i-14}$, $ Z_i = Z_{i-48} \oplus Z_{i-42}$, 

 

The result bit and $X_i, Y_i, Z_i$ are same in 75% of probability, which is vulnerable to correlation attack.

 

moreover, if $a ! \equiv b (mod 6), Z_{a}, Z_{b}$ is independent. So you can recover $Z$ in $O(2^8 \times 8)$ by correlation.

 

$X$, $Y$ can be recovered paritally if $R_i = 0, Z_i = 1$, then $X_i = Y_i = 0$ and if $R_i = 1, Z_i = 0$, then $X_i = Y_i = 1$. And then recover other bits using$ X_i = X_{i-48} \oplus X_{i-23}$, $ Y_i = Y_{i-48} \oplus Y_{i-14}$

 

It is not guaranteed every bits can be recovered but fortunately it does.

#include <bits/stdc++.h>
using namespace std;
const int LEN = 8192 * 8;

int result[8192] = {
    0x32, 0xdb, 0xa9, 0xbf, 0xa,  0x23, 0x7,  0x53, 0x4e, 0x41, 0x9b, 0xe0,
    0x98, 0x44, 0xcf, 0x54, 0xa4, 0xa4, 0x30, 0xbe, 0x75, 0x3d, 0x5f, 0x5b,
    0x14, 0xa3, 0x12, 0x9a, 0x89, 0xe5, 0x24, 0xc5, 0x8f, 0xd1, 0x1a, 0x42,
    0xc4, 0x22, 0x36, 0xd5, 0x18, 0xbb, 0x2c, 0xa1, 0x6,  0x25, 0xa0, 0x4a,
    0x26, 0xa8, 0x26, 0xee, 0xaa, 0x55, 0x26, 0xf3, 0x9d, 0xd,  0xe9, 0x65,
    0xb8, 0x22, 0x53, 0x68, 0x89, 0xc1, 0x5a, 0x7b, 0xd2, 0x44, 0x72, 0x62,
    0xf9, 0x60, 0xf,  0xb2, 0x76, 0xc5, 0x14, 0x34, 0xb4, 0x34, 0xa,  0x21,
    0x4,  0x2,  0x69, 0x16, 0xaa, 0xeb, 0xa,  0x65, 0x90, 0xb,  0x92, 0xe8,
    0xa6, 0xbf, 0x80, 0xbc, 0xf8, 0x43, 0x94, 0x61, 0x81, 0x24, 0x29, 0xc8,
    0xe,  0xa0, 0x4a, 0x3e, 0x43, 0x3,  0x26, 0xe9, 0xc3, 0x54, 0x89, 0xc6,
    0x0,  0x90, 0x8c, 0x9e, 0xb9, 0xcc, 0xb0, 0xb8, 0x18, 0x3a, 0xea, 0x50,
    0x87, 0x62, 0x4d, 0x2f, 0x3a, 0xce, 0xfc, 0x76, 0x82, 0xad, 0x86, 0xe,
    0xa6, 0xfa, 0xce, 0x80, 0x10, 0xc,  0x2a, 0xd0, 0xba, 0xc3, 0x43, 0x43,
    0xa8, 0xda, 0xb1, 0x92, 0xc9, 0xad, 0xb4, 0x64, 0x6c, 0x2,  0x33, 0x86,
    0x48, 0x4b, 0x85, 0xee, 0x10, 0x37, 0x29, 0x7,  0x6b, 0xaa, 0xa0, 0x88,
    0xba, 0xd3, 0x62, 0x7e, 0x36, 0x86, 0x4e, 0xd2, 0xdf, 0xac, 0x9b, 0x31,
    0x78, 0x3e, 0xb1, 0x26, 0xd3, 0x5a, 0x10, 0x9a, 0xd0, 0x5,  0x94, 0x6f,
    0xc8, 0xa2, 0xe9, 0xb0, 0xb2, 0xcd, 0xa,  0x3b, 0xf0, 0x95, 0x61, 0x80,
    0x98, 0x78, 0xab, 0x85, 0xe1, 0x9f, 0x8b, 0x10, 0xc,  0x84, 0x13, 0xae,
    0xe4, 0x30, 0xbb, 0xca, 0xaa, 0x86, 0xab, 0x6a, 0x40, 0xac, 0xac, 0x37,
    0xb,  0xbb, 0x61, 0x13, 0x11, 0x98, 0x25, 0xb2, 0x25, 0x60, 0x70, 0x81,
    0x6d, 0x5f, 0xa2, 0x1c, 0xd3, 0xd7, 0x6,  0x82, 0x2e, 0xa,  0xf0, 0x8e,
    0xdf, 0x7f, 0xe4, 0x11, 0x23, 0xa8, 0x25, 0x96, 0xe0, 0xa,  0x89, 0xa2,
    0xa5, 0xbc, 0xe1, 0x2a, 0x79, 0x7c, 0x8e, 0xc2, 0x69, 0x7a, 0x13, 0xe6,
    0xaa, 0x39, 0x5,  0xb6, 0xf9, 0x85, 0x25, 0x8,  0x4a, 0x8c, 0x3,  0x7a,
    0x2a, 0xca, 0xa,  0x24, 0xd7, 0x40, 0xb6, 0xc9, 0xc3, 0xa,  0x3,  0xe2,
    0xda, 0x4f, 0xc6, 0x19, 0xe8, 0xad, 0x24, 0xde, 0x50, 0x3,  0x26, 0x49,
    0xe,  0xbc, 0xee, 0x99, 0x58, 0x2,  0xf7, 0x87, 0x43, 0xa4, 0xd2, 0xfc,
    0xa6, 0x31, 0xc9, 0x3a, 0x51, 0x42, 0x4b, 0x42, 0x27, 0x88, 0x54, 0x1f,
    0xda, 0x0,  0xc5, 0x3c, 0x54, 0x2f, 0x22, 0xb3, 0x6,  0x60, 0x4b, 0xa3,
    0x9e, 0x11, 0x3e, 0x3a, 0x2,  0x38, 0x62, 0x30, 0x98, 0xb0, 0x20, 0x40,
    0xc5, 0x73, 0xb0, 0x9a, 0xa2, 0xe9, 0x60, 0xbe, 0x31, 0x7a, 0xb3, 0x81,
    0x84, 0x59, 0x40, 0x34, 0xa3, 0xc6, 0x4a, 0x80, 0x6e, 0xb4, 0x15, 0x4c,
    0x3c, 0xb0, 0x4f, 0xd4, 0x16, 0xcf, 0x9d, 0x21, 0x0,  0x6a, 0xe3, 0x4f,
    0xc8, 0x15, 0x8c, 0x38, 0xa7, 0xde, 0x94, 0x6a, 0x72, 0x85, 0x71, 0xa8,
    0xa4, 0xa8, 0x8b, 0xa6, 0x2b, 0x68, 0xef, 0xca, 0x45, 0xbf, 0x95, 0x8d,
    0x10, 0xd1, 0x82, 0x1d, 0x3c, 0x28, 0x20, 0x32, 0x83, 0x38, 0x39, 0xac,
    0x88, 0x90, 0xa9, 0x35, 0xf0, 0x26, 0x4b, 0x49, 0xcd, 0x3a, 0x6b, 0x64,
    0x19, 0xeb, 0xa1, 0x24, 0x86, 0xe8, 0x0,  0x89, 0xa9, 0xc,  0xa8, 0xaa,
    0x4a, 0x61, 0xe0, 0x1e, 0x82, 0x4b, 0xa0, 0xb,  0xef, 0xb2, 0x98, 0x0,
    0x15, 0x41, 0x40, 0x2c, 0x9,  0xc,  0x4,  0x80, 0x42, 0x6c, 0x85, 0x82,
    0x34, 0x81, 0x91, 0x7e, 0x95, 0xce, 0x60, 0x27, 0x2f, 0x9e, 0xdb, 0x54,
    0x1c, 0xa8, 0x19, 0x20, 0xb8, 0xe2, 0x36, 0xe2, 0x4d, 0xa9, 0xbc, 0x30,
    0x80, 0x3a, 0xf,  0x20, 0x89, 0x6e, 0x6,  0xf8, 0xd1, 0x84, 0x10, 0xcd,
    0x1c, 0x79, 0x4b, 0x1,  0x62, 0x2,  0x74, 0x6a, 0xbf, 0x90, 0xa4, 0xc0,
    0x84, 0xe0, 0x26, 0x27, 0x30, 0x86, 0x0,  0xfb, 0x26, 0xa6, 0x57, 0xc5,
    0x2a, 0x4a, 0x48, 0x6a, 0x92, 0x98, 0xb8, 0x90, 0x53, 0x9c, 0xf8, 0xb6,
    0x56, 0xa0, 0xe8, 0x1a, 0x89, 0x23, 0xf5, 0x2e, 0xb1, 0x64, 0xd9, 0x29,
    0x0,  0x93, 0x5,  0xd0, 0xf6, 0xca, 0xb9, 0xe2, 0xe0, 0xa0, 0x32, 0x26,
    0x2d, 0x5a, 0xcd, 0xbe, 0x23, 0x98, 0x62, 0xa1, 0xcd, 0x31, 0x47, 0x8a,
    0xb1, 0x5a, 0x1a, 0x1,  0x2,  0x3f, 0xa3, 0x3e, 0xb9, 0x9f, 0xbc, 0x95,
    0xb0, 0xbb, 0x4a, 0x26, 0xd8, 0x2b, 0x32, 0x73, 0x20, 0x14, 0x13, 0x80,
    0x55, 0x5a, 0x24, 0x32, 0x80, 0x4,  0x20, 0x6b, 0xec, 0x1c, 0x17, 0xde,
    0x2c, 0xf2, 0x1,  0xc,  0x64, 0xc,  0x3e, 0x2f, 0xe9, 0x40, 0xe7, 0xa2,
    0xfc, 0x2,  0xa8, 0x99, 0xc3, 0xe9, 0xc4, 0x82, 0xe3, 0x0,  0x64, 0xb9,
    0x8c, 0x5a, 0x1,  0xb2, 0x90, 0x31, 0xfd, 0xba, 0x45, 0x61, 0xe5, 0x6,
    0x28, 0xe1, 0xa0, 0xe,  0x23, 0x2e, 0x36, 0x4a, 0x3f, 0x26, 0xf2, 0xd5,
    0xba, 0x88, 0xd1, 0x1c, 0x82, 0xe7, 0x9e, 0xe1, 0x58, 0x10, 0xc0, 0x80,
    0x28, 0xa0, 0xf2, 0x32, 0xce, 0xf5, 0x48, 0x78, 0xd2, 0x98, 0x72, 0x3,
    0xa4, 0x9b, 0xec, 0x82, 0x63, 0xaa, 0x8a, 0x10, 0x8c, 0x38, 0x60, 0xcb,
    0xc,  0x4a, 0x17, 0x9a, 0x96, 0x8d, 0x92, 0x74, 0xdd, 0x28, 0x74, 0x6e,
    0x6a, 0x4e, 0x87, 0x5b, 0x63, 0xe5, 0x8f, 0x4d, 0xca, 0x6c, 0x2a, 0x48,
    0x6c, 0x99, 0x28, 0x78, 0x88, 0x82, 0x9e, 0x20, 0x71, 0x5f, 0x88, 0xef,
    0x22, 0x19, 0x5,  0x3e, 0xfa, 0x24, 0x4,  0xc1, 0x4e, 0x98, 0x10, 0x9a,
    0x0,  0x89, 0xda, 0x16, 0x22, 0xe1, 0xc0, 0x22, 0xcc, 0x94, 0x13, 0xd8,
    0xc8, 0x81, 0x90, 0x12, 0xcd, 0xfe, 0x95, 0x1,  0x2,  0x8c, 0xd2, 0x9,
    0xfc, 0x2a, 0x32, 0xa4, 0x10, 0x79, 0x8d, 0xa8, 0x85, 0x24, 0x8,  0x49,
    0xbb, 0x48, 0x2f, 0x36, 0xa8, 0x63, 0x14, 0x90, 0xd0, 0x45, 0xc0, 0xe4,
    0x2f, 0x22, 0x45, 0x2,  0x5b, 0x2c, 0x69, 0xb1, 0xc4, 0x10, 0xda, 0x63,
    0x8,  0x39, 0x4e, 0xf2, 0x3a, 0xed, 0xce, 0xd2, 0xa0, 0x9c, 0x82, 0xd4,
    0x26, 0xcb, 0xb9, 0x34, 0x28, 0xa7, 0x34, 0xe4, 0x68, 0xc,  0x63, 0x26,
    0xa0, 0xe,  0x4f, 0xd8, 0x1c, 0x45, 0x94, 0x11, 0xc,  0x18, 0x8f, 0x0,
    0x20, 0x32, 0x6e, 0x3a, 0x43, 0x69, 0x25, 0xf6, 0x98, 0xb0, 0x99, 0x43,
    0x20, 0x9,  0xbe, 0xfe, 0xda, 0x60, 0x9a, 0xf8, 0x47, 0x29, 0x2a, 0x46,
    0x2,  0xab, 0x9,  0x8a, 0x7c, 0xe3, 0xe8, 0x30, 0x81, 0x6,  0x28, 0x2d,
    0x86, 0x7a, 0xaa, 0xd6, 0x51, 0x4e, 0x38, 0x50, 0x4f, 0x21, 0x73, 0x1b,
    0x8,  0x11, 0xaf, 0x92, 0xc2, 0x9c, 0x7c, 0x74, 0x9e, 0x32, 0x38, 0x86,
    0x1f, 0x63, 0xe4, 0xab, 0x79, 0x32, 0x3a, 0x8b, 0x2a, 0x3a, 0x92, 0x2c,
    0x3a, 0x1d, 0x42, 0xaa, 0x90, 0x86, 0x5c, 0x86, 0xe9, 0x30, 0x9b, 0x6a,
    0x9f, 0xbe, 0xa0, 0x6,  0xc3, 0x6e, 0x10, 0x7a, 0x55, 0xa2, 0x9c, 0xcf,
    0x6,  0x47, 0x74, 0xbe, 0xb6, 0x4e, 0xbf, 0x19, 0xa4, 0x98, 0x65, 0x24,
    0x2b, 0xe9, 0xeb, 0x8e, 0x43, 0x8e, 0x4,  0xf2, 0xc,  0x4,  0x22, 0xae,
    0xa4, 0x5a, 0x8b, 0x46, 0xb9, 0x7,  0x91, 0x1a, 0x6c, 0x2c, 0x8b, 0x7,
    0x2e, 0xda, 0x61, 0x4,  0x53, 0x2,  0x4,  0xf0, 0x4e, 0x28, 0x72, 0xa5,
    0xec, 0x9d, 0x2c, 0x2c, 0x8b, 0xdf, 0xd6, 0x1e, 0xab, 0x12, 0xe0, 0xe,
    0xb1, 0x2f, 0x6f, 0xd8, 0x8,  0xa0, 0x4,  0xaf, 0xe1, 0x50, 0x9b, 0xba,
    0x24, 0x4a, 0xe1, 0xf,  0x40, 0xcd, 0xf,  0xd2, 0xed, 0xa6, 0xeb, 0x60,
    0xaa, 0x18, 0x15, 0x24, 0xe0, 0xe,  0x1d, 0x11, 0x8,  0xf,  0xa1, 0x4a,
    0x2e, 0x53, 0xab, 0x4,  0x53, 0x40, 0x4,  0xd8, 0xf6, 0x52, 0xe2, 0x8e,
    0xae, 0x7b, 0x44, 0x18, 0xec, 0xc,  0x10, 0xbf, 0x66, 0x22, 0xe9, 0xb1,
    0x8e, 0xa8, 0x9e, 0x9a, 0x38, 0x5,  0xe2, 0x8e, 0xe4, 0x5c, 0xea, 0xc2,
    0xdb, 0x11, 0x8f, 0x2a, 0x84, 0x4a, 0xa,  0x66, 0xb3, 0xbc, 0x52, 0x8b,
    0xc2, 0xc2, 0x68, 0x31, 0xc0, 0x6f, 0xa3, 0x7c, 0xa6, 0x21, 0x79, 0xf3,
    0x96, 0x74, 0x86, 0xba, 0x6,  0x60, 0xba, 0x80, 0x89, 0x3a, 0x92, 0xd2,
    0xbf, 0x92, 0xae, 0x16, 0x82, 0xa8, 0x3d, 0x8b, 0x2d, 0xb9, 0x1a, 0x60,
    0xc,  0x5b, 0x4c, 0x94, 0x3e, 0x60, 0xb0, 0xa0, 0xca, 0x74, 0xa3, 0xe4,
    0xe2, 0x23, 0x76, 0x7c, 0xc9, 0x8a, 0x9d, 0x21, 0x2,  0x2b, 0xe7, 0xae,
    0x85, 0x85, 0x4e, 0x90, 0xf5, 0xcb, 0x94, 0x22, 0x38, 0xa6, 0x90, 0x31,
    0x8,  0xff, 0x99, 0xe2, 0x3a, 0xa,  0xee, 0x8c, 0x3f, 0x8e, 0x24, 0x77,
    0x94, 0xd6, 0xc4, 0x8b, 0xa5, 0xfc, 0x20, 0xb6, 0x5,  0x20, 0xbb, 0x2e,
    0x3c, 0xb9, 0x8f, 0x4,  0xe2, 0x24, 0xaa, 0x7c, 0xc,  0x3f, 0x19, 0xd4,
    0xb9, 0x64, 0xb0, 0x65, 0x82, 0xa3, 0x0,  0xb,  0xe9, 0x40, 0x1a, 0x60,
    0xa0, 0x61, 0xe0, 0x6,  0xd0, 0xa1, 0x92, 0xb,  0xe9, 0x9a, 0xf8, 0x96,
    0x2c, 0x71, 0x95, 0xa,  0xb,  0x9c, 0xa,  0x47, 0x48, 0x3e, 0xd3, 0x6b,
    0x5,  0xeb, 0xc1, 0xb0, 0x4d, 0x42, 0x39, 0x62, 0xe,  0xbe, 0xcd, 0x42,
    0x58, 0xe8, 0xbf, 0x4,  0xb9, 0xc8, 0x0,  0x2b, 0xc3, 0x82, 0xf0, 0x42,
    0xd8, 0x62, 0x42, 0x25, 0xbe, 0xe5, 0x27, 0xba, 0x66, 0x90, 0x8,  0x4c,
    0x1a, 0x44, 0x4b, 0x20, 0x43, 0xb3, 0x3d, 0xb2, 0x8f, 0x8a, 0xd6, 0x8b,
    0x20, 0xd8, 0x6b, 0x6,  0x54, 0x2,  0x30, 0xc3, 0xa3, 0xbc, 0xd0, 0x24,
    0x5a, 0x2,  0xca, 0xdb, 0xc1, 0x89, 0xfd, 0x89, 0xab, 0x36, 0x76, 0xe2,
    0x4e, 0x0,  0x6b, 0x32, 0x9b, 0x2e, 0xee, 0xb8, 0xb1, 0x98, 0xc7, 0x48,
    0x54, 0x16, 0x63, 0xf0, 0x2,  0xca, 0x94, 0x88, 0x94, 0x90, 0x36, 0x46,
    0xa4, 0x1e, 0xc9, 0x98, 0x33, 0x80, 0x2a, 0x99, 0xef, 0x94, 0xc9, 0x72,
    0x92, 0x90, 0x3a, 0xc5, 0xa,  0x27, 0xec, 0x11, 0xa1, 0x2c, 0xa9, 0xc7,
    0xa0, 0x70, 0xcc, 0xa9, 0x59, 0x6b, 0xa4, 0xca, 0x41, 0x90, 0xd6, 0xa,
    0x34, 0x70, 0xa4, 0x22, 0x32, 0xa1, 0xa1, 0xb9, 0xb9, 0x2c, 0x51, 0xc0,
    0xa0, 0xb0, 0x33, 0x8,  0x60, 0x32, 0xf6, 0x7b, 0xe2, 0x1,  0x52, 0xa4,
    0x2c, 0x84, 0xd0, 0xd8, 0x29, 0xad, 0x54, 0x28, 0x31, 0x34, 0x61, 0xac,
    0x1e, 0xce, 0x29, 0x29, 0x8b, 0xfb, 0xa9, 0x98, 0x4d, 0x30, 0xf3, 0x27,
    0xc,  0xd,  0x8,  0x4c, 0x85, 0x4e, 0xc,  0x68, 0x48, 0x6c, 0xf7, 0xf9,
    0xbc, 0x89, 0x22, 0x1,  0x8c, 0xae, 0xbe, 0xb0, 0x4,  0x9e, 0xf4, 0x89,
    0x62, 0xfd, 0x42, 0x7a, 0x4a, 0x29, 0x96, 0xb0, 0x41, 0xb2, 0xe,  0x22,
    0xa1, 0x1c, 0x34, 0x94, 0xfa, 0xe3, 0x82, 0x91, 0x1b, 0x3e, 0x46, 0x9,
    0x12, 0x7e, 0x53, 0x8,  0x66, 0x9a, 0x8e, 0xc1, 0xeb, 0xf6, 0xec, 0x6f,
    0xa0, 0xb1, 0xa4, 0x12, 0xbf, 0x27, 0x6f, 0x7,  0x2e, 0xa,  0x90, 0x68,
    0x3e, 0xb2, 0x9e, 0xf9, 0xd4, 0xc0, 0xaf, 0x3a, 0x96, 0x1e, 0xa3, 0xe8,
    0x22, 0x98, 0x1,  0xaa, 0x32, 0x28, 0xa4, 0x5b, 0x1a, 0x16, 0x36, 0x50,
    0x91, 0x2,  0xee, 0xd0, 0xe2, 0xe6, 0xb2, 0xb6, 0xf,  0x3d, 0x1e, 0x41,
    0x98, 0xa2, 0x80, 0x24, 0xf9, 0xdf, 0x94, 0x58, 0x9a, 0x86, 0x92, 0xa,
    0xcc, 0xaa, 0x2e, 0xaf, 0x52, 0xa7, 0x62, 0x2f, 0xa6, 0xd0, 0xb4, 0x62,
    0xa6, 0xf0, 0x6f, 0xb9, 0x8,  0x61, 0x2,  0xf6, 0xa4, 0xac, 0x80, 0x4,
    0x8,  0x78, 0x81, 0x9,  0x9c, 0x64, 0x2d, 0xd6, 0xcd, 0x93, 0xf4, 0xa7,
    0x48, 0x61, 0xf,  0x9c, 0x9a, 0xfd, 0x32, 0x23, 0x20, 0x21, 0x8e, 0x71,
    0x10, 0x1b, 0xed, 0x0,  0xaf, 0xfb, 0x2a, 0x61, 0xfa, 0xaf, 0x92, 0xc,
    0xb9, 0x2b, 0x2b, 0x63, 0x71, 0x4b, 0x24, 0xc2, 0xa,  0x78, 0x5d, 0x2e,
    0xc,  0x29, 0x7a, 0xa6, 0xa7, 0x3,  0x6,  0xe7, 0xc0, 0xb4, 0x28, 0xf2,
    0x1d, 0x27, 0xa4, 0xbf, 0x60, 0x7c, 0x1c, 0xbb, 0x45, 0x44, 0xfa, 0x42,
    0x21, 0xea, 0x61, 0x44, 0xf8, 0xda, 0x98, 0xda, 0x3,  0xe4, 0xcb, 0xca,
    0xc6, 0xe1, 0x7a, 0xe3, 0x11, 0xf,  0x3c, 0xd4, 0x4a, 0x2,  0x46, 0xb,
    0x29, 0x50, 0x9e, 0x52, 0xc7, 0x41, 0x98, 0xf2, 0x77, 0x6a, 0x30, 0x25,
    0x2,  0xa3, 0xf3, 0xb6, 0xd9, 0x6,  0x33, 0xd6, 0x5c, 0x2b, 0x11, 0x8a,
    0xd1, 0xd5, 0x62, 0x32, 0xa2, 0x6c, 0x16, 0x82, 0xf9, 0x2a, 0xca, 0xa5,
    0x5f, 0x72, 0x80, 0x84, 0x57, 0x5c, 0x92, 0x90, 0xd0, 0x53, 0x8c, 0xea,
    0x34, 0x71, 0xe5, 0xb4, 0xb2, 0x67, 0x3c, 0x1f, 0x68, 0x99, 0x22, 0x2,
    0x3c, 0xc1, 0xdb, 0x96, 0x27, 0xe,  0x80, 0x9e, 0x1,  0xa4, 0x2b, 0x4f,
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    0x41, 0x2a, 0xc1, 0x8e, 0x44, 0x48, 0x5f, 0x2,  0x9,  0xa0, 0x1b, 0x4b,
    0x9f, 0x10, 0x55, 0x11, 0xbb, 0x49, 0x2e, 0x49, 0x88, 0xd,  0xa6, 0xcb,
    0x2c, 0xb,  0x19, 0x24, 0xf3, 0xd5, 0xe8, 0x4a, 0x82, 0x58, 0x3,  0xba,
    0x9d, 0xa1, 0x12, 0x5d, 0xe2, 0xd,  0x24, 0x88, 0x68, 0x2a, 0xeb, 0x60,
    0x4a, 0x90, 0xd,  0x59, 0x7a, 0x7,  0x94, 0x86, 0x6c, 0x54, 0xc3, 0xce,
    0x9c, 0x11, 0x4d, 0x28, 0x84, 0x46, 0x42, 0xa,  0x29, 0x20, 0x52, 0x87,
    0x82, 0x82, 0x41, 0x34, 0xc6, 0x4e, 0x67, 0x70, 0xd6, 0x55, 0xab, 0xa6,
    0x9e, 0x41, 0x36, 0x58, 0x62, 0x58, 0x22, 0x84, 0xf,  0x38, 0x18, 0x46,
    0xee, 0x33, 0x86, 0x1b, 0x83, 0xc9, 0x22, 0x32, 0x5,  0xfe, 0x3e, 0xc1,
    0x81, 0x31, 0x47, 0x11, 0x10, 0xc0, 0xc3, 0x84, 0x4a, 0x6,  0x4,  0x45,
    0x73, 0x30, 0xc6, 0x64, 0xd,  0xcd, 0x9f, 0x25, 0x9,  0x5a, 0x69, 0xed,
    0x86, 0x51, 0x86, 0xc,  0x82, 0x1b, 0x4,  0xa2, 0xc,  0x24, 0x0,  0xb1,
    0x8c, 0x23, 0x87, 0xbc, 0x2c, 0x4c, 0x92, 0x4b, 0x4f, 0x9c, 0xa8, 0x61,
    0x81, 0xc7, 0x84, 0x44, 0x31, 0x50, 0x26, 0x0,  0x1d, 0x21, 0xc5, 0x2c,
    0x74, 0x93, 0x4b, 0x0,  0x50, 0x67, 0x44, 0x60, 0x1d, 0x90, 0x21, 0x45,
    0xc0, 0x63, 0x30, 0xc,  0x40, 0x24, 0x41, 0xca, 0x6c, 0x4,  0x48, 0xe5,
    0x22, 0x41, 0xea, 0x4f, 0x52, 0x38, 0xf2, 0x3f, 0xcf, 0x9a, 0xa,  0x45,
    0xd0, 0xe0, 0x42, 0x1e, 0x6b, 0xa,  0x1e, 0x21, 0xe,  0x62, 0x4b, 0x8b,
    0x3d, 0x64, 0xc3, 0x39, 0xa9, 0xc3, 0x8,  0x3,  0x8b, 0xe,  0x8b, 0x55,
    0x19, 0xe8, 0x29, 0x21, 0xba, 0x53, 0x60, 0xd9, 0x41, 0xa,  0x18, 0xc8,
    0x8,  0x6e, 0x3,  0x84, 0x98, 0x60, 0xcf, 0x62, 0xea, 0x82, 0x11, 0x49,
    0x78, 0x41, 0x4b, 0x26, 0xb8, 0x97, 0x2a, 0x50, 0x8f, 0x10, 0xe0, 0xcd,
    0xbd, 0xd1, 0x3,  0x6e, 0x78, 0xc4, 0xc,  0xef, 0x23, 0x15, 0xd5, 0x26,
    0x2e, 0x1,  0xc9, 0x1a, 0x0,  0x79, 0x38, 0xd1, 0x66, 0xa1, 0x32, 0x2e,
    0x96, 0x4,  0xea, 0x1a, 0x99, 0x17, 0x28, 0x7a, 0xe5, 0x85, 0x77, 0x4e,
    0x32, 0x12, 0xca, 0x30, 0xc8, 0x8b, 0xc3, 0xe,  0xe5, 0xaa, 0xd2, 0x4a,
    0xbe, 0x8b, 0xc8, 0x9d, 0xa0, 0xc1, 0x1a, 0xa0, 0xae, 0xd4, 0x41, 0x8c,
    0xc8, 0x33, 0xa,  0x90, 0x3,  0x26, 0xe9, 0x20, 0xa3, 0x80, 0xd9, 0x87,
    0xac, 0x3a, 0x8,  0xab, 0xf9, 0xc6, 0xab, 0x2a, 0x24, 0x55, 0xc3, 0x8f,
    0x0,  0x30, 0x24, 0x2f, 0x52, 0xa6, 0x28, 0x8a, 0xee, 0x34, 0xc6, 0x65,
    0xf,  0x12, 0x7,  0xe,  0x42, 0x4a, 0x32, 0x36, 0xd3, 0x91, 0x4f, 0x8c,
    0x20, 0x2,  0x1,  0x9,  0xcb, 0x29, 0x24, 0xea, 0xe3, 0x26, 0x63, 0xba,
    0x2e, 0x92, 0x29, 0xbb, 0x93, 0xa9, 0xaa, 0x18, 0xe5, 0xb4, 0xe0, 0x6c,
    0x28, 0x61, 0x1,  0xc,  0x26, 0x49, 0x2c, 0x4b, 0xb,  0x20, 0xfe, 0xc8,
    0xb9, 0x81, 0xca, 0xb9, 0xc3, 0x67, 0xca, 0x7b, 0x40, 0x1c, 0xe9, 0xd,
    0x0,  0xa8, 0x5a, 0x2f, 0x68, 0x41, 0x8a, 0x88, 0xca, 0x18, 0x60, 0x3,
    0xab, 0xa,  0x6e, 0x66, 0xf8, 0x6e, 0x86, 0x90, 0x4c, 0x30, 0x20, 0xee,
    0x20, 0x2,  0x2c, 0x22, 0x52, 0x8b, 0xc0, 0xc4, 0xcb, 0x3c, 0xf2, 0xe9,
    0xa3, 0x72, 0xc2, 0x9,  0xa8, 0x5,  0x32, 0x53, 0x2,  0x3a, 0x7,  0xc8,
    0x2a, 0x14, 0xb8, 0x3a, 0xf3, 0x7,  0xce, 0xfb, 0xb2, 0xf,  0x1,  0xb3,
    0x20, 0x9a, 0x23, 0xb6, 0xb3, 0x4d, 0xc5, 0x1b, 0xcc, 0x78, 0x10, 0xc1,
    0x30, 0x93, 0x42, 0x15, 0xa2, 0x6d, 0x3b, 0xf2, 0xcf, 0x2f, 0xf,  0xc1,
    0xd9, 0xed, 0x80, 0xb8, 0xed, 0xed, 0x30, 0x61, 0x8e, 0x88, 0x9a, 0x83,
    0x80, 0x72, 0x2c, 0x84, 0x1a, 0x8b, 0x8c, 0x29, 0x98, 0xa2, 0x6a, 0x4a,
    0xc4, 0xc8, 0xcf, 0x22, 0x29, 0x61, 0x2a, 0x94, 0x4,  0x44, 0x90, 0x6c,
    0x60, 0x3e, 0xc4, 0xa8, 0xf8, 0x5c, 0x20, 0x63, 0xcf, 0x3,  0xf6, 0x25,
    0xb,  0x21, 0x2d, 0xa5, 0x78, 0x65, 0xb8, 0x63, 0xe0, 0x7c, 0x67, 0xa5,
    0xc,  0x8f, 0xa3, 0xe4, 0x2a, 0xb2, 0xa6, 0x61, 0xe2, 0x1c, 0x8b, 0x78,
    0xab, 0x8b, 0xca, 0x83, 0x18, 0x4d, 0xc8, 0x7c, 0xc1, 0x3c, 0xaa, 0x18,
    0x6a, 0x29, 0x6e, 0x5,  0x5a, 0xa,  0x20, 0x9f, 0x41, 0x3c, 0xaa, 0xe2,
    0x38, 0x9,  0xae, 0xde, 0x79, 0x44, 0x90, 0xaa, 0x59, 0x77, 0x28, 0x59,
    0x26, 0xea, 0x43, 0xa,  0x68, 0xda, 0x88, 0x3b, 0xc7, 0xf6, 0x2a, 0x24,
    0x86, 0x7c, 0xe2, 0x8e, 0xf0, 0x1d, 0x31, 0xc4, 0x67, 0x15, 0x6e, 0x43,
    0x8,  0x7a, 0xc,  0x9d, 0xc8, 0xcc, 0x72, 0x79, 0xac, 0x2b, 0x5a, 0xe4,
    0x1,  0xdf, 0xdf, 0xaa, 0x61, 0x5c, 0x58, 0x1a, 0xe8, 0xa,  0x58, 0x0,
    0x79, 0xb2, 0x4e, 0xae, 0x32, 0x88, 0x2,  0x80, 0xdc, 0x24, 0xcb, 0x21,
    0x9f, 0x3a, 0xab, 0x9e, 0x61, 0x4c, 0x13, 0x32, 0xc4, 0xc4, 0xe2, 0x82,
    0xd4, 0xa1, 0xa5, 0x81, 0xb2, 0x4f, 0x35, 0x99, 0xb8, 0x64, 0xab, 0x3c,
    0x3a, 0x69, 0xc6, 0x80, 0x0,  0xba, 0x24, 0x92, 0xa8, 0xc6, 0x73, 0x27,
    0xe0, 0x8,  0x23, 0xaf, 0xa9, 0xdd, 0xa0, 0x3a, 0xb8, 0xc7, 0x74, 0xd,
    0xbe, 0xf9, 0x68, 0x34, 0xd3, 0x4c, 0x5,  0xe1, 0x64, 0x2d, 0x13, 0xe0,
    0x2c, 0xb9, 0xc,  0xa,  0x9f, 0xdb, 0xc2, 0xc2, 0x3f, 0x2,  0x6a, 0x7,
    0xee, 0xdb, 0xe4, 0x18, 0x57, 0xa0, 0x34, 0x2,  0xad, 0x1,  0xab, 0xad,
    0x4,  0xd,  0xc5, 0x76, 0x32, 0xf4, 0xbf, 0x42, 0xa9, 0x3e, 0x1b, 0xcf,
    0xab, 0x1c, 0x65, 0xa4, 0xe9, 0x9,  0x2d, 0x18, 0x1a, 0xa4, 0x81, 0xea,
    0x2e, 0x63, 0xcb, 0x64, 0xfb, 0x45, 0x9a, 0xa9, 0xc2, 0x10, 0x2d, 0xe6,
    0x8e, 0xfb, 0x10, 0xc,  0xd9, 0x45, 0x89, 0x28, 0x11, 0xf6, 0xca, 0xf5,
    0x61, 0xfa, 0xf2, 0x19, 0x76, 0x19, 0xae, 0xa,  0x4c, 0x2,  0xba, 0xe2,
    0x17, 0x11, 0x45, 0x3a, 0x78, 0x48, 0x2a, 0x63, 0xc9, 0xe9, 0x52, 0x8f,
    0x90, 0xc2, 0xc9, 0xae, 0xf6, 0x7b, 0x20, 0x74, 0x13, 0xf2, 0xab, 0xbf,
    0x36, 0x79, 0x80, 0x5c, 0x80, 0xe9, 0x2c, 0x0,  0x94, 0xa9, 0xd4, 0x42,
    0xe6, 0x30, 0xf6, 0x1a, 0x84, 0xa4, 0x62, 0xe1, 0x2b, 0xaf, 0x3a, 0x91,
    0x86, 0x97, 0x4d, 0x32, 0x17, 0xc0, 0xb8, 0x83, 0xca, 0x14, 0xa3, 0xe0,
    0xa0, 0xf1, 0xf,  0x28, 0x9b, 0x4a, 0x9d, 0x45, 0xa0, 0x38, 0x79, 0xdb,
    0xc1, 0x0,  0xe,  0x0,  0x93, 0x41, 0xae, 0xe,  0x8e, 0xa4, 0xb0, 0xea,
    0x6,  0xa5, 0x15, 0xb0, 0xa6, 0x78, 0xa5, 0x88, 0xe3, 0xa2, 0xa1, 0x32,
    0x10, 0xf3, 0x86, 0xd5, 0xb2, 0x24, 0x20, 0x76, 0xe5, 0x28, 0xbf, 0x64,
    0x9,  0xbb, 0x6e, 0x84, 0xaf, 0x7,  0x0,  0x66, 0x2e, 0x2b, 0x73, 0xfb,
    0x12, 0x60, 0xa0, 0x29, 0xa2, 0x21, 0x29, 0x98, 0xab, 0x9,  0x4a, 0xf3,
    0x3e, 0x61, 0xf0, 0x3e, 0x80, 0x39, 0x92, 0x33, 0xea, 0xb9, 0xe,  0x25,
    0x34, 0xed, 0x1,  0x29, 0x9,  0x1a, 0x1c, 0xa4, 0x63, 0x1c, 0x48, 0x59,
    0x2c, 0x51, 0x42, 0x3d, 0x98, 0xde, 0x79, 0x39, 0xaa, 0xcf, 0x73, 0xa3,
    0x31, 0xb9, 0x2d, 0x28, 0xac, 0x41, 0x27, 0x87, 0x43, 0x22, 0xba, 0xce,
    0x80, 0xfb, 0xd1, 0xa4, 0x88, 0xec, 0xa3, 0x38, 0x4d, 0xb6, 0x55, 0x4d,
    0x5b, 0x2,  0x43, 0x66, 0x40, 0x93, 0xb4, 0x52, 0xc0, 0x7,  0xc3, 0x4b,
    0x19, 0xc9, 0xa7, 0x22, 0x5c, 0x67, 0xe0, 0xed, 0x7,  0xbe, 0x57, 0x86,
    0xba, 0x52, 0xc8, 0x68, 0x2,  0x84, 0x32, 0xd6, 0x42, 0xac, 0x39, 0x64,
    0x5e, 0x1,  0xe9, 0x38, 0x13, 0x31, 0x9e, 0x3b, 0xeb, 0xc4, 0xe3, 0xc2,
    0x12, 0x12, 0xc6, 0x8a, 0xa0, 0xec, 0xc0, 0xc2, 0xe4, 0x3e, 0xb2, 0x57,
    0x3e, 0x19, 0xce, 0x5c, 0x69, 0xe0, 0x3a, 0xe8, 0xef, 0x37, 0x94, 0x9a,
    0xc4, 0xd3, 0x4a, 0xcc, 0x2a, 0x2e, 0x6d, 0x80, 0x22, 0x9c, 0x2c, 0xa,
    0x41, 0x7b, 0x62, 0x94, 0xcb, 0x6f, 0x2c, 0xc8, 0x64, 0x50, 0xd2, 0x7,
    0x4,  0x68, 0x7,  0xe0, 0x92, 0x90, 0x60, 0xad};
int key[LEN + 48];

int a[LEN + 48];
int b[LEN + 48];
int c[LEN + 48];

int main(void) {
  fill(a, a + LEN + 48, -1);
  fill(b, b + LEN + 48, -1);
  fill(c, c + LEN + 48, -1);
  for (int i = 0; i < 8192; i++)
    for (int j = 0; j < 8; j++)
      key[48 + 8 * i + j] = (result[i] >> (7 - j)) & 1;

  ////////////// 1. Recover C ///////////
  // 10922개 있으므로 8200개 정도 나와줘야 함
  for (int r = 0; r < 6; r++) {
    printf("r : %d\n",r);
    int mx = -1;
    int val = -1;
    for (int brute = 0; brute < (1 << 8); brute++) {
      int tmp = brute;
      for (int i = 0; i < 8; i++) {
        c[r + 6 * i] = (tmp & 1);
        tmp >>= 1;
      }
      int score = 0;
      for (int i = r + 48; i < LEN + 48; i += 6) {
        c[i] = c[i - 42] ^ c[i - 48];
        if (c[i] == key[i]) score++;
      }
      if(score >= 6500){
        printf("%d %d\n",score,brute);
      }
      if (score > mx) {
        mx = score;
        val = brute;
      }
    }
    printf("%d %d\n", mx, val);

    int tmp = val;
    for (int i = 0; i < 8; i++) {
      c[r + 6 * i] = (tmp & 1);
      tmp >>= 1;
    }
  }
  for (int i = 48; i < LEN + 48; i++) c[i] = c[i - 48] ^ c[i - 42];

  ////////////// 2. Recover Trivial A, B ////////
  int cnt = 0;
  for (int i = 48; i < LEN + 48; i++) {
    if (c[i] == 1 and key[i] == 0) {
      a[i] = b[i] = 0;
      cnt++;
    } else if (c[i] == 0 and key[i] == 1) {
      a[i] = b[i] = 1;
      cnt++;
    }
  }

  while (1) {
    for (int j = 0; j < 48; j++) {
      printf("%d ", a[j]);
    }
    printf("\n");
    for (int j = 0; j < 48; j++) {
      printf("%d ", b[j]);
    }
    printf("\n\n");
    bool changed = 0;
    for (int i = 0; i < LEN + 48; i++) {
      if (i < LEN) {
        if (a[i] == -1 and a[i + 25] >= 0 and a[i + 48] >= 0)
          changed = 1, a[i] = a[i + 25] ^ a[i + 48];
        if (b[i] == -1 and b[i + 34] >= 0 and b[i + 48] >= 0)
          changed = 1, b[i] = b[i + 34] ^ b[i + 48];
      }
      if (i >= 25 and i < LEN + 48 - 23)
        if (a[i] == -1 and a[i - 25] >= 0 and a[i + 23] >= 0)
          changed = 1, a[i] = a[i - 25] ^ a[i + 23];
      if (i >= 34 and i < LEN + 48 - 14)
        if (b[i] == -1 and b[i - 34] >= 0 and b[i + 14] >= 0)
          changed = 1, b[i] = b[i - 34] ^ b[i + 14];
      if (i >= 48) {
        if (a[i] == -1 and a[i - 23] >= 0 and a[i - 48] >= 0)
          changed = 1, a[i] = a[i - 23] ^ a[i - 48];
        if (b[i] == -1 and b[i - 14] >= 0 and b[i - 48] >= 0)
          changed = 1, b[i] = b[i - 14] ^ b[i - 48];
        if (a[i] == -1 and b[i] != -1) {
          if (key[i] == 1 and b[i] + c[i] == 1) changed = 1, a[i] = 1;
          if (key[i] == 0 and b[i] + c[i] == 1) changed = 1, a[i] = 0;
        }
        if (a[i] != -1 and b[i] == -1) {
          if (key[i] == 1 and a[i] + c[i] == 1) changed = 1, b[i] = 1;
          if (key[i] == 0 and a[i] + c[i] == 1) changed = 1, b[i] = 0;
        }
      }
    }
    if (!changed) break;
  }
  for (int i = 0; i < 48; i++) printf("%d ", a[i]);
  printf("\n");
  for (int i = 0; i < 48; i++) printf("%d ", b[i]);
  printf("\n");
  for(int i = 48; i < LEN+48; i++){
    assert(a[i] == a[i-48]^a[i-23]);
    assert(b[i] == b[i-48]^b[i-14]);
    assert((a[i]+b[i]+c[i])/2 == key[i]);
  }
  long long va = 0;
  long long vb = 0;
  long long vc = 0;
  for(int i = 0; i < 48; i++){
    va = (va<<1) | a[i];
    vb = (vb<<1) | b[i];
    vc = (vc<<1) | c[i];    
  }
  printf("%lld \n%lld \n%lld\n", va,vb,vc);

}

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