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Old 08-11-2018, 01:38
dila dila is offline
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Question The Mutilated AES Challenge

I have replaced the S-Box of this AES-128 cipher implementation with an identity mapping which eliminates the non-linear behaviour of the cipher.

Given the following modified AES implementation, the challenge (if you are interested) is to recover the key that was used to encrypt the given plaintext/ciphertext pair:

Plaintext: 6669786564746573746d657373616765
Ciphertext: 8e554c54fcc0c71225760405e20c9e3a
Key: ????????????????????????????????

The 128-bit AES key that performs this mapping also spells out a secret message when printed as an ASCII string.

----- BEGIN C HEADER FILE -----

Code:
#ifndef _AES_H_
#define _AES_H_

#include <stdint.h>

// #define the macros below to 1/0 to enable/disable the mode of operation.
//
// CBC enables AES encryption in CBC-mode of operation.
// CTR enables encryption in counter-mode.
// ECB enables the basic ECB 16-byte block algorithm. All can be enabled simultaneously.

// The #ifndef-guard allows it to be configured before #include'ing or at compile time.
#ifndef CBC
  #define CBC 1
#endif

#ifndef ECB
  #define ECB 1
#endif

#ifndef CTR
  #define CTR 1
#endif


#define AES128 1
//#define AES192 1
//#define AES256 1

#define AES_BLOCKLEN 16 //Block length in bytes AES is 128b block only

#if defined(AES256) && (AES256 == 1)
    #define AES_KEYLEN 32
    #define AES_keyExpSize 240
#elif defined(AES192) && (AES192 == 1)
    #define AES_KEYLEN 24
    #define AES_keyExpSize 208
#else
    #define AES_KEYLEN 16   // Key length in bytes
    #define AES_keyExpSize 176
#endif

struct AES_ctx
{
  uint8_t RoundKey[AES_keyExpSize];
#if (defined(CBC) && (CBC == 1)) || (defined(CTR) && (CTR == 1))
  uint8_t Iv[AES_BLOCKLEN];
#endif
};

void AES_init_ctx(struct AES_ctx* ctx, const uint8_t* key);
#if (defined(CBC) && (CBC == 1)) || (defined(CTR) && (CTR == 1))
void AES_init_ctx_iv(struct AES_ctx* ctx, const uint8_t* key, const uint8_t* iv);
void AES_ctx_set_iv(struct AES_ctx* ctx, const uint8_t* iv);
#endif

#if defined(ECB) && (ECB == 1)
// buffer size is exactly AES_BLOCKLEN bytes; 
// you need only AES_init_ctx as IV is not used in ECB 
// NB: ECB is considered insecure for most uses
void AES_ECB_encrypt(struct AES_ctx* ctx, uint8_t* buf);
void AES_ECB_decrypt(struct AES_ctx* ctx, uint8_t* buf);

#endif // #if defined(ECB) && (ECB == !)


#if defined(CBC) && (CBC == 1)
// buffer size MUST be mutile of AES_BLOCKLEN;
// Suggest https://en.wikipedia.org/wiki/Padding_(cryptography)#PKCS7 for padding scheme
// NOTES: you need to set IV in ctx via AES_init_ctx_iv() or AES_ctx_set_iv()
//        no IV should ever be reused with the same key 
void AES_CBC_encrypt_buffer(struct AES_ctx* ctx, uint8_t* buf, uint32_t length);
void AES_CBC_decrypt_buffer(struct AES_ctx* ctx, uint8_t* buf, uint32_t length);

#endif // #if defined(CBC) && (CBC == 1)


#if defined(CTR) && (CTR == 1)

// Same function for encrypting as for decrypting. 
// IV is incremented for every block, and used after encryption as XOR-compliment for output
// Suggesting https://en.wikipedia.org/wiki/Padding_(cryptography)#PKCS7 for padding scheme
// NOTES: you need to set IV in ctx with AES_init_ctx_iv() or AES_ctx_set_iv()
//        no IV should ever be reused with the same key 
void AES_CTR_xcrypt_buffer(struct AES_ctx* ctx, uint8_t* buf, uint32_t length);

#endif // #if defined(CTR) && (CTR == 1)


#endif //_AES_H_
----- END C HEADER FILE -----

----- BEGIN C SOURCE FILE -----

Code:
/*
This is an implementation of the AES algorithm, specifically ECB, CTR and CBC mode.
Block size can be chosen in aes.h - available choices are AES128, AES192, AES256.
The implementation is verified against the test vectors in:
  National Institute of Standards and Technology Special Publication 800-38A 2001 ED
ECB-AES128
----------
  plain-text:
    6bc1bee22e409f96e93d7e117393172a
    ae2d8a571e03ac9c9eb76fac45af8e51
    30c81c46a35ce411e5fbc1191a0a52ef
    f69f2445df4f9b17ad2b417be66c3710
  key:
    2b7e151628aed2a6abf7158809cf4f3c
  resulting cipher
    3ad77bb40d7a3660a89ecaf32466ef97 
    f5d3d58503b9699de785895a96fdbaaf 
    43b1cd7f598ece23881b00e3ed030688 
    7b0c785e27e8ad3f8223207104725dd4 
NOTE:   String length must be evenly divisible by 16byte (str_len % 16 == 0)
        You should pad the end of the string with zeros if this is not the case.
        For AES192/256 the key size is proportionally larger.
*/


/*****************************************************************************/
/* Includes:                                                                 */
/*****************************************************************************/
#include <stdint.h>
#include <string.h> // CBC mode, for memset
#include "aes.h"

/*****************************************************************************/
/* Defines:                                                                  */
/*****************************************************************************/
// The number of columns comprising a state in AES. This is a constant in AES. Value=4
#define Nb 4

#if defined(AES256) && (AES256 == 1)
    #define Nk 8
    #define Nr 14
#elif defined(AES192) && (AES192 == 1)
    #define Nk 6
    #define Nr 12
#else
    #define Nk 4        // The number of 32 bit words in a key.
    #define Nr 10       // The number of rounds in AES Cipher.
#endif

// jcallan@github points out that declaring Multiply as a function 
// reduces code size considerably with the Keil ARM compiler.
// See this link for more information: https://github.com/kokke/tiny-AES-C/pull/3
#ifndef MULTIPLY_AS_A_FUNCTION
  #define MULTIPLY_AS_A_FUNCTION 0
#endif




/*****************************************************************************/
/* Private variables:                                                        */
/*****************************************************************************/
// state - array holding the intermediate results during decryption.
typedef uint8_t state_t[4][4];



// The lookup-tables are marked const so they can be placed in read-only storage instead of RAM
// The numbers below can be computed dynamically trading ROM for RAM - 
// This can be useful in (embedded) bootloader applications, where ROM is often limited.
static const uint8_t sbox[256] = {
  //0     1    2      3     4    5     6     7      8    9     A      B    C     D     E     F
  0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,
  0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f,
  0x20, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, 0x2b, 0x2c, 0x2d, 0x2e, 0x2f,
  0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3a, 0x3b, 0x3c, 0x3d, 0x3e, 0x3f,
  0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48, 0x49, 0x4a, 0x4b, 0x4c, 0x4d, 0x4e, 0x4f,
  0x50, 0x51, 0x52, 0x53, 0x54, 0x55, 0x56, 0x57, 0x58, 0x59, 0x5a, 0x5b, 0x5c, 0x5d, 0x5e, 0x5f,
  0x60, 0x61, 0x62, 0x63, 0x64, 0x65, 0x66, 0x67, 0x68, 0x69, 0x6a, 0x6b, 0x6c, 0x6d, 0x6e, 0x6f,
  0x70, 0x71, 0x72, 0x73, 0x74, 0x75, 0x76, 0x77, 0x78, 0x79, 0x7a, 0x7b, 0x7c, 0x7d, 0x7e, 0x7f,
  0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89, 0x8a, 0x8b, 0x8c, 0x8d, 0x8e, 0x8f,
  0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98, 0x99, 0x9a, 0x9b, 0x9c, 0x9d, 0x9e, 0x9f,
  0xa0, 0xa1, 0xa2, 0xa3, 0xa4, 0xa5, 0xa6, 0xa7, 0xa8, 0xa9, 0xaa, 0xab, 0xac, 0xad, 0xae, 0xaf,
  0xb0, 0xb1, 0xb2, 0xb3, 0xb4, 0xb5, 0xb6, 0xb7, 0xb8, 0xb9, 0xba, 0xbb, 0xbc, 0xbd, 0xbe, 0xbf,
  0xc0, 0xc1, 0xc2, 0xc3, 0xc4, 0xc5, 0xc6, 0xc7, 0xc8, 0xc9, 0xca, 0xcb, 0xcc, 0xcd, 0xce, 0xcf,
  0xd0, 0xd1, 0xd2, 0xd3, 0xd4, 0xd5, 0xd6, 0xd7, 0xd8, 0xd9, 0xda, 0xdb, 0xdc, 0xdd, 0xde, 0xdf,
  0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe8, 0xe9, 0xea, 0xeb, 0xec, 0xed, 0xee, 0xef,
  0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6, 0xf7, 0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff };

static const uint8_t rsbox[256] = {
  0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,
  0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f,
  0x20, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, 0x2b, 0x2c, 0x2d, 0x2e, 0x2f,
  0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3a, 0x3b, 0x3c, 0x3d, 0x3e, 0x3f,
  0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48, 0x49, 0x4a, 0x4b, 0x4c, 0x4d, 0x4e, 0x4f,
  0x50, 0x51, 0x52, 0x53, 0x54, 0x55, 0x56, 0x57, 0x58, 0x59, 0x5a, 0x5b, 0x5c, 0x5d, 0x5e, 0x5f,
  0x60, 0x61, 0x62, 0x63, 0x64, 0x65, 0x66, 0x67, 0x68, 0x69, 0x6a, 0x6b, 0x6c, 0x6d, 0x6e, 0x6f,
  0x70, 0x71, 0x72, 0x73, 0x74, 0x75, 0x76, 0x77, 0x78, 0x79, 0x7a, 0x7b, 0x7c, 0x7d, 0x7e, 0x7f,
  0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89, 0x8a, 0x8b, 0x8c, 0x8d, 0x8e, 0x8f,
  0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98, 0x99, 0x9a, 0x9b, 0x9c, 0x9d, 0x9e, 0x9f,
  0xa0, 0xa1, 0xa2, 0xa3, 0xa4, 0xa5, 0xa6, 0xa7, 0xa8, 0xa9, 0xaa, 0xab, 0xac, 0xad, 0xae, 0xaf,
  0xb0, 0xb1, 0xb2, 0xb3, 0xb4, 0xb5, 0xb6, 0xb7, 0xb8, 0xb9, 0xba, 0xbb, 0xbc, 0xbd, 0xbe, 0xbf,
  0xc0, 0xc1, 0xc2, 0xc3, 0xc4, 0xc5, 0xc6, 0xc7, 0xc8, 0xc9, 0xca, 0xcb, 0xcc, 0xcd, 0xce, 0xcf,
  0xd0, 0xd1, 0xd2, 0xd3, 0xd4, 0xd5, 0xd6, 0xd7, 0xd8, 0xd9, 0xda, 0xdb, 0xdc, 0xdd, 0xde, 0xdf,
  0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe8, 0xe9, 0xea, 0xeb, 0xec, 0xed, 0xee, 0xef,
  0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6, 0xf7, 0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff };

// The round constant word array, Rcon[i], contains the values given by 
// x to the power (i-1) being powers of x (x is denoted as {02}) in the field GF(2^8)
static const uint8_t Rcon[11] = {
  0x8d, 0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1b, 0x36 };

/*
 * Jordan Goulder points out in PR #12 (https://github.com/kokke/tiny-AES-C/pull/12),
 * that you can remove most of the elements in the Rcon array, because they are unused.
 *
 * From Wikipedia's article on the Rijndael key schedule @ https://en.wikipedia.org/wiki/Rijndael_key_schedule#Rcon
 * 
 * "Only the first some of these constants are actually used – up to rcon[10] for AES-128 (as 11 round keys are needed), 
 *  up to rcon[8] for AES-192, up to rcon[7] for AES-256. rcon[0] is not used in AES algorithm."
 */


/*****************************************************************************/
/* Private functions:                                                        */
/*****************************************************************************/
/*
static uint8_t getSBoxValue(uint8_t num)
{
  return sbox[num];
}
*/
#define getSBoxValue(num) (sbox[(num)])
/*
static uint8_t getSBoxInvert(uint8_t num)
{
  return rsbox[num];
}
*/
#define getSBoxInvert(num) (rsbox[(num)])

// This function produces Nb(Nr+1) round keys. The round keys are used in each round to decrypt the states. 
static void KeyExpansion(uint8_t* RoundKey, const uint8_t* Key)
{
  unsigned i, j, k;
  uint8_t tempa[4]; // Used for the column/row operations
  
  // The first round key is the key itself.
  for (i = 0; i < Nk; ++i)
  {
    RoundKey[(i * 4) + 0] = Key[(i * 4) + 0];
    RoundKey[(i * 4) + 1] = Key[(i * 4) + 1];
    RoundKey[(i * 4) + 2] = Key[(i * 4) + 2];
    RoundKey[(i * 4) + 3] = Key[(i * 4) + 3];
  }

  // All other round keys are found from the previous round keys.
  for (i = Nk; i < Nb * (Nr + 1); ++i)
  {
    {
      k = (i - 1) * 4;
      tempa[0]=RoundKey[k + 0];
      tempa[1]=RoundKey[k + 1];
      tempa[2]=RoundKey[k + 2];
      tempa[3]=RoundKey[k + 3];

    }

    if (i % Nk == 0)
    {
      // This function shifts the 4 bytes in a word to the left once.
      // [a0,a1,a2,a3] becomes [a1,a2,a3,a0]

      // Function RotWord()
      {
        k = tempa[0];
        tempa[0] = tempa[1];
        tempa[1] = tempa[2];
        tempa[2] = tempa[3];
        tempa[3] = k;
      }

      // SubWord() is a function that takes a four-byte input word and 
      // applies the S-box to each of the four bytes to produce an output word.

      // Function Subword()
      {
        tempa[0] = getSBoxValue(tempa[0]);
        tempa[1] = getSBoxValue(tempa[1]);
        tempa[2] = getSBoxValue(tempa[2]);
        tempa[3] = getSBoxValue(tempa[3]);
      }

      tempa[0] = tempa[0] ^ Rcon[i/Nk];
    }
#if defined(AES256) && (AES256 == 1)
    if (i % Nk == 4)
    {
      // Function Subword()
      {
        tempa[0] = getSBoxValue(tempa[0]);
        tempa[1] = getSBoxValue(tempa[1]);
        tempa[2] = getSBoxValue(tempa[2]);
        tempa[3] = getSBoxValue(tempa[3]);
      }
    }
#endif
    j = i * 4; k=(i - Nk) * 4;
    RoundKey[j + 0] = RoundKey[k + 0] ^ tempa[0];
    RoundKey[j + 1] = RoundKey[k + 1] ^ tempa[1];
    RoundKey[j + 2] = RoundKey[k + 2] ^ tempa[2];
    RoundKey[j + 3] = RoundKey[k + 3] ^ tempa[3];
  }
}

void AES_init_ctx(struct AES_ctx* ctx, const uint8_t* key)
{
  KeyExpansion(ctx->RoundKey, key);
}
#if (defined(CBC) && (CBC == 1)) || (defined(CTR) && (CTR == 1))
void AES_init_ctx_iv(struct AES_ctx* ctx, const uint8_t* key, const uint8_t* iv)
{
  KeyExpansion(ctx->RoundKey, key);
  memcpy (ctx->Iv, iv, AES_BLOCKLEN);
}
void AES_ctx_set_iv(struct AES_ctx* ctx, const uint8_t* iv)
{
  memcpy (ctx->Iv, iv, AES_BLOCKLEN);
}
#endif

// This function adds the round key to state.
// The round key is added to the state by an XOR function.
static void AddRoundKey(uint8_t round,state_t* state,uint8_t* RoundKey)
{
  uint8_t i,j;
  for (i = 0; i < 4; ++i)
  {
    for (j = 0; j < 4; ++j)
    {
      (*state)[i][j] ^= RoundKey[(round * Nb * 4) + (i * Nb) + j];
    }
  }
}

// The SubBytes Function Substitutes the values in the
// state matrix with values in an S-box.
static void SubBytes(state_t* state)
{
  uint8_t i, j;
  for (i = 0; i < 4; ++i)
  {
    for (j = 0; j < 4; ++j)
    {
      (*state)[j][i] = getSBoxValue((*state)[j][i]);
    }
  }
}

// The ShiftRows() function shifts the rows in the state to the left.
// Each row is shifted with different offset.
// Offset = Row number. So the first row is not shifted.
static void ShiftRows(state_t* state)
{
  uint8_t temp;

  // Rotate first row 1 columns to left  
  temp           = (*state)[0][1];
  (*state)[0][1] = (*state)[1][1];
  (*state)[1][1] = (*state)[2][1];
  (*state)[2][1] = (*state)[3][1];
  (*state)[3][1] = temp;

  // Rotate second row 2 columns to left  
  temp           = (*state)[0][2];
  (*state)[0][2] = (*state)[2][2];
  (*state)[2][2] = temp;

  temp           = (*state)[1][2];
  (*state)[1][2] = (*state)[3][2];
  (*state)[3][2] = temp;

  // Rotate third row 3 columns to left
  temp           = (*state)[0][3];
  (*state)[0][3] = (*state)[3][3];
  (*state)[3][3] = (*state)[2][3];
  (*state)[2][3] = (*state)[1][3];
  (*state)[1][3] = temp;
}

static uint8_t xtime(uint8_t x)
{
  return ((x<<1) ^ (((x>>7) & 1) * 0x1b));
}

// MixColumns function mixes the columns of the state matrix
static void MixColumns(state_t* state)
{
  uint8_t i;
  uint8_t Tmp, Tm, t;
  for (i = 0; i < 4; ++i)
  {  
    t   = (*state)[i][0];
    Tmp = (*state)[i][0] ^ (*state)[i][1] ^ (*state)[i][2] ^ (*state)[i][3] ;
    Tm  = (*state)[i][0] ^ (*state)[i][1] ; Tm = xtime(Tm);  (*state)[i][0] ^= Tm ^ Tmp ;
    Tm  = (*state)[i][1] ^ (*state)[i][2] ; Tm = xtime(Tm);  (*state)[i][1] ^= Tm ^ Tmp ;
    Tm  = (*state)[i][2] ^ (*state)[i][3] ; Tm = xtime(Tm);  (*state)[i][2] ^= Tm ^ Tmp ;
    Tm  = (*state)[i][3] ^ t ;              Tm = xtime(Tm);  (*state)[i][3] ^= Tm ^ Tmp ;
  }
}

// Multiply is used to multiply numbers in the field GF(2^8)
// Note: The last call to xtime() is unneeded, but often ends up generating a smaller binary
//       The compiler seems to be able to vectorize the operation better this way.
//       See https://github.com/kokke/tiny-AES-c/pull/34
#if MULTIPLY_AS_A_FUNCTION
static uint8_t Multiply(uint8_t x, uint8_t y)
{
  return (((y & 1) * x) ^
       ((y>>1 & 1) * xtime(x)) ^
       ((y>>2 & 1) * xtime(xtime(x))) ^
       ((y>>3 & 1) * xtime(xtime(xtime(x)))) ^
       ((y>>4 & 1) * xtime(xtime(xtime(xtime(x)))))); /* this last call to xtime() can be omitted */
  }
#else
#define Multiply(x, y)                                \
      (  ((y & 1) * x) ^                              \
      ((y>>1 & 1) * xtime(x)) ^                       \
      ((y>>2 & 1) * xtime(xtime(x))) ^                \
      ((y>>3 & 1) * xtime(xtime(xtime(x)))) ^         \
      ((y>>4 & 1) * xtime(xtime(xtime(xtime(x))))))   \

#endif

// MixColumns function mixes the columns of the state matrix.
// The method used to multiply may be difficult to understand for the inexperienced.
// Please use the references to gain more information.
static void InvMixColumns(state_t* state)
{
  int i;
  uint8_t a, b, c, d;
  for (i = 0; i < 4; ++i)
  { 
    a = (*state)[i][0];
    b = (*state)[i][1];
    c = (*state)[i][2];
    d = (*state)[i][3];

    (*state)[i][0] = Multiply(a, 0x0e) ^ Multiply(b, 0x0b) ^ Multiply(c, 0x0d) ^ Multiply(d, 0x09);
    (*state)[i][1] = Multiply(a, 0x09) ^ Multiply(b, 0x0e) ^ Multiply(c, 0x0b) ^ Multiply(d, 0x0d);
    (*state)[i][2] = Multiply(a, 0x0d) ^ Multiply(b, 0x09) ^ Multiply(c, 0x0e) ^ Multiply(d, 0x0b);
    (*state)[i][3] = Multiply(a, 0x0b) ^ Multiply(b, 0x0d) ^ Multiply(c, 0x09) ^ Multiply(d, 0x0e);
  }
}


// The SubBytes Function Substitutes the values in the
// state matrix with values in an S-box.
static void InvSubBytes(state_t* state)
{
  uint8_t i, j;
  for (i = 0; i < 4; ++i)
  {
    for (j = 0; j < 4; ++j)
    {
      (*state)[j][i] = getSBoxInvert((*state)[j][i]);
    }
  }
}

static void InvShiftRows(state_t* state)
{
  uint8_t temp;

  // Rotate first row 1 columns to right  
  temp = (*state)[3][1];
  (*state)[3][1] = (*state)[2][1];
  (*state)[2][1] = (*state)[1][1];
  (*state)[1][1] = (*state)[0][1];
  (*state)[0][1] = temp;

  // Rotate second row 2 columns to right 
  temp = (*state)[0][2];
  (*state)[0][2] = (*state)[2][2];
  (*state)[2][2] = temp;

  temp = (*state)[1][2];
  (*state)[1][2] = (*state)[3][2];
  (*state)[3][2] = temp;

  // Rotate third row 3 columns to right
  temp = (*state)[0][3];
  (*state)[0][3] = (*state)[1][3];
  (*state)[1][3] = (*state)[2][3];
  (*state)[2][3] = (*state)[3][3];
  (*state)[3][3] = temp;
}


// Cipher is the main function that encrypts the PlainText.
static void Cipher(state_t* state, uint8_t* RoundKey)
{
  uint8_t round = 0;

  // Add the First round key to the state before starting the rounds.
  AddRoundKey(0, state, RoundKey); 
  
  // There will be Nr rounds.
  // The first Nr-1 rounds are identical.
  // These Nr-1 rounds are executed in the loop below.
  for (round = 1; round < Nr; ++round)
  {
    SubBytes(state);
    ShiftRows(state);
    MixColumns(state);
    AddRoundKey(round, state, RoundKey);
  }
  
  // The last round is given below.
  // The MixColumns function is not here in the last round.
  SubBytes(state);
  ShiftRows(state);
  AddRoundKey(Nr, state, RoundKey);
}

static void InvCipher(state_t* state,uint8_t* RoundKey)
{
  uint8_t round = 0;

  // Add the First round key to the state before starting the rounds.
  AddRoundKey(Nr, state, RoundKey); 

  // There will be Nr rounds.
  // The first Nr-1 rounds are identical.
  // These Nr-1 rounds are executed in the loop below.
  for (round = (Nr - 1); round > 0; --round)
  {
    InvShiftRows(state);
    InvSubBytes(state);
    AddRoundKey(round, state, RoundKey);
    InvMixColumns(state);
  }
  
  // The last round is given below.
  // The MixColumns function is not here in the last round.
  InvShiftRows(state);
  InvSubBytes(state);
  AddRoundKey(0, state, RoundKey);
}


/*****************************************************************************/
/* Public functions:                                                         */
/*****************************************************************************/
#if defined(ECB) && (ECB == 1)


void AES_ECB_encrypt(struct AES_ctx *ctx, uint8_t* buf)
{
  // The next function call encrypts the PlainText with the Key using AES algorithm.
  Cipher((state_t*)buf, ctx->RoundKey);
}

void AES_ECB_decrypt(struct AES_ctx* ctx, uint8_t* buf)
{
  // The next function call decrypts the PlainText with the Key using AES algorithm.
  InvCipher((state_t*)buf, ctx->RoundKey);
}


#endif // #if defined(ECB) && (ECB == 1)





#if defined(CBC) && (CBC == 1)


static void XorWithIv(uint8_t* buf, uint8_t* Iv)
{
  uint8_t i;
  for (i = 0; i < AES_BLOCKLEN; ++i) // The block in AES is always 128bit no matter the key size
  {
    buf[i] ^= Iv[i];
  }
}

void AES_CBC_encrypt_buffer(struct AES_ctx *ctx,uint8_t* buf, uint32_t length)
{
  uintptr_t i;
  uint8_t *Iv = ctx->Iv;
  for (i = 0; i < length; i += AES_BLOCKLEN)
  {
    XorWithIv(buf, Iv);
    Cipher((state_t*)buf, ctx->RoundKey);
    Iv = buf;
    buf += AES_BLOCKLEN;
    //printf("Step %d - %d", i/16, i);
  }
  /* store Iv in ctx for next call */
  memcpy(ctx->Iv, Iv, AES_BLOCKLEN);
}

void AES_CBC_decrypt_buffer(struct AES_ctx* ctx, uint8_t* buf,  uint32_t length)
{
  uintptr_t i;
  uint8_t storeNextIv[AES_BLOCKLEN];
  for (i = 0; i < length; i += AES_BLOCKLEN)
  {
    memcpy(storeNextIv, buf, AES_BLOCKLEN);
    InvCipher((state_t*)buf, ctx->RoundKey);
    XorWithIv(buf, ctx->Iv);
    memcpy(ctx->Iv, storeNextIv, AES_BLOCKLEN);
    buf += AES_BLOCKLEN;
  }

}

#endif // #if defined(CBC) && (CBC == 1)



#if defined(CTR) && (CTR == 1)

/* Symmetrical operation: same function for encrypting as for decrypting. Note any IV/nonce should never be reused with the same key */
void AES_CTR_xcrypt_buffer(struct AES_ctx* ctx, uint8_t* buf, uint32_t length)
{
  uint8_t buffer[AES_BLOCKLEN];
  
  unsigned i;
  int bi;
  for (i = 0, bi = AES_BLOCKLEN; i < length; ++i, ++bi)
  {
    if (bi == AES_BLOCKLEN) /* we need to regen xor compliment in buffer */
    {
      
      memcpy(buffer, ctx->Iv, AES_BLOCKLEN);
      Cipher((state_t*)buffer,ctx->RoundKey);

      /* Increment Iv and handle overflow */
      for (bi = (AES_BLOCKLEN - 1); bi >= 0; --bi)
      {
  /* inc will owerflow */
        if (ctx->Iv[bi] == 255)
  {
          ctx->Iv[bi] = 0;
          continue;
        } 
        ctx->Iv[bi] += 1;
        break;   
      }
      bi = 0;
    }

    buf[i] = (buf[i] ^ buffer[bi]);
  }
}

#endif // #if defined(CTR) && (CTR == 1)
----- END C SOURCE FILE -----

Hint: The solution can be found without extensive analysis of the code by treating the cipher as a black-box function acting on 128-element bit-vectors.
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  #2  
Old 08-26-2018, 09:32
chants chants is offline
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Well the mathematical or formulaic "white-box" strategy does seem like a total dead-end here. 10 rounds through the AES substitution-permutation network (well I suppose 8 + the first and last which are slightly different) and even with a linear s-box, its pretty much hard to mathematically deduce anything.


From the "black-box" way you mentioned. Well first we know the high bit of each byte is 0, giving 16 bits of 128. But 2^112 is still way too big and even playing with ascii character ranges does not get us within brute force range. So my guess here is quite obvious: linear cryptanalysis. Obviously differential is useless here as you did not give us two or more input-output pairs. But the linear s-boxes should cause a linear bias: Statistical bias in the output bits based on the key bits. It should theoretically get this within range for a practical attack. Is this the right direction?
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Old 08-27-2018, 04:06
dila dila is offline
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Yes that sounds right. You can use techniques from linear cryptanalysis. My understanding is that this will lead to linear approximations for the function, but note that in this case the approximation will be exact, which should mean there is less computation involved.

By the way, if you solve the challenge you can give your solution as SHA256(your_name||solution) so that your solution is hidden but can be verified.
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