SHA 256 pseuedocode?

Question

He estado intentando averiguar cómo funciona SHA-256. Una cosa que he estado haciendo para otros algoritmos es que he desarrollado una especie de función de pseudocódigo paso a paso para el algoritmo.

He intentado hacer lo mismo con SHA256, pero hasta el momento estoy teniendo bastantes problemas.

He intentado averiguar cómo funciona el diagrama de la wikipedia, pero además de la parte de texto que explica las funciones, no estoy seguro de haberlo hecho bien.

Esto es lo que tengo hasta ahora:

Input is an array 8 items long where each item is 32 bits. 
Output is an array 8 items long where each item is 32 bits. 
Calculate all the function boxes and store those values. 
|I'll refer to them by function name 
Store input, right shifted by 32 bits, into output. 
| At this point, in the out array, E is the wrong value and A is empty 
Store the function boxes. 
| now we need to calculate out E and out A. 
| note: I've replaced the modulo commands with a bitwise AND 2^(32-1) 
| I can't figure out how the modulus adding lines up, but I think it is like this 
Store (Input H + Ch + ((Wt+Kt) AND 2^31)) AND 2^31 As mod1 
Store (sum1 + mod1) AND 2^31 as mod2 
Store (d + mod2) AND 2^31 into output E 
|now output E is correct and all we need is output A 
Store (MA + mod2) AND 2^31 as mod3 
Store (sum0 + mod3) AND 2^31 into output A 
|output now contains the correct hash of input. 
|Do we return now or does this need to be run repeatedly? 

¿Obtuve todos aquellos módulos de adición de la derecha? Además, ¿qué son Wt y Kt? También esto se ejecutará una vez y habrá terminado o necesita ejecutarse una cierta cantidad de veces, con la salida siendo reutilizada como entrada.

Aquí está el enlace por cierto. http://en.wikipedia.org/wiki/SHA-2#Hash_function

Muchas gracias, Brian

Answer 1

Echa un vistazo a la norma oficial que describe el algoritmo, se describen las variables aquí: http://csrc.nist.gov/publications/fips/fips180-4/fips-180-4.pdf

(Oh, ahora veo que soy casi un año tarde con mi respuesta, ah, no importa ...)

Answer 2

initial_hash_values=[ 
'6a09e667','bb67ae85','3c6ef372','a54ff53a', 
'510e527f','9b05688c','1f83d9ab','5be0cd19' 
] 

sha_256_constants=[ 
'428a2f98','71374491','b5c0fbcf','e9b5dba5', 
'3956c25b','59f111f1','923f82a4','ab1c5ed5', 
'd807aa98','12835b01','243185be','550c7dc3', 
'72be5d74','80deb1fe','9bdc06a7','c19bf174', 
'e49b69c1','efbe4786','0fc19dc6','240ca1cc', 
'2de92c6f','4a7484aa','5cb0a9dc','76f988da', 
'983e5152','a831c66d','b00327c8','bf597fc7', 
'c6e00bf3','d5a79147','06ca6351','14292967', 
'27b70a85','2e1b2138','4d2c6dfc','53380d13', 
'650a7354','766a0abb','81c2c92e','92722c85', 
'a2bfe8a1','a81a664b','c24b8b70','c76c51a3', 
'd192e819','d6990624','f40e3585','106aa070', 
'19a4c116','1e376c08','2748774c','34b0bcb5', 
'391c0cb3','4ed8aa4a','5b9cca4f','682e6ff3', 
'748f82ee','78a5636f','84c87814','8cc70208', 
'90befffa','a4506ceb','bef9a3f7','c67178f2' 
] 

def bin_return(dec): 
    return(str(format(dec,'b'))) 

def bin_8bit(dec): 
    return(str(format(dec,'08b'))) 

def bin_32bit(dec): 
    return(str(format(dec,'032b'))) 

def bin_64bit(dec): 
    return(str(format(dec,'064b'))) 

def hex_return(dec): 
    return(str(format(dec,'x'))) 

def dec_return_bin(bin_string): 
    return(int(bin_string,2)) 

def dec_return_hex(hex_string): 
    return(int(hex_string,16)) 

def L_P(SET,n): 
    to_return=[] 
    j=0 
    k=n 
    while k<len(SET)+1: 
     to_return.append(SET[j:k]) 
     j=k 
     k+=n 
    return(to_return) 

def s_l(bit_string): 
    bit_list=[] 
    for i in range(len(bit_string)): 
     bit_list.append(bit_string[i]) 
    return(bit_list) 

def l_s(bit_list): 
    bit_string='' 
    for i in range(len(bit_list)): 
     bit_string+=bit_list[i] 
    return(bit_string) 

def rotate_right(bit_string,n): 
    bit_list = s_l(bit_string) 
    count=0 
    while count <= n-1: 
     list_main=list(bit_list) 
     var_0=list_main.pop(-1) 
     list_main=list([var_0]+list_main) 
     bit_list=list(list_main) 
     count+=1 
    return(l_s(list_main)) 

def shift_right(bit_string,n): 
    bit_list=s_l(bit_string) 
    count=0 
    while count <= n-1: 
     bit_list.pop(-1) 
     count+=1 
    front_append=['0']*n 
    return(l_s(front_append+bit_list)) 

def mod_32_addition(input_set): 
    value=0 
    for i in range(len(input_set)): 
     value+=input_set[i] 
    mod_32 = 4294967296 
    return(value%mod_32) 

def xor_2str(bit_string_1,bit_string_2): 
    xor_list=[] 
    for i in range(len(bit_string_1)): 
     if bit_string_1[i]=='0' and bit_string_2[i]=='0': 
      xor_list.append('0') 
     if bit_string_1[i]=='1' and bit_string_2[i]=='1': 
      xor_list.append('0') 
     if bit_string_1[i]=='0' and bit_string_2[i]=='1': 
      xor_list.append('1') 
     if bit_string_1[i]=='1' and bit_string_2[i]=='0': 
      xor_list.append('1') 
    return(l_s(xor_list)) 

def and_2str(bit_string_1,bit_string_2): 
    and_list=[] 
    for i in range(len(bit_string_1)): 
     if bit_string_1[i]=='1' and bit_string_2[i]=='1': 
      and_list.append('1') 
     else: 
      and_list.append('0') 

    return(l_s(and_list)) 

def or_2str(bit_string_1,bit_string_2): 
    or_list=[] 
    for i in range(len(bit_string_1)): 
     if bit_string_1[i]=='0' and bit_string_2[i]=='0': 
      or_list.append('0') 
     else: 
      or_list.append('1') 
    return(l_s(or_list)) 

def not_str(bit_string): 
    not_list=[] 
    for i in range(len(bit_string)): 
     if bit_string[i]=='0': 
      not_list.append('1') 
     else: 
      not_list.append('0') 
    return(l_s(not_list)) 

''' 
SHA-256 Specific Functions: 
''' 

def Ch(x,y,z): 
    return(xor_2str(and_2str(x,y),and_2str(not_str(x),z))) 

def Maj(x,y,z): 
    return(xor_2str(xor_2str(and_2str(x,y),and_2str(x,z)),and_2str(y,z))) 

def e_0(x): 
    return(xor_2str(xor_2str(rotate_right(x,2),rotate_right(x,13)),rotate_right(x,22))) 

def e_1(x): 
    return(xor_2str(xor_2str(rotate_right(x,6),rotate_right(x,11)),rotate_right(x,25))) 

def s_0(x): 
    return(xor_2str(xor_2str(rotate_right(x,7),rotate_right(x,18)),shift_right(x,3))) 

def s_1(x): 
    return(xor_2str(xor_2str(rotate_right(x,17),rotate_right(x,19)),shift_right(x,10))) 

def message_pad(bit_list): 
    pad_one = bit_list + '1' 
    pad_len = len(pad_one) 
    k=0 
    while ((pad_len+k)-448)%512 != 0: 
     k+=1 
    back_append_0 = '0'*k 
    back_append_1 = bin_64bit(len(bit_list)) 
    return(pad_one+back_append_0+back_append_1) 

def message_bit_return(string_input): 
    bit_list=[] 
    for i in range(len(string_input)): 
     bit_list.append(bin_8bit(ord(string_input[i]))) 
    return(l_s(bit_list)) 

def message_pre_pro(input_string): 
    bit_main = message_bit_return(input_string) 
    return(message_pad(bit_main)) 

def message_parsing(input_string): 
    return(L_P(message_pre_pro(input_string),32)) 

def message_schedule(index,w_t): 
    new_word = bin_32bit(mod_32_addition([int(s_1(w_t[index-2]),2),int(w_t[index-7],2),int(s_0(w_t[index-15]),2),int(w_t[index-16],2)])) 
    return(new_word) 

''' 
This example of SHA_256 works for an input string >56 characters. 
''' 

def sha_256(input_string): 
    w_t=message_parsing(input_string) 
    a=bin_32bit(dec_return_hex(initial_hash_values[0])) 
    b=bin_32bit(dec_return_hex(initial_hash_values[1])) 
    c=bin_32bit(dec_return_hex(initial_hash_values[2])) 
    d=bin_32bit(dec_return_hex(initial_hash_values[3])) 
    e=bin_32bit(dec_return_hex(initial_hash_values[4])) 
    f=bin_32bit(dec_return_hex(initial_hash_values[5])) 
    g=bin_32bit(dec_return_hex(initial_hash_values[6])) 
    h=bin_32bit(dec_return_hex(initial_hash_values[7])) 
    for i in range(0,64): 
     if i <= 15: 
      t_1=mod_32_addition([int(h,2),int(e_1(e),2),int(Ch(e,f,g),2),int(sha_256_constants[i],16),int(w_t[i],2)]) 
      t_2=mod_32_addition([int(e_0(a),2),int(Maj(a,b,c),2)]) 
      h=g 
      g=f 
      f=e 
      e=mod_32_addition([int(d,2),t_1]) 
      d=c 
      c=b 
      b=a 
      a=mod_32_addition([t_1,t_2]) 
      a=bin_32bit(a) 
      e=bin_32bit(e) 
     if i > 15: 
      w_t.append(message_schedule(i,w_t)) 
      t_1=mod_32_addition([int(h,2),int(e_1(e),2),int(Ch(e,f,g),2),int(sha_256_constants[i],16),int(w_t[i],2)]) 
      t_2=mod_32_addition([int(e_0(a),2),int(Maj(a,b,c),2)]) 
      h=g 
      g=f 
      f=e 
      e=mod_32_addition([int(d,2),t_1]) 
      d=c 
      c=b 
      b=a 
      a=mod_32_addition([t_1,t_2]) 
      a=bin_32bit(a) 
      e=bin_32bit(e) 
    hash_0 = mod_32_addition([dec_return_hex(initial_hash_values[0]),int(a,2)]) 
    hash_1 = mod_32_addition([dec_return_hex(initial_hash_values[1]),int(b,2)]) 
    hash_2 = mod_32_addition([dec_return_hex(initial_hash_values[2]),int(c,2)]) 
    hash_3 = mod_32_addition([dec_return_hex(initial_hash_values[3]),int(d,2)]) 
    hash_4 = mod_32_addition([dec_return_hex(initial_hash_values[4]),int(e,2)]) 
    hash_5 = mod_32_addition([dec_return_hex(initial_hash_values[5]),int(f,2)]) 
    hash_6 = mod_32_addition([dec_return_hex(initial_hash_values[6]),int(g,2)]) 
    hash_7 = mod_32_addition([dec_return_hex(initial_hash_values[7]),int(h,2)]) 
    final_hash = (hex_return(hash_0), 
        hex_return(hash_1), 
        hex_return(hash_2), 
        hex_return(hash_3), 
        hex_return(hash_4), 
        hex_return(hash_5), 
        hex_return(hash_6), 
        hex_return(hash_7)) 
    return(final_hash) 

Answer 3

W_t se deriva del ser bloque actual procesado mientras que K_t es una constante fija determinada por el número de iteración. La función de compresión se repite 64 veces para cada bloque en SHA256. Hay una constante específica K_t y un valor derivado W_t para cada iteración 0 < = t < = 63.

He proporcionado mi propia implementación de SHA256 usando Python 3.6. La tupla K contiene los 64 valores constantes de K_t. La función Sha256 muestra cómo se calcula el valor de W_t en la lista W. La implementación se centra en la claridad del código y no en el alto rendimiento.

W = 32   #Number of bits in word 
M = 1 << W 
FF = M - 1  #0xFFFFFFFF (for performing addition mod 2**32) 

#Constants from SHA256 definition 
K = (0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 
    0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5, 
    0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 
    0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174, 
    0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 
    0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da, 
    0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 
    0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967, 
    0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 
    0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85, 
    0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 
    0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070, 
    0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 
    0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3, 
    0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 
    0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2) 

#Initial values for compression function 
I = (0x6a09e667, 0xbb67ae85, 0x3c6ef372, 0xa54ff53a, 
    0x510e527f, 0x9b05688c, 0x1f83d9ab, 0x5be0cd19) 

def RR(x, b): 
    ''' 
    32-bit bitwise rotate right 
    ''' 
    return ((x >> b) | (x << (W - b))) & FF 

def Pad(W): 
    ''' 
    Pads a message and converts to byte array 
    ''' 
    mdi = len(W) % 64   
    L = (len(W) << 3).to_bytes(8, 'big')  #Binary of len(W) in bits 
    npad = 55 - mdi if mdi < 56 else 119 - mdi #Pad so 64 | len; add 1 block if needed 
    return bytes(W, 'ascii') + b'\x80' + (b'\x00' * npad) + L #64 | 1 + npad + 8 + len(W) 

def Sha256CF(Wt, Kt, A, B, C, D, E, F, G, H): 
    ''' 
    SHA256 Compression Function 
    ''' 
    Ch = (E & F)^(~E & G) 
    Ma = (A & B)^(A & C)^(B & C)  #Major 
    S0 = RR(A, 2)^RR(A, 13)^RR(A, 22) #Sigma_0 
    S1 = RR(E, 6)^RR(E, 11)^RR(E, 25) #Sigma_1 
    T1 = H + S1 + Ch + Wt + Kt 
    return (T1 + S0 + Ma) & FF, A, B, C, (D + T1) & FF, E, F, G 

def Sha256(M): 
    ''' 
    Performs SHA256 on an input string 
    M: The string to process 
    return: A 32 byte array of the binary digest 
    ''' 
    M = Pad(M)   #Pad message so that length is divisible by 64 
    DG = list(I)  #Digest as 8 32-bit words (A-H) 
    for j in range(0, len(M), 64): #Iterate over message in chunks of 64 
     S = M[j:j + 64]    #Current chunk 
     W = [0] * 64 
     W[0:16] = [int.from_bytes(S[i:i + 4], 'big') for i in range(0, 64, 4)] 
     for i in range(16, 64): 
      s0 = RR(W[i - 15], 7)^RR(W[i - 15], 18)^(W[i - 15] >> 3) 
      s1 = RR(W[i - 2], 17)^RR(W[i - 2], 19)^(W[i - 2] >> 10) 
      W[i] = (W[i - 16] + s0 + W[i-7] + s1) & FF 
     A, B, C, D, E, F, G, H = DG #State of the compression function 
     for i in range(64): 
      A, B, C, D, E, F, G, H = Sha256CF(W[i], K[i], A, B, C, D, E, F, G, H) 
     DG = [(X + Y) & FF for X, Y in zip(DG, (A, B, C, D, E, F, G, H))] 
    return b''.join(Di.to_bytes(4, 'big') for Di in DG) #Convert to byte array 

if __name__ == "__main__": 
    bd = Sha256('Hello World') 
    print(''.join('{:02x}'.format(i) for i in bd))