SHA 256 pusedocode?

Question

Ich habe versucht herauszufinden, wie SHA-256 funktioniert. Eine Sache, die ich für andere Algorithmen gemacht habe, ist, dass ich eine Art Schritt für Schritt Pseudocode-Funktion für den Algorithmus ausgearbeitet habe.

Ich habe versucht, das gleiche für SHA256 zu tun, aber bis jetzt habe ich ziemlich viel Ärger.

Ich habe versucht herauszufinden, wie das Wikipedia-Diagramm funktioniert, aber neben dem Textteil, der die Funktionen erklärt, bin ich mir nicht sicher, ob ich es richtig verstanden habe.

Hier ist, was ich bisher:

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? 

Habe ich alle diese zusätzlich modulos Recht bekommen? Auch was sind Wt und Kt? Würde dies auch einmal ausgeführt und Sie sind fertig oder muss es eine bestimmte Anzahl von Mal ausgeführt werden, mit der Ausgabe als Eingabe verwendet wird.

Hier ist der Link übrigens. http://en.wikipedia.org/wiki/SHA-2#Hash_function

Thanks a lot, Brian

Answer 1

einen Blick auf dem offiziellen Standard hat, dass der Algorithmus beschreibt, werden die Variablen hier beschrieben: http://csrc.nist.gov/publications/fips/fips180-4/fips-180-4.pdf

(Oh, jetzt sehe ich, ich bin fast ein Jahr spät mit meiner Antwort, ah, geschweige denn ...)

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 wird aus dem aktuellen Block, abgeleitet verarbeitet, während K_t ist eine feste Konstante durch die Iterationszahl bestimmt. Die Komprimierungsfunktion wird für jeden Block in SHA256 64-mal wiederholt. Es gibt eine spezifische Konstante k_t und ein abgeleitete Wert W_t für jede Iteration 0 < = t < = 63.

Ich habe meine eigene Implementierung von SHA256 versehen mit Python 3.6. Das Tupel K enthält die 64 konstanten Werte von K_t. Die Sha256 Funktion zeigt, wie der Wert von W_t in der Liste W berechnet wird. Die Implementierung konzentriert sich auf Code-Klarheit und nicht auf hohe Leistung.

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))