SHA 256 pseuedocode?

Question

I've been trying to work out how SHA-256 works. One thing I've been doing for other algorithms is I've worked out a sort of step by step pseudocode function for the algorithm.

I've tried to do the same for SHA256 but thus far I'm having quite a bit of trouble.

I've tried to work out how the Wikipedia diagram works but besides the text part explaining the functions I'm not sure I've got it right.

Here's what I have so far:

• 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?

Did I get all of those addition modulos right?

what are Wt and Kt?

Would this get run once, and you're done or does it need to be run a certain number of times, with the output being re-used as input?

Here's the link by the way. http://en.wikipedia.org/wiki/SHA-2#Hash_function

Thanks alot, Brian

Answer 1

Have a look at the official standard that describes the algorithm, the variables are described here: http://csrc.nist.gov/publications/fips/fips180-4/fips-180-4.pdf

(Oh, now I see I'm almost a year late with my answer, ah, never mind...)

Answer 2

W_t is derived from the current block being processed while K_t is a fixed constant determined by the iteration number. The compression function is repeated 64 times for each block in SHA256. There is a specific constant K_t and a derived value W_t for each iteration 0 <= t <= 63.

I have provided my own implementation of SHA256 using Python 3.6. The tuple K contains the 64 constant values of K_t. The Sha256 function shows how the value of W_t is computed in the list W. The implementation focuses on code clarity and not high-performance.

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))

Answer 3

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)