SHA Hash Algorithm

Important property:

• One way from input to hash value, cannot reverse
• Different input cannot generate the same hash value

Actual SHA example:

• Choose a word to hash, eg CRYPTO
• Convert the word to ASCII

         CRYPTO becomes 67 82 89 80 84 79

• Convert from ASCII to binary

         01000011-01010010-01011001-01010000-01010100-01001111 

        (it becomes a 48 bit message)

• Join and add 1 at the end

         0100001101010010010110010101000001010100010011111

• Add zeros to make message equal to 448 mod 512, a 48 bit message with the added one will need to have 399 zeros added to the end
• Add original message length to the 64 bit field (which is the left over field after the 448 modular arithmetic), and let the message become 16 sections of 32 bits
01000011010100100101100101010000
01010100010011111000000000000000
00000000000000000000000000000000
00000000000000000000000000000000
00000000000000000000000000000000
00000000000000000000000000000000
00000000000000000000000000000000
00000000000000000000000000000000
00000000000000000000000000000000
00000000000000000000000000000000
00000000000000000000000000000000
00000000000000000000000000000000
00000000000000000000000000000000
00000000000000000000000000000000
00000000000000000000000000000000
00000000000000000000000000110000
• Transform the 16 x 32 message into 80 words using step loop function, firstly, do ((14 XOR 9) XOR 3) XOR 1), we get

         01000011010100100101100101010000

• Rotate left, we get

         10000110101001001011001010100000

• Process is repeated until there are 80 words (one word = 32 bits)

• The 1st, 3rd, 9th 14th words are chosen from the algorithm:
for i from 16 to 79
      w[i] = (w[i-3] xor w[i-8] xor w[i-14] xor w[i-16]) leftrotate 1

Run a set of operations on the 80 words in specific order using the five variables

H0 - 01100111010001010010001100000001

H1 - 11101111110011011010101110001001

H2 - 10011000101110101101110011111110

H3 - 00010000001100100101010001110110

H4 – 11000011110100101110000111110000

• The Operations are combination of AND, OR and NOT operators
• The five variables are from first 32 bits of the fractional part of the square roots of the first 5 prime numbers
• The result : get five variables

H0 – 01000100101010010111000100110011

H1- 01010000111001010011100001011000

H2-11110000010110000100011000111101

H3-01001011111101111111000111100101

H4-01000010110110011100101001001011

• Convert the five variables to hex

H0- 44a97133

H1- 50e53858

H2- f058463d

H3 - 4bf7f1e5

H4 - 42d9ca4b

• Join the variables together, get the hash

44a9713350e53858f058463d4bf7f1e542d9ca4b