Simplifying Simplified DES
1. SDES Overview
SDES Stands for “Simlified DES” or “Simplified Data Encryption Standard”. This cipher was developed by Professor Edward Schaefer of Santa Clara University. He developed SDES cipher for educational purpose. SDES has much similiar properties compared to real DES. It is usefull for anyone who wants to learn DES. By learning SDES you will gain more understanding on DES.
2. Detailed Step of SDES
SDES is a symetric cipher. It was able to encrypt 8 bit plain text with 10 bit of key. SDES cipher consisted of two round processes and adopt feistel structure, means each block has divided into left side process and right side process. Each side contains 4 bit.
At first, 8 bit plaintext will propagate through (IP) Initial Permutation. The upper nibble of Initial Permutation’s result, which are 4 left most bits, will go to left side process as well as lower nibble, which are 4 right most bits, will enter right process. On the right side process, the lower nibble of IP will be expanded into 8 bit by Expansion Process named “E/P”. This expanded lower nibble of IP then XOR-ed by K1 that comes out from key scheduling process which will explained later. The 8 bits of the result of XORing between K1 and expanded lower nibble of IP then splitted again into 2 nibbles. This two nibbles of XORing result will be used for SBOX input, the higher nibble for SBOX0 and the lower nibble for SBOX1. Since each SBOX results two bits, then total results of SBOX0 and SBOX1 will be 4 bits. These 4 bits then enter another permutation named “P4″ becoming another 4 bit. These another 4 bits will be used to XOR higher nibble of Initial Permutation that we had before. Thats all for first round.
On the second round, the result of XOR between previous complex function and higher nibble of IP will goes to Right side Process. On the other hand the original lower nibble of IP will goes to Left Side Process. The nibble that enter right process of second round will be expanded into 8 bit by expansion process named “E/P”. These expanded 8 bits then XORed by K2 that comes out form key scheduling. The result of that XORing process will be divided into 2 nibble as SBOX inputs. The higher nibble will enter SBOX0 and the lower niblle will enter SBOX1. Again, since each SBOX results2 bits then the total result of SBOX0 and SBOX1 will be 4 bits. These 4 bits then enter another permutation named “P4″. The result of P4 permutation will be used to XOR Left side process of second round.
At Last, the result of XORing process between complex function of senond round and left side process of second round will recombined again with right process of second round becoming 8 bits of data. These 8 bits data the enter last permutation named “Inverse of Initial Permutation” or (IP’). The result of IP’ then called ciphered text.
Moreover, key scheduling process will goes as follows: Key, which 10 bits will enter “P10″ permutation. The 5 left most bits of P10 and the 4 bits rightmost of P10 then experience Circular Left Shift and enter P8 permutation becoming K1. For K2, the each of the result of Circular Left Shift Process will experince another Left Circular Shift by 2 and enter “P8″ and results K2.
For Decrypting process, the step goes along provious process but with switched subkey. Means first round uses K2 and second round uses K1, the result of this process become original plaintext.
3. Permutation and SBOX details
To analyze SDES, first we have to see the detail of IP, IP’, P10, P8, P4, E/P, and SBOX. Roughly, permutation and expansion are nothing just bit scrambling. We can actually skip do this while brushing tooths 
(That was the joke of Mr. Hendra Tarigan’s joke during electromagnetic class). SBOX is nothing than boolean function, we can easily decompose this as express ach bit as boolean algebra. I’ve got this from Mr. Achmad Fuad Mas’ud, 5 thumbs up and big thanks to him.
Lets go back to our business and start the game: see all description below,
IP maps [abcdefgh] into [bfcadheg]
IP’ maps [abcdefgh] into [dacegbhf]
P10 maps [abcdefghij] into [cebgdjaihf]
P8 maps [abcdefghij] into [fcgdheji]
E/P maps [abcd] into [dabcdabc]
P4 maps [abcd] into [bdca]
4. Decomposing SBOX
From the truth table we can decompose each output as the function of input. These are the results:
SBOX0 Bit 1 : W'X'Z + W'XZ' + WY'Z + WYZ' + WXZ
SBOX0 Bit 2 : W’Y’ + WX’Z + Y’Z + WXZ’ SBOX1 Bit 1 : W’XZ’ + WX’Y’ + X’Y'Z + XYZ
SBOX1 Bit 2 : W’YZ’ + W’XZ + WY’Z’ + WYZ5. Simulation
I have made two simple program to emulate key scheduling and encryption/decryption process. Click on two links below, to download the file
6. Simplifying SDES
Key Scheduling Process:
- initailly key was [klmnopqrst]
- key enter P10 becoming [molqntksrp]
- divided into two becoming [molqn] and [tksrp]
- perform circular left shift by 1 becoming [olqnm] and [ksrpt]
- enter P8 become k1 = [kqsnrmtp]
- perform circular left shift by 1 becoming [qnmol] and [rptks]
- enter P8 become k2 = [rmpotlsk]
Encryption Process:
- initially plaintext was [abcdefgh]
- then plain text enter IP becoming [bfcadheg]
- IP result splitted into [bcfa] and [dheg]
- “dheg” enter “E/P” becoming [gdhehegd]
- XORed with [kqsnrmtp] becoming [g^k][d^q][h^s][e^n][h^r][e^m][g^t][d^p]
- [g^k][d^q][h^s][e^n] entering sbox0 become
Bit 1 = [[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]
Bit 2 = [[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]
- [h^r][e^m][g^t][d^p] entering sbox1 become
Bit 1 = [[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]
Bit 2 = [[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]
- Entering P4 becoming
Bit 1 = [[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]
Bit 2 = [[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]
Bit 3 = [[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]
Bit 4 = [[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]
- XORed by [bcfa] becoming
Bit 1 = b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]
Bit 2 = c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]
Bit 3 = f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]
Bit 4 = a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]
- Entering E/P becoming
Bit 1 = a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]
Bit 2 = b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]
Bit 3 = c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]
Bit 4 = f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]
Bit 5 = c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]
Bit 6 = f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]
Bit 7 = a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]
Bit 8 = b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]
- XORED by [rmpotlsk] becoming
Bit 1 = r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]
Bit 2 = m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]
Bit 3 = p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]
Bit 4 = o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]
Bit 5 = t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]
Bit 6 = l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]
Bit 7 = s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]
Bit 8 = k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]
- Bit 1:4 entering SBOX0 become
Bit 1 = [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’ + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’ + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]
Bit 2 = [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’ + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’
- Bit 5:7 entering SBOX0 become
Bit 1 = [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’ + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’[s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’ + [l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’[s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]] + [l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]][s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]
Bit 2 = [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’ + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]] + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’ + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]
- entering P4 become
Bit 1 = [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’ + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’
Bit 2 = [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’ + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]] + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’ + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]
Bit 3 = [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’ + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’[s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’ + [l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’[s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]] + [l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]][s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]
Bit 4 = [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’ + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’ + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]
- XORed by [dheg] become
Bit 1 = d^[r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’ + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’
Bit 2 = h^[t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’ + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]] + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’ + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]
Bit 3 = e^[t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’ + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’[s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’ + [l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’[s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]] + [l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]][s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]
Bit 4 = g^[r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’ + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’ + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]
- Combined with result of step 9 become
Bit 1 = d^[r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’ + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’
Bit 2 = h^[t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’ + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]] + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’ + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]
Bit 3 = e^[t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’ + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’[s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’ + [l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’[s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]] + [l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]][s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]
Bit 4 = g^[r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’ + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’ + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]
Bit 5 = b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]
Bit 6 = c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]
Bit 7 = f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]
Bit 8 = a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]
- Enter Inverse Initial Permutation becoming
Bit 1 = g^[r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’ + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’ + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]
Bit 2 = d^[r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’ + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [p^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]] + [r^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][m^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]][o^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’
Bit 3 = e^[t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’ + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’[s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’ + [l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]]’[s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]] + [l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]][s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]
Bit 4 = b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]
Bit 5 = f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]
Bit 6 = h^[t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’ + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]]’[l^[f^[[h^r]‘[e^m][d^p]‘ + [h^r][e^m]‘[g^t]‘ + [e^m]‘[g^t]‘[d^p] + [e^m][g^t][d^p]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]] + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]]’[k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]’ + [t^[c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]]][s^[a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]]][k^[b^[[g^k]‘[h^s]‘ + [g^k][d^q]‘[e^n] + [h^s]‘[e^n] + [g^k][d^q][e^n]‘]]]
Bit 7 = a^[[g^k]‘[d^q]‘[e^n] + [g^k]‘[d^q][e^n]‘ + [g^k][h^s]‘[e^n] + [g^k][h^s][e^n]‘ + [g^k][d^q][e^n]]
Bit 8 = c^[[h^r]‘[g^t][d^p]‘ + [h^r]‘[e^m][d^p] + [h^r][g^t]‘[d^p]‘ + [h^r][g^t][d^p]]
Finally we get all of those huge equation
