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# Implement Secure Hashing Algorithm – 512 ( SHA-512 ) as Functional Programming Paradigm

• Difficulty Level : Medium
• Last Updated : 13 Jan, 2023

Given a string S of length N, the task is to find the SHA-512 Hash Value of the given string S.

Examples:

Input: S = “GeeksforGeeks”

Input: S = “hello world”
Output:
309ecc489c12d6eb4cc40f50c902f2b4d0ed77ee511a7c7a9bcd3ca86d4cd86f989dd35bc5ff499670da34255b45b0cfd830e81f605dcf7dc5542e93ae9cd76f

Approach: Follow the steps below to solve the problem:

• Convert the given string into the binary form.
• Append ‘1’ to the string and then ‘0’ continuously until length of the string is < (N%(1024 – 128)).
• Add the 128-bit binary representation of N in the string S.
• Find the number of chunks of the size of 1024 and store it in a variable, say chunks as N/1024.
• Divide the string S into 16 chunks of 64 characters.
• Extend the number of chunks to 80 by performing the following operations:
• Iterate over the range [16, 80] and then find 4 values say WordA, WordB, WordC, WordD as:
• WordA = rotate_right(Message[g – 2], 19) ^ rotate_right(Message[g – 2], 61) ^ shift_right(Message[g – 2], 6).
• WordB = Message[g – 7].
• WordC = rotate_right(Message[g – 15], 1) ^ rotate_right(Message[g – 15], 8) ^ shift_right(Message[g – 15], 7).
• WordD = Message[g – 16].
• Update the value of Message[g] as (WordA + WordB + WordC + WordD).
• Initialize 8 variables say A, B, C, D, E, F, G, H of type 64-bit to store the final hash value of the given string S.
• Traverse the array Block[] and perform the following steps:
• Update the value of A, B, C, D, E, F, G, H using the Hash Function till 80 iterations by rotating one by one.
• Now, update the value of A, B, C, D, E, F, G, H by the summation of previous values of A, B, C, D, E, F, G, H and the newly updated value of A, B, C, D, E, F, G, H.
• After completing the above steps, print the hexadecimal values of A, B, C, D, E, F, G, H to get the Hash Value of the given string.

Below is the implementation of the above approach:

## C++14

 `// C++ program for the above approach` `#include ` `using` `namespace` `std;` `typedef` `unsigned ``long` `long` `int` `int64;`   `int64 Message[80];`   `// Stores the hexadecimal values for` `// calculating hash values` `const` `int64 Constants[80]` `    ``= { 0x428a2f98d728ae22, 0x7137449123ef65cd,` `        ``0xb5c0fbcfec4d3b2f, 0xe9b5dba58189dbbc,` `        ``0x3956c25bf348b538, 0x59f111f1b605d019,` `        ``0x923f82a4af194f9b, 0xab1c5ed5da6d8118,` `        ``0xd807aa98a3030242, 0x12835b0145706fbe,` `        ``0x243185be4ee4b28c, 0x550c7dc3d5ffb4e2,` `        ``0x72be5d74f27b896f, 0x80deb1fe3b1696b1,` `        ``0x9bdc06a725c71235, 0xc19bf174cf692694,` `        ``0xe49b69c19ef14ad2, 0xefbe4786384f25e3,` `        ``0x0fc19dc68b8cd5b5, 0x240ca1cc77ac9c65,` `        ``0x2de92c6f592b0275, 0x4a7484aa6ea6e483,` `        ``0x5cb0a9dcbd41fbd4, 0x76f988da831153b5,` `        ``0x983e5152ee66dfab, 0xa831c66d2db43210,` `        ``0xb00327c898fb213f, 0xbf597fc7beef0ee4,` `        ``0xc6e00bf33da88fc2, 0xd5a79147930aa725,` `        ``0x06ca6351e003826f, 0x142929670a0e6e70,` `        ``0x27b70a8546d22ffc, 0x2e1b21385c26c926,` `        ``0x4d2c6dfc5ac42aed, 0x53380d139d95b3df,` `        ``0x650a73548baf63de, 0x766a0abb3c77b2a8,` `        ``0x81c2c92e47edaee6, 0x92722c851482353b,` `        ``0xa2bfe8a14cf10364, 0xa81a664bbc423001,` `        ``0xc24b8b70d0f89791, 0xc76c51a30654be30,` `        ``0xd192e819d6ef5218, 0xd69906245565a910,` `        ``0xf40e35855771202a, 0x106aa07032bbd1b8,` `        ``0x19a4c116b8d2d0c8, 0x1e376c085141ab53,` `        ``0x2748774cdf8eeb99, 0x34b0bcb5e19b48a8,` `        ``0x391c0cb3c5c95a63, 0x4ed8aa4ae3418acb,` `        ``0x5b9cca4f7763e373, 0x682e6ff3d6b2b8a3,` `        ``0x748f82ee5defb2fc, 0x78a5636f43172f60,` `        ``0x84c87814a1f0ab72, 0x8cc702081a6439ec,` `        ``0x90befffa23631e28, 0xa4506cebde82bde9,` `        ``0xbef9a3f7b2c67915, 0xc67178f2e372532b,` `        ``0xca273eceea26619c, 0xd186b8c721c0c207,` `        ``0xeada7dd6cde0eb1e, 0xf57d4f7fee6ed178,` `        ``0x06f067aa72176fba, 0x0a637dc5a2c898a6,` `        ``0x113f9804bef90dae, 0x1b710b35131c471b,` `        ``0x28db77f523047d84, 0x32caab7b40c72493,` `        ``0x3c9ebe0a15c9bebc, 0x431d67c49c100d4c,` `        ``0x4cc5d4becb3e42b6, 0x597f299cfc657e2a,` `        ``0x5fcb6fab3ad6faec, 0x6c44198c4a475817 };`   `// Function to convert a binary string` `// to hexa-decimal value` `string gethex(string bin)` `{` `    ``if` `(bin == ``"0000"``)` `        ``return` `"0"``;` `    ``if` `(bin == ``"0001"``)` `        ``return` `"1"``;` `    ``if` `(bin == ``"0010"``)` `        ``return` `"2"``;` `    ``if` `(bin == ``"0011"``)` `        ``return` `"3"``;` `    ``if` `(bin == ``"0100"``)` `        ``return` `"4"``;` `    ``if` `(bin == ``"0101"``)` `        ``return` `"5"``;` `    ``if` `(bin == ``"0110"``)` `        ``return` `"6"``;` `    ``if` `(bin == ``"0111"``)` `        ``return` `"7"``;` `    ``if` `(bin == ``"1000"``)` `        ``return` `"8"``;` `    ``if` `(bin == ``"1001"``)` `        ``return` `"9"``;` `    ``if` `(bin == ``"1010"``)` `        ``return` `"a"``;` `    ``if` `(bin == ``"1011"``)` `        ``return` `"b"``;` `    ``if` `(bin == ``"1100"``)` `        ``return` `"c"``;` `    ``if` `(bin == ``"1101"``)` `        ``return` `"d"``;` `    ``if` `(bin == ``"1110"``)` `        ``return` `"e"``;` `    ``if` `(bin == ``"1111"``)` `        ``return` `"f"``;` `}`   `// Function to convert a decimal value` `// to hexa decimal value` `string decimaltohex(int64 deci)` `{` `    ``// Stores the value as string` `    ``string EQBIN = bitset<64>(deci).to_string();`   `    ``// Stores the equivalent hexa decimal` `    ``string hexstring = ``""``;` `    ``string temp;`   `    ``// Traverse the string EQBIN` `    ``for` `(unsigned ``int` `i = 0;` `         ``i < EQBIN.length(); i += 4) {` `        ``temp = EQBIN.substr(i, 4);` `        ``hexstring += gethex(temp);` `    ``}`   `    ``// Return the hexstring` `    ``return` `hexstring;` `}`   `// Function to convert a binary` `// string to decimal value` `int64 BintoDec(string bin)` `{`   `    ``int64 value = bitset<64>(bin)` `                      ``.to_ullong();` `    ``return` `value;` `}`   `// Function to right rotate x by n bits` `int64 rotate_right(int64 x, ``int` `n)` `{` `    ``return` `(x >> n) | (x << (64 - n));` `}`   `// Function to right shift x by n bits` `int64 shift_right(int64 x, ``int` `n)` `{` `    ``return` `(x >> n);` `}`   `// Function to divide the string` `// into chunks` `void` `separator(string getBlock)` `{` `    ``// Stores the size of chunks` `    ``int` `chunknum = 0;`   `    ``// Traverse the string S` `    ``for` `(unsigned ``int` `i = 0;` `         ``i < getBlock.length();` `         ``i += 64, ++chunknum) {`   `        ``// Update the Message[chunknum]` `        ``Message[chunknum]` `            ``= BintoDec(getBlock.substr(i, 64));` `    ``}`   `    ``// Iterate over the range [16, 80]` `    ``for` `(``int` `g = 16; g < 80; ++g) {`   `        ``// Find the WordA` `        ``int64 WordA = rotate_right(Message[g - 2], 19)` `                      ``^ rotate_right(Message[g - 2], 61)` `                      ``^ shift_right(Message[g - 2], 6);`   `        ``// Find the WordB` `        ``int64 WordB = Message[g - 7];`   `        ``// Find the WordC` `        ``int64 WordC = rotate_right(Message[g - 15], 1)` `                      ``^ rotate_right(Message[g - 15], 8)` `                      ``^ shift_right(Message[g - 15], 7);`   `        ``// Find the WordD` `        ``int64 WordD = Message[g - 16];`   `        ``// Find the resultant code` `        ``int64 T = WordA + WordB + WordC + WordD;`   `        ``// Return the resultant Hash Code` `        ``Message[g] = T;` `    ``}` `}`   `// Function to find the major of a, b, c` `int64 maj(int64 a, int64 b, int64 c)` `{` `    ``return` `(a & b) ^ (b & c) ^ (c & a);` `}`   `// Function to find the ch value of a,` `// b, and c` `int64 Ch(int64 e, int64 f, int64 g)` `{` `    ``return` `(e & f) ^ (~e & g);` `}`   `// Function to find the Bitwise XOR with` `// the right rotate over 14, 18, and 41` `int64 sigmaE(int64 e)` `{` `    ``// Return the resultant value` `    ``return` `rotate_right(e, 14)` `           ``^ rotate_right(e, 18)` `           ``^ rotate_right(e, 41);` `}`   `// Function to find the Bitwise XOR with` `// the right rotate over 28, 34, and 39` `int64 sigmaA(int64 a)` `{`   `    ``// Return the resultant value` `    ``return` `rotate_right(a, 28)` `           ``^ rotate_right(a, 34)` `           ``^ rotate_right(a, 39);` `}`   `// Function to generate the hash code` `void` `Func(int64 a, int64 b, int64 c,` `          ``int64& d, int64 e, int64 f,` `          ``int64 g, int64& h, ``int` `K)` `{` `    ``// Find the Hash Code` `    ``int64 T1 = h + Ch(e, f, g) + sigmaE(e) + Message[K]` `               ``+ Constants[K];` `    ``int64 T2 = sigmaA(a) + maj(a, b, c);`   `    ``d = d + T1;` `    ``h = T1 + T2;` `}`   `// Function to convert the hash value` `// of a given string` `string SHA512(string myString)` `{` `    ``// Stores the 8 blocks of size 64` `    ``int64 A = 0x6a09e667f3bcc908;` `    ``int64 B = 0xbb67ae8584caa73b;` `    ``int64 C = 0x3c6ef372fe94f82b;` `    ``int64 D = 0xa54ff53a5f1d36f1;` `    ``int64 E = 0x510e527fade682d1;` `    ``int64 F = 0x9b05688c2b3e6c1f;` `    ``int64 G = 0x1f83d9abfb41bd6b;` `    ``int64 H = 0x5be0cd19137e2179;`   `    ``int64 AA, BB, CC, DD, EE, FF, GG, HH;`   `    ``stringstream fixedstream;`   `    ``// Traverse the string S` `    ``for` `(``int` `i = 0;` `         ``i < myString.size(); ++i) {`   `        ``// Add the character to stream` `        ``fixedstream << bitset<8>(myString[i]);` `    ``}`   `    ``// Stores string of size 1024` `    ``string s1024;`   `    ``// Stores the string in the` `    ``// fixedstream` `    ``s1024 = fixedstream.str();`   `    ``// Stores the length of string` `    ``int` `orilen = s1024.length();` `    ``int` `tobeadded;`   `    ``// Find modded string length` `    ``int` `modded = s1024.length() % 1024;`   `    ``// If 1024-128 is greater than modded` `    ``if` `(1024 - modded >= 128) {` `        ``tobeadded = 1024 - modded;` `    ``}`   `    ``// Else if 1024-128 is less than modded` `    ``else` `if` `(1024 - modded < 128) {` `        ``tobeadded = 2048 - modded;` `    ``}`   `    ``// Append 1 to string` `    ``s1024 += ``"1"``;`   `    ``// Append tobeadded-129 zeros` `    ``// in the string` `    ``for` `(``int` `y = 0; y < tobeadded - 129; y++) {` `        ``s1024 += ``"0"``;` `    ``}`   `    ``// Stores the binary representation` `    ``// of string length` `    ``string lengthbits` `        ``= std::bitset<128>(orilen).to_string();`   `    ``// Append the lengthbits to string` `    ``s1024 += lengthbits;`   `    ``// Find the count of chunks of` `    ``// size 1024 each` `    ``int` `blocksnumber = s1024.length() / 1024;`   `    ``// Stores the numbering of chunks` `    ``int` `chunknum = 0;`   `    ``// Stores hash value of each blocks` `    ``string Blocks[blocksnumber];`   `    ``// Traverse the string s1024` `    ``for` `(``int` `i = 0; i < s1024.length();` `         ``i += 1024, ++chunknum) {` `        ``Blocks[chunknum] = s1024.substr(i, 1024);` `    ``}`   `    ``// Traverse the array Blocks[]` `    ``for` `(``int` `letsgo = 0;` `         ``letsgo < blocksnumber;` `         ``++letsgo) {`   `        ``// Divide the current string` `        ``// into 80 blocks size 16 each` `        ``separator(Blocks[letsgo]);`   `        ``AA = A;` `        ``BB = B;` `        ``CC = C;` `        ``DD = D;` `        ``EE = E;` `        ``FF = F;` `        ``GG = G;` `        ``HH = H;`   `        ``int` `count = 0;`   `        ``// Find hash values` `        ``for` `(``int` `i = 0; i < 10; i++) {`   `            ``// Find the Hash Values`   `            ``Func(A, B, C, D, E, F, G, H, count);` `            ``count++;` `            ``Func(H, A, B, C, D, E, F, G, count);` `            ``count++;` `            ``Func(G, H, A, B, C, D, E, F, count);` `            ``count++;` `            ``Func(F, G, H, A, B, C, D, E, count);` `            ``count++;` `            ``Func(E, F, G, H, A, B, C, D, count);` `            ``count++;` `            ``Func(D, E, F, G, H, A, B, C, count);` `            ``count++;` `            ``Func(C, D, E, F, G, H, A, B, count);` `            ``count++;` `            ``Func(B, C, D, E, F, G, H, A, count);` `            ``count++;` `        ``}`   `        ``// Update the value of A, B, C,` `        ``// D, E, F, G, H`   `        ``A += AA;` `        ``B += BB;` `        ``C += CC;` `        ``D += DD;` `        ``E += EE;` `        ``F += FF;` `        ``G += GG;` `        ``H += HH;` `    ``}`   `    ``stringstream output;`   `    ``// Print the hexadecimal value of` `    ``// strings as the resultant SHA-512` `    ``output << decimaltohex(A);` `    ``output << decimaltohex(B);` `    ``output << decimaltohex(C);` `    ``output << decimaltohex(D);` `    ``output << decimaltohex(E);` `    ``output << decimaltohex(F);` `    ``output << decimaltohex(G);` `    ``output << decimaltohex(H);`   `    ``// Return the string` `    ``return` `output.str();` `}`   `// Driver Code` `int` `main()` `{` `    ``// Input` `    ``string S = ``"GeeksForGeeks"``;`   `    ``// Function Call` `    ``cout << S << ``": "` `<< SHA512(S);`   `    ``return` `0;` `}`

Output:

`GeeksForGeeks: 0acc10c4e0b38617f59e88e49215e2e894afaee5ec948c2af6f44039f03c9fe47a9210e01d5cd926c142bdc9179c2ad30f927a8faf69421ff60a5eaddcf8cb9c`

Time Complexity: O(N)
Auxiliary Space: O(1)

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