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

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)