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Program to Implement the RSA Algorithm

/* Program to Implement the RSA Algorithm This C++ program encodes any message using RSA Algorithm. Input is case sensitive and works only for all characters. RSA is one of the first practicable public-key cryptosystems and is widely used for secure data transmission. In such a cryptosystem, the encryption key is public and differs from the decryption key which is kept secret. In RSA, this asymmetry is based on the practical difficulty of factoring the product of two large prime numbers, the factoring problem. RSA stands for Ron Rivest, Adi Shamir and Leonard Adleman. */ #include<iostream> #include<math.h> #include<string.h> #include<stdlib.h> using namespace std; long int p, q, n, t, flag, e[100], d[100], temp[100], j, m[100], en[100], i; char msg[100]; int prime(long int); void ce(); long int cd(long int); void encrypt(); void decrypt(); int prime(long int pr) { int i; j = sqrt(pr); for (i = 2; i <= j; i++) { if (pr % i == 0) return 0; } return 1; } int main() { cout << "\nenter first prime number\n"; cin >> p; flag = prime(p); if (flag == 0) { cout << "\nwrong input\n"; exit(1); } cout << "\nenter another prime number\n"; cin >> q; flag = prime(q); if (flag == 0 || p == q) { cout << "\nwrong input\n"; exit(1); } cout << "\nenter message\n"; fflush(stdin); cin >> msg; for (i = 0; msg[i] != NULL; i++) m[i] = msg[i]; n = p * q; t = (p - 1) * (q - 1); ce(); cout << "\npossible values of e and d are\n"; for (i = 0; i < j - 1; i++) cout << e[i] << "\t" << d[i] << "\n"; encrypt(); decrypt(); return 0; } void ce() { int k; k = 0; for (i = 2; i < t; i++) { if (t % i == 0) continue; flag = prime(i); if (flag == 1 && i != p && i != q) { e[k] = i; flag = cd(e[k]); if (flag > 0) { d[k] = flag; k++; } if (k == 99) break; } } } long int cd(long int x) { long int k = 1; while (1) { k = k + t; if (k % x == 0) return (k / x); } } void encrypt() { long int pt, ct, key = e[0], k, len; i = 0; len = strlen(msg); while (i != len) { pt = m[i]; pt = pt - 96; k = 1; for (j = 0; j < key; j++) { k = k * pt; k = k % n; } temp[i] = k; ct = k + 96; en[i] = ct; i++; } en[i] = -1; cout << "\nthe encrypted message is\n"; for (i = 0; en[i] != -1; i++) printf("%c", en[i]); } void decrypt() { long int pt, ct, key = d[0], k; i = 0; while (en[i] != -1) { ct = temp[i]; k = 1; for (j = 0; j < key; j++) { k = k * ct; k = k % n; } pt = k + 96; m[i] = pt; i++; } m[i] = -1; cout << "\nthe decrypted message is\n"; for (i = 0; m[i] != -1; i++) printf("%c", m[i]); }

Break statement in C++ is a loop control statement defined using the break keyword. It is used to stop the current execution and proceed with the next one. When a compiler calls the break statement, it immediately stops the execution of the loop and transfers the control outside the loop and executes the other statements. In the case of a nested loop, break the statement stops the execution of the inner loop and proceeds with the outer loop. The statement itself says it breaks the loop. When the break statement is called in the program, it immediately terminates the loop and transfers the flow control to the statement mentioned outside the loop.

#include is a way of including a standard or user-defined file in the program and is mostly written at the beginning of any C/C++ program. This directive is read by the preprocessor and orders it to insert the content of a user-defined or system header file into the following program. These files are mainly imported from an outside source into the current program. The process of importing such files that might be system-defined or user-defined is known as File Inclusion. This type of preprocessor directive tells the compiler to include a file in the source code program.

Strings are objects that represent sequences of characters. The standard string class provides support for such objects with an interface similar to that of a standard container of bytes, but adding features specifically designed to operate with strings of single-byte characters. The string class is an instantiation of the basic_string class template that uses char (i.e., bytes) as its character type, with its default char_traits and allocator types. Note that this class handles bytes independently of the encoding used: If used to handle sequences of multi-byte or variable-length characters (such as UTF-8), all members of this class (such as length or size), as well as its iterators, will still operate in terms of bytes (not actual encoded characters).

Get string length. Returns the length of the C string str. C++ strlen() is an inbuilt function that is used to calculate the length of the string. It is a beneficial method to find the length of the string. The strlen() function is defined under the string.h header file. The strlen() takes a null-terminated byte string str as its argument and returns its length. The length does not include a null character. If there is no null character in the string, the behavior of the function is undefined.

In computer programming, loops are used to repeat a block of code. For example, when you are displaying number from 1 to 100 you may want set the value of a variable to 1 and display it 100 times, increasing its value by 1 on each loop iteration. When you know exactly how many times you want to loop through a block of code, use the for loop instead of a while loop. A for loop is a repetition control structure that allows you to efficiently write a loop that needs to execute a specific number of times.

The cin object is used to accept input from the standard input device i.e. keyboard. It is defined in the iostream header file. C++ cin statement is the instance of the class istream and is used to read input from the standard input device which is usually a keyboard. The extraction operator(>>) is used along with the object cin for reading inputs. The extraction operator extracts the data from the object cin which is entered using the keyboard. The "c" in cin refers to "character" and "in" means "input". Hence cin means "character input". The cin object is used along with the extraction operator >> in order to receive a stream of characters.

In while loop, condition is evaluated first and if it returns true then the statements inside while loop execute, this happens repeatedly until the condition returns false. When condition returns false, the control comes out of loop and jumps to the next statement in the program after while loop. The important point to note when using while loop is that we need to use increment or decrement statement inside while loop so that the loop variable gets changed on each iteration, and at some point condition returns false. This way we can end the execution of while loop otherwise the loop would execute indefinitely. A while loop that never stops is said to be the infinite while loop, when we give the condition in such a way so that it never returns false, then the loops becomes infinite and repeats itself indefinitely.

Consider a situation, when we have two persons with the same name, jhon, in the same class. Whenever we need to differentiate them definitely we would have to use some additional information along with their name, like either the area, if they live in different area or their mother's or father's name, etc. Same situation can arise in your C++ applications. For example, you might be writing some code that has a function called xyz() and there is another library available which is also having same function xyz(). Now the compiler has no way of knowing which version of xyz() function you are referring to within your code.

A program shall contain a global function named main, which is the designated start of the program in hosted environment. main() function is the entry point of any C++ program. It is the point at which execution of program is started. When a C++ program is executed, the execution control goes directly to the main() function. Every C++ program have a main() function.

The if...else statement executes two different codes depending upon whether the test expression is true or false. Sometimes, a choice has to be made from more than 2 possibilities. The if...else ladder allows you to check between multiple test expressions and execute different statements. In C/C++ if-else-if ladder helps user decide from among multiple options. The C/C++ if statements are executed from the top down. As soon as one of the conditions controlling the if is true, the statement associated with that if is executed, and the rest of the C else-if ladder is bypassed. If none of the conditions is true, then the final else statement will be executed.

Flush stream. The fflush() function in C++ flushes any buffered data to the respective device. Buffered data is the temporary or application specific data stored in the physical memory of the computer until a certain time. If the given stream was open for writing (or if it was open for updating and the last i/o operation was an output operation) any unwritten data in its output buffer is written to the file. If stream is a null pointer, all such streams are flushed. In all other cases, the behavior depends on the specific library implementation. In some implementations, flushing a stream open for reading causes its input buffer to be cleared (but this is not portable expected behavior).

Logical Operators are used to compare and connect two or more expressions or variables, such that the value of the expression is completely dependent on the original expression or value or variable. We use logical operators to check whether an expression is true or false. If the expression is true, it returns 1 whereas if the expression is false, it returns 0. Assume variable A holds 1 and variable B holds 0:

The exit function terminates the program normally. Automatic objects are not destroyed, but static objects are. Then, all functions registered with atexit are called in the opposite order of registration. The code is returned to the operating system. An exit code of 0 or EXIT_SUCCESS means successful completion. If code is EXIT_FAILURE, an indication of program failure is returned to the operating system. Other values of code are implementation-defined. Calls all functions registered with the atexit() function, and destroys C++ objects with static storage duration, all in last-in-first-out (LIFO) order. C++ objects with static storage duration are destroyed in the reverse order of the completion of their constructor. (Automatic objects are not destroyed as a result of calling exit().)

Continue statement is used inside loops. Whenever a continue statement is encountered inside a loop, control directly jumps to the beginning of the loop for next iteration, skipping the execution of statements inside loop's body for the current iteration. The continue statement works somewhat like the break statement. Instead of forcing termination, however, continue forces the next iteration of the loop to take place, skipping any code in between. For the for loop, continue causes the conditional test and increment portions of the loop to execute. For the while and do...while loops, program control passes to the conditional tests.

Compute square root. Returns the square root of x. The sqrt() function in C++ returns the square root of a number. This function is defined in the cmath header file. There are various functions available in the C++ Library to calculate the square root of a number. Most prominently, sqrt is used. It takes double as an argument. The <cmath> header defines two more inbuilt functions for calculating the square root of a number (apart from sqrt) which has an argument of type float and long double. Therefore, all the functions used for calculating square root in C++ are. Mathematically, sqrt(x) = √x.

In computer programming, we use the if statement to run a block code only when a certain condition is met. An if statement can be followed by an optional else statement, which executes when the boolean expression is false. There are three forms of if...else statements in C++: • if statement, • if...else statement, • if...else if...else statement, The if statement evaluates the condition inside the parentheses ( ). If the condition evaluates to true, the code inside the body of if is executed. If the condition evaluates to false, the code inside the body of if is skipped.

Program demonstrates the implementation of Ternary Seach Tree. Create a new ternary search tree node. And insert a new word in a Ternary Search Tree. Search a given word in