crypto file2

8/8/2019 crypto file2

1/22

Cryptography and Network SecurityPRACTICAL FILE

TIT-751

SUBMITTED TO SUBMITTED BY

1


2/22

INDEX

Sl.No

.Name of Practicals PageNo. Date

Remarks &

Signature

1.Caesar Cipher

implementation 3-5

2.Eucledian

Algorithm 6-7

3.

Euclidean

Algorithm for 10

numbers stored in

array

8-9

4.Implementation of

RSA algorithm 10-12

5.

Implementation of

LCG algorithm 13-18

6.

Implementation of

miller rabinalgorithm

19-22

7.

2


3/22

PROGRAM 1

Caesar Cipher Algorithm:

Earliest known use of substitution cipher was by Julius Caesar.

1. assign a numerical equivalent to each letter

a = 0

b = 1

c = 2

.

.

.

.

.

.

y = 24

z = 25.

2. For each plain text letter p, substitute the cipher text letter C

As

C = E(3,p) = ( p+3) mod 26.3. general Caesar algorithm is

C = E(k,p) = (p+k) mod26

P = D(k,C) = (C- k)mod26

3


4/22

Implementation of caesar cipher :

/*ceasar cipher .. */

#include#include

void main()

{

int a, i, d;

char arr[5];

clrscr();

printf("Enter the character to be encoded\n");

for(i=0;i


5/22

/*******************OUTPUT******************/

Enter the character to be encoded

abcdef

Enter the value to be added3

defghi

5


6/22

PROGRAM #2

Eucledian algorithm

EUCLID(a,b)

1. A a; B b;

2. if B=0 return A = gcd(a,b)

3. R = A mod B

4. A B

5. B R

6. goto step 2.

Implementation of Eucledian algorithm in C

#include

#include

int gcd(int,int);

void main()

{

int x,y,GCD;

clrscr();

printf("Enter the number whose GCD is to be calculated\n");

scanf("%d \n%d", &x,&y);

if(x==0)GCD = y;

else if(y==0)

GCD = x;

else

GCD = gcd(x,y);

6


7/22

printf("The GCD of the given numbers is \n%d", GCD);

getch();

}

int gcd(int a, int b)

{

int g, k;

if(b==0)

g=a;

else{

k = a%b;

g = gcd(b,k);

}

return(g);}

/********************OUTPUT*******************/

Enter the number whose GCD is to be calculated

55

35

The GCD of the given numbers is5

7


8/22

PROGRAM #3

Finding GCD of 10 numbers stored in array using Eucledian

algorithm.

#include

#include

int gcd(int x,int y);

void main()

{int x,y,i,j,sml;

int a[10],b[9];

clrscr();

printf("enter ten numbers");

for(i=0;i


9/22

}

int gcd(int x,int y)

{

if(x==0)

return y;if(y==0)

return x;

return(gcd((y%x),x));

}

9


10/22

PROGRAM #4

RSA algorithm.

1. Select two prime number p & q.2. Calculate n=p*q.

3. Calculate (n)=(p-1)*(q-1).

4. Select e such that e relatively prime to (n) and e


11/22

for(i=0;i< e;i++)

C=C*M%n;

C = C%n;

printf("\n\tEncrypted keyword : %d",C);

}

void decrypt()

{

int i;

M = 1;

for(i=0;i< d;i++)

M=M*C%n;

M = M%n;

printf("\n\tDecrypted keyword : %d",M);}

void main()

{

int p,q,s;

clrscr();

printf("Enter Two Relatively Prime Numbers\t: ");

scanf("%d%d",&p,&q);

n = p*q;

phi=(p-1)*(q-1);

printf("\n\tF(n)\t= %d",phi);

do

{

printf("\n\nEnter e\t: ");

scanf("%d",&e);

check();

}while(FLAG==1);d = 1;

do

{

s = (d*e)%phi;

d++;

11


12/22

}while(s!=1);

d = d-1;

printf("\n\tPublic Key\t: {%d,%d}",e,n);

printf("\n\tPrivate Key\t: {%d,%d}",d,n);

printf("\n\nEnter The Plain Text\t: ");

scanf("%d",&M);

encrypt();

printf("\n\nEnter the Cipher text\t: ");

scanf("%d",&C);

decrypt();

getch();

}

/*************** OUTPUT *****************/

Enter Two Relatively Prime Numbers : 7

17

F(n) = 96

Enter e : 5

Public Key : {5,119}

Private Key : {77,119}

Enter The Plain Text : 19

Encrypted keyword : 66

Enter the Cipher text : 66

Decrypted keyword : 19

12


13/22

PROGRAM #5

LCG Algorithm:

A linear congruential generator(LCG) represents one of the oldest and

best-known pseudorandom number generator algorithms. The theory behind

them is easy to understand, and they are easily implemented and fast.

The generator is defined by the recurrence relation:

where Xn is the sequence of pseudorandom values, and

the "modulus"

the "multiplier"

the "increment" (the special case ofc =

0 corresponds to ParkMiller RNG)

the "seed" or "start value"

are integer constants that specify the generator.

The period of a general LCG is at most m, and for some

choices ofa much less than that. The LCG will have a full

period if and only if:

1. and are relatively prime,

2. is divisible by all prime factors of ,

3. is a multiple of 4 if is a multiple of 4.[2]

13


14/22

Implementation of Linear congruential generator.

/**********************************************

/* A Basic Linear Congruential Generator/* ---------------------------------------

/**********************************************/

#include

#include

#include

//This class will give satisfy basic

// random number considerations for

// games an general apps.

class BasicLCG {

private:

unsigned long iCurrent;

public:

BasicLCG();

BasicLCG(unsigned long);

void seed(unsigned long iSeed);unsigned long nextNumber(); //get the next random number

unsigned short int nextInt();

unsigned char nextChar();

int nextBit();

double nextDouble();

int inRange(int min, int max);

};

//Just a little test code to print some numbersint main()

{

BasicLCG rng(time(NULL));

int i;

clrscr();

14


15/22

//Lets see some bits...

for( i=1; i


16/22

}

void BasicLCG::seed(unsigned long iSeed)

{

iCurrent = iSeed;

}

unsigned long BasicLCG::nextNumber()

{

unsigned long iOutput;

unsigned long iTemp;

int i;

//take the top two bits//This will shorten our period to (2^32)/16=268,435,456

//Which seems like plenty

for(i=0; i> 30;

iOutput = iOutput


17/22

//Since this is mod 2^32 and our data type is 32 bits long

// there is no need for the MOD operator.

iCurrent = (3039177861 * iCurrent + 1);

iTemp = iCurrent >> 30;

iOutput = iOutput 30;

cOutput = cOutput > 31;

}

double BasicLCG::nextDouble()

{

return (double)nextNumber()/0xFFFFFFFF;

}

int BasicLCG::inRange(int iMin, int iMax)

17


18/22

{

int Diff;

//IF the user put them in backwards then swap them

if (iMax


19/22

PROGRAM #6

Miller Rabin Algorithm

TEST(n)1. Find integers k, q, with k>0 , q odd, so that (n-1 = 2kq);

2. select a random integer a, 1 < a < n-1;

3. if aq mod n = 1 then return (inconclusive);

4. for j = 0 to k-1 do

5. if a2^j q mod n n-1 then return(inconclusive);

6. return(composite);

Implementation in c

#include

#include

#include #include

#include "c:\tc\bin\integer.h"

#define COMPOSITE 0

#define PRIME 1

integer modular_exponent(integer base, integer power, integer modulus) {

int i, bit;integer result = create_integer(modulus.num_components + 1);

integer temp = create_integer(modulus.num_components*2 + 1);

set_zero_integer(result);

result.c[0] = 1;

19


20/22

for(i=power.num_components - 1; i>=0; i--) {

for(bit=COMPONENT_BITS-1; bit>=0; bit--) {

multiply_integer(result, result, temp);

mod_integer(temp, modulus, result);

if ((power.c[i] & (1


21/22

if (compare_integers(a_to_power, one) == 0) { result=PRIME; goto

exit; }

for(i=0; i < s-1; i++) {

if (compare_integers(a_to_power, n_minus_one) == 0)

{ result=PRIME; goto exit; }

multiply_integer(a_to_power, a_to_power, temp);

mod_integer(temp, n, a_to_power);

}

if (compare_integers(a_to_power, n_minus_one) == 0) { result=PRIME;

goto exit; }

result = COMPOSITE;

exit:

free_integer(temp);free_integer(a_to_power);

free_integer(one);

free_integer(n_minus_one);

return result;

}

void random_integer(integer max, integer result) {

int i, most_sig = max.num_components - 1;

while (max.c[most_sig] == 0) most_sig--;

for (i=0; i


22/22

random_integer(n, a);

} while (is_zero_integer(a));

if (miller_rabin_pass(a, n) == COMPOSITE) {

return COMPOSITE;

}

}

return PRIME;

}

int main(int argc, char* argv[]) {

srand(time(NULL));

if (strcmp(argv[1], "test") == 0) {

integer n = string_to_integer(argv[2]);puts(miller_rabin(n) == PRIME ? "PRIME" : "COMPOSITE");

} else if (strcmp(argv[1], "genprime") == 0) {

integer max = create_integer(atoi(argv[2])/COMPONENT_BITS);

integer p = create_integer(max.num_components);

set_zero_integer(max);

max.c[max.num_components-1] = MAX_COMPONENT;

do {

random_integer(max, p);

if ((p.c[0] % 2) == 0) continue;

if (mod_small_integer(p, 3) == 0) continue;



} while (miller_rabin(p) == COMPOSITE);

puts(integer_to_string(p));

}

return 0;}

Documents

crypto file2