RSA algorithm in the SSL - rsa

Question

I want to know about the explanation of RSA, here is the example
Select primes: p=17 & q=11
Compute n = pq =17×11=187
Compute ø(n)=(p–1)(q-1)=16×10=160
Select e : gcd(e,160)=1; choose e=7
Determine d: de=1 mod 160 and d < 160 Value is d=23 since 23×7=161= 10×160+1
Publish public key KU={7,187}
Keep secret private key KR={23,17,11}
Look at the prime numbers written above, how can i know from where those prime numbers are generated.

Answer 1

Those prime numbers can be generated randomly by the RSA algorithm. In this example they are very small, but in real life the would be very very large. The algorithm will also take some other precautions when generating the primes. For instance, p and q should not be close to one another.

Answer 2

here is the code that implements RSA
try out this code
/*Arpana*/
#include<stdio.h>
#include<conio.h>
#include<stdlib.h>
#include<math.h>
#include<string.h>
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();
void main()
{
clrscr();
printf("\nENTER FIRST PRIME NUMBER\n");
scanf("%d",&p);
flag=prime(p);
if(flag==0)
{
printf("\nWRONG INPUT\n");
getch();
exit(1);
}
printf("\nENTER ANOTHER PRIME NUMBER\n");
scanf("%d",&q);
flag=prime(q);
if(flag==0||p==q)
{
printf("\nWRONG INPUT\n");
getch();
exit(1);
}
printf("\nENTER MESSAGE\n");
fflush(stdin);
scanf("%s",msg);
for(i=0;msg[i]!=NULL;i++)
m[i]=msg[i];
n=p*q;
t=(p-1)*(q-1);
ce();
printf("\nPOSSIBLE VALUES OF e AND d ARE\n");
for(i=0;i<j-1;i++)
printf("\n%ld\t%ld",e[i],d[i]);
encrypt();
decrypt();
getch();
}
int prime(long int pr)
{
int i;
j=sqrt(pr);
for(i=2;i<=j;i++)
{
if(pr%i==0)
return 0;
}
return 1;
}
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;
printf("\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;
printf("\nTHE DECRYPTED MESSAGE IS\n");
for(i=0;m[i]!=-1;i++)
printf("%c",m[i]);
}