WARNIG: It is not allowed, in the description of a video, to use either the left angled bracket character (in Latex such character is $\langle$) or the right angled bracket character (in Latex such character is $
angle$). Therefore, before compile the C source codes below change any character "¿" to the left angled bracket character ($\langle$) and any character "?" to the right angled bracket character ($
angle$).
gerardov@vega:~/ShorA$ cat ord_a_mod_n.c
#include¿stdio.h?
main(argc, argv)
int argc;
char *argv[];
{
int a, mod_n, y, i;
long unsigned int x=1;
a = atoi(argv[1]);
mod_n = atoi(argv[2]);
for(i=1;;i++) {
y = x;
x = (x*a)%mod_n;
printf("%d^%d (mod %d) = %d*%d (mod %d) = %d
",a,i,mod_n,a,y,mod_n,x);
if(x==1) break;
}
printf("Therefore the multiplicative order r is an ");
if(i&1) printf("odd number
");
else printf("even number and r/2=%d
",i/2);
}
gerardov@vega:~/ShorA$ cat FEA.c
#include¿stdio.h?
main(argc, argv)
int argc;
char *argv[];
{
int a, p, mod_n, nb, bit, e=0, i;
long unsigned int x=1;
a = atoi(argv[1]);
p = atoi(argv[2]);
mod_n = atoi(argv[3]);
for(nb=0,e=p;;nb++) {
if(!e) break;
e ??= 1;
}
for(i=1,e=0;i¿nb+1;i++) {
x = (x*x)%mod_n;
bit=(p??(nb-i))&1;
e*=2;
printf("%d^%d (mod %d) = %d | %d | ",a,e,mod_n,x,bit);
if(bit) {
x = (a*x)%mod_n;
e+=1;
printf("%d^%d (mod %d) = %d
",a,e,mod_n,x);
} else printf(" do nothing
");
}
printf(" Therefore v = %d
",x);
}
gerardov@vega:~/ShorA$ cat gcd.c
#include¿stdio.h?
main(argc, argv)
int argc;
char *argv[];
{
int vp1, mod_n, a, b, r;
a = vp1 = (atoi(argv[1]));
b = mod_n = (atoi(argv[2]));
if((a==0)||(b==0)) { printf("gcd: Error
"); exit(1); }
if(a¿0) a = -a;
if(b¿0) b = -b;
do {
r = a % b;
a = b;
b = r;
} while(r!=0);
printf("p=gcd(%d,%d)=%d and q=%d
",vp1,mod_n,a,mod_n/a);
}
drive.google.com/file/d/1hjusTkn6acid7G7_4rAuimRDhXN5Jy23/view?usp=drive_link
drive.google.com/file/d/1CBH0Xw9nSfnQimeqdvLiP-FdMdtSCggm/view?usp=drive_link
drive.google.com/file/d/1BJYVYNf1GdrY_tv4ly8RM9A-dM9eReD-/view?usp=drive_link
drive.google.com/file/d/1mjdCp1Ri77RPl5ySedquo10i_lY81rKR/view?usp=drive_link