#C2.txt, Jan. 22, 2024
Help:=proc(): print(` NextPrime1(n),MakeRSAkey(D1), ME1s(a,e,n), ME1(a,e,n) `): end:

#NextPrime1(n): inputs a pos. integer n
#and outputs the first prime >=n
NextPrime1:=proc(n) local i:

for i from n while not isprime(i) do od:
i:
end:

#MakeRSAkey: The key [n,e]: a->a^e mod n
#n must be a product of two primes
#inputs D1 and outputs an RSA key
#[n,e], where n is a product of two primes
#with D1 digits. Try:
#MakeRSAkey(100);
MakeRSAkey:=proc(D1) local n:
n:=NextPrime1(rand(10^(D1-1)..10^D1-1)())*
NextPrime1(rand(10^(D1-1)..10^D1-1)()):
n:
end:

#ME1s(a,e,n): a^e mod n,the stupid way
ME1s:=proc(a,e,n) local i,s:
s:=1:
for i from 1 to e do
 s:=s*a mod n:
od:
s:
end:

#ME1(a,e,n): a^e mod n,the smart way
ME1:=proc(a,e,n) local i,s:
if e=1 then
 RETURN(a mod n):
fi:
if e mod 2=0 then
 RETURN(ME1(a,e/2,n)^2 mod n):
else
 RETURN(ME1(a,e-1,n)*a mod n):
fi:
end: