Write a procecure that takes as input a positive integer r and gives the private and public keys for RSA using two primes of r digits each.with(RandomTools);RSAKey:=proc(r)
local p, q, phi, n,rn,e,d;
rn:=randomize();
p:=nextprime(Generate(integer(range=10^(r-1)..10^r)));
q:=nextprime(Generate(integer(range=10^(r-1)..10^r)));
n:=p*q;
phi:=(p-1)*(q-1);
e:=2^16+1;
while(gcd(phi,e)<>1) do
e:=e+2;
od;
d:= modp ( 1/e, phi);
return([[n,e],[n,d]]);
end:RSAKey(3);Try to factor "n" of the key you found. How many digits do you need to make it not possible for Maple to factor.r:=40:
key:=RSAKey(r):
n:=key[1][1];
ifactor(n);
with(StringTools):
Alphabet:=cat("\134t\134n", Select( IsPrintable , Implode([seq(convert([i],bytes),i=1..127)])));
StringToList:=proc(plaintext)
global Alphabet;
local i;
[seq( -1+ SearchText(plaintext[i],Alphabet) ,i=1..length(plaintext))];
end proc:
ListToString:=proc(listnum)
global Alphabet;
Implode([seq(Alphabet[listnum[i]+1],i=1..nops(listnum))]);
end proc:
length(Alphabet);ListToKgraf := proc( lis, K)
local newl, i, j, max, t,M,zeroes,lis1;
M:=length(Alphabet);
zeroes:=seq(0, i=1..K-modp(nops(lis),K));
newl := [];
if modp(nops(lis),K )<> 0 then lis1:=[zeroes, op(lis)];
else lis1:=lis; fi;
max:= nops(lis1)/K;
for i from 1 to max do
t:=sum( lis1[(max-i+1)*K - j] * M^j,j = 0..K-1 );
newl:= [t, op(newl) ];
od;
return(newl);
end:
convertPkTop:=proc(n, p, K)
local answer, n1,i;
n1:=n;
answer:=[];
for i from 1 to K do
answer:=[modp(n1,p),op(answer)];
n1:= (n1 - answer[1])/p;
od:
answer;
end:KgrafToList:=proc(listn,p,K)
[seq( op( convertPkTop(listn[i],p,K ) ), i=1..nops(listn) )];
end:
key:=RSAKey(3);
plaintext:="This is a test of RSA":
list1:=StringToList(plaintext);
K:=3:
ListToKgraf(list1,K);
map(x-> x &^key[1][2] mod key[1][1],%);
KgrafToList(%, length(Alphabet), K);
ciphertext:=ListToString(%);
list1:=StringToList(ciphertext);
K:=3:
ListToKgraf(list1,K);
map(x-> x &^key[2][2] mod key[1][1],%);
KgrafToList(%, length(Alphabet), K);
ListToString(%);1) The chosen primes let us encode and decode messages that are numbers approximately in certain range (what is this range?). Randomly pick 5 numbers in that range and verify that encoding and decoding act as inverse operations on these numbers.2) Of the numbers found so far, explain which numbers I want to publish, which ones I want to save but keep secret, and which ones I want to destroy and forget if I am using RSA as a public key system.3) Randomly pick two primes with a product of 150 digits and prepare your own keys. Test that your keys encrypt and decrypt on two numbers of your choice.