/* rsa.gp */
{alphabet=[" ","A","B","C","D","E","F","G","H","I","J","K","L","M",
           "N","O","P","Q","R","S","T","U","V","W","X","Y","Z"];
}
{letter_to_number(l, 
     n)=
     for(n=1,27,if(alphabet[n]==l,return(n-1))); 
     error("invalid input.")
}
{number_to_message(n,    
     s="")= 
     while(n>0, s = concat(s,alphabet[n%27+1]); n = n \ 27); 
     return(s)
}
{message_to_number(w,     
     i,n=0)=
     for(i=1,length(w), n = n + 27^(i-1)*letter_to_number(w[i]));
     return(n);
}
{make_rsa_key(len,  
     p,q,n,e,d)=
     p = nextprime(random(10^(len\2+1)));
     q = nextprime(random(10^(len\2+3)));
     n = p*q;
     phin = (p-1)*(q-1);
     e = random(phin);
     while(gcd(e,phin)!=1,e=e+1);
     d = lift(Mod(e,phin)^(-1));
     return([n,e,d]);
}
encrypt(message, n, e)=lift(Mod(message_to_number(message),n)^e);
decrypt(secret, n, d)=number_to_message(lift(Mod(secret,n)^d));