I don't remember the exact details of RSA, but consider:
and , so , ergo . This is quadratic with the roots, can you take it from there?
I have this problem:
Eve is trying to break an RSA mssage which she knows is based on the modulus n = 3454039
Suppose she discovers that the primes p,q giving n = pq sum to 4880
Knowing that the encrypting exponent is e = 151
help her compute the decrypting exponent d. also, help her reconstruct the primes p,q giving n=pq
so my first problem is how do factor out n? Is there a trick to it considering that p and q sum to 4880? Then after I factor n, I compute the Euler phi function of n to compute the decrypting exponent through d*e = 1 mod phi(n) right?
Along with that, do you have the actual message that Eve is attempting to de-crypt?
What we know:
n = 3454039 = p*q
p+q = 4880
e = 151
(p-1)(q-1) = pq -p -q +1 = phi(n)