What's the difference between Trapdoor Functions and Encryption Functions?

Typically, trapdoor functions are used in asymmetric cryptography. For instance, if you have a RSA public key $(n,e)$, it is easy to compute a cipher text $c = Pad(m)^e\mod n$, but hard to get back to $Pad(m)$ from $c$ even if you have the public key. In order to easily reverse the operation you need the corresponding private key $d = e^{-1}\mod\phi(n)$. The reason RSA is a trapdoor function in this sense, is because it is based on the hardness of the Integer Factorization Problem. You can't calculate the private exponent $d$ unless you know $\phi(n)$, and you can't calculate $\phi(n)$ unless you know the prime factors of $n$.

AES and other symmetric ciphers are not trapdoor functions in this sense. You are only able to compute $c = AES_k(m)$ if you got the key $k$, but if you got this key it is equally easy to compute $m = AES_k^{-1}(c)$

Solved by user1564 (10,246 )
Mar 31, 2013 at 22:03