Trapdoor One-Way Function

Trapdoor One-Way Function is a One-Way Function# with additional information that is known to the user so that the function is easy to compute and invert if all the information is given. However, if one of the information is not known, it is infeasible to invert.

For example:

$$ \begin{align} Y &= f_k(X)\\ X &= f_k^{-1}(Y)\\ \end{align} $$

Given both $k$, $X$ and $Y$, it is easy to compute both function. However, if the $k$ or $Y$ is not known, the corresponding algorithm will be hardly useful for inverting.

Applications of Trapdoor One-Way Function are:

Links to this page

TAC3121 Chapter 4: Asymmetric (Public-Key) Encryption

Trapdoor One-Way Function
Rivest-Shamir-Adleman (RSA)

The security of RSA is guarantee by its Trapdoor One-Way Function# nature as primes $p$ and $q$ are only known to the key owner. It is impossible to do a Brute Force Attack on RSA due to the large key size. Other Cryptanalytic Attack such as mathematical attack based on difficulty of computing $\phi(n)$, by factoring modulus $n$ (can be overcome by having a larger $n$), timing attacks# on decryption algorithm, and chosen ciphertext attacks (CCA) can be done on RSA.

#math #cryptography