# Key Recovery for Content Protection Using Ternary PUFs Designed with Pre-Formed ReRAM
## 2 One Way Unclonable Functions with Ternary States
### Use of Ternary States to Protect the One-Way Unclonable Functions  
The addition of a third state allows the tracking of the portions of the PUF that should be masked because they are fuzzy, marginal, unstable, or fragile. The objective is then  
\begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**PUF**} & \multicolumn{2}{c}{**Challenges**} & \multirow{2}{*}{**Resposes**} \\ \cline{2-2} \cline{4-4}  & **T** & & **IDA Access** \\ \hline \multirow{2}{*}{**RO**} & To point at a set of M pairs & To point at a subset of & To avoid pairs oscillating at a & Each N pair of ROs \\  & of ROs & N pairs of RO (N \(<\) M) & similar frequency & generates a 0 or 1 \\ \hline \multirow{2}{*}{**Arbiter**} & M sets of instructions driving & To point at a subset of & To avoid the sets of & Each N set of \\  & MUXs in the up or & N instructions (N \(<\) M) & instructions known to be & instructions \\  & down position & & unstable & generates a 0 or 1 \\ \hline \multirow{2}{*}{**SRAM**} & To point at M addresses in the & To point at a subset of & To avoid the SRAM cells & Each N cell of SRAM \\  & SRAM array & N addresses (N \(<\) M) & known to be unstable & array \\  & & & generates a 0 or 1 \\ \hline \multirow{2}{*}{**ReRAM**} & To point at M addresses in the & To point at a subset of & To avoid the ReRAM cells & Each N cell of ReRAM \\  & ReRAM array & N addresses (N \(<\) M) & known to be unstable & array \\  & & & generates a 0 or 1 \\ \hline \end{tabular}
\end{table}
Table 1: Examples of challenge-response configurations for various PUFs.  
to reduce BERs and improve reliability [22; 23]. A thorough enrollment cycle to identify these \"weak\" portions and their masking during response generation, results in a better quality PUF, requiring little to no error-correcting scheme for cryptographic key generation. The knowledge of the addresses with fragile physical elements that can be damaged during normal operations have tamper-resistance properties [15]. A cryptographic protocol generating keys solely from the addresses of PUFs that are known to be reliable does not damage the weak portions of the PUF. However, an opponent trying to interact with the PUF without such knowledge could partially damage the PUF, leaving behind traces of the attack. A protocol to sense attacks could include reading these addresses at a very low electric current, to detect abnormal BERs.  
Ternary-based logic, as opposed to mainstream binary logic, offers additional levels of security in cryptographic systems. The number of possible states is higher, which adds obfuscation and entropy. The addition of an additional state has been successfully integrated into PUF-based key generation schemes [23]. The handshake between a server initiating a new key generation cycle, and a client device equipped with a PUF, cannot be successfully initiated by a man-in-the-middle attack, which is unaware of the positions of the tri-states. Such a ternary representation can be combined with a scheme in which the keys generated by the addressable PUFs are different when the electrical currents injected into the physical elements change [15].