# Post Quantum Cryptographic Keys Generated with Physical Unclonable Functions
## 6 Conclusions and Future Work  
The PQC algorithms under standardization are encouraging and the latencies are reasonable, making the protocols suitable for PKIs securing networks of client devices and IoTs. The generation, distribution, and storage of the public-private key pairs for PQC can be complex because the keys are usually very long. This paper proposes to generate the public-private key pairs by replacing the random number generators with data streams generated from addressable PUFs to get the seeds needed in the PQC algorithms. Unlike the key pairs computed by PQC algorithms, the seeds are relatively short, typically 256-bits long. The use of PUFs as a source of randomness is applicable to all five lattice-based codes  
Figure 11: Maximum effective throughput relative to the performance of ECC Secp256r1 achieved for each response based cryptographic (RBC) cryptosystem implementation powered by AMD Ryzen 9 3900X. Light SABER performance is approximately 14 times faster than elliptic curve cryptography (ECC). Figure 10: Key performance index (KPI) and the effective throughput in keys per second achieved by the response based cryptographic (RBC) search engine powered with AMD Ryzen 9 3900X. Benchmark of the post quantum cryptographic (PQC) algorithms are compared to the reference codes AES 256 and ECC. under consideration in the phase III investigation of NIST, and to the code-based Classic McEliece scheme. In order to simultaneously generate key pairs from a server acting as the certificate authority, and the client device with access to its PUF, it is critical to handle the bit error rates (BERs) that are frequent with physical elements. We verified in the experimental section that the RBC can find the erratic seeds by testing an excess of \(10^{5}\) seeds per second with CRYSTALS-Dilithium 2 and LightSABER, which is faster than what we measured with mature algorithms such as the ones with elliptic curves. The experimental evaluation conducted in this work, with the RBC, also lets us conclude that the pre-selection by NIST of CRYSTALS-Dilithium for DSA and SABER for KEM are promising from a performance standpoint. Our results show that the key generation performance is at least comparable to that of ECC. The PQC algorithms under consideration are excellent in an environment targeting PUF-based key exchange. The AES hardware-accelerated AES-NI implementation yields roughly 220 million keys per second throughput on a single machine, which serves a practical real world upper bound for future hardware-accelerated PQC implementations. In this work we have not yet studied the multivariate-based RAINBOW code, which is also an important scheme under consideration for standardization; we are currently studying ways to use PUFs for key generation. The task needed to deploy PUF-based PQC solutions is not underestimated by the authors of this paper. This will include the use of highly reliable PUFs, and the optimization of the cryptographic protocol pointing simultaneously at the same set of addresses in the PUF, and in the look up table capturing the challenge-response pairs stored in the server. Further optimizing the PUF's protocols and the RBC for PQC algorithms is seen as an opportunity. The use of noises, nonces, errors, and rounding vectors can exploit the stochasticity of PUFs, and the ability to handle erratic streams of the RBC. The PQC algorithms analyzed in this paper can also benefit from the use of distributed memories, high performance computing, and parallel computing, which have the potential to further reduce the latencies of the RBC. Not applicable. The authors thank the staff, students, and faculty from Northern Arizona University (NAU) in particular, [PERSON] who is a software engineer in NAU's cybersecurity lab. We also thank the professionals of the Information Directorate of the Air Force Research laboratory (AFRL) of Rome, New York (US), who supported this effort. The authors declare no conflict of interest.