## 5 Statistical Analysis of the Protocols Based on Subsets of Responses and ECC
### Error Management in the Cryptographic Keys
#### 5.3.3 Failure to Detect Matching Responses
In these mechanisms, similarly with tracking blockchains, the digital files are hashed to be unique for non-repudiable and non-alterable operations. Two actual situations were discussed: (i) the encryption with proof of authenticity of the digital files distributed in storage nodes and (ii) the protection of the files kept in devices operating in zero-trust networks. * In distributed networks, client devices provide the data needed for verification to agents driving smart contracts and storage nodes, the proposed protocols balance both security and transparency. * In zero-trust networks, the sole priority is to enhance security and to protect the terminal devices. We developed a protocol allowing the injection of obfuscating noise in the keys transmitted by the controlling server to the exposed terminal device. BERS in the 25% range do not prevent the noisy key from decrypting the digital files stored in the device. To eliminate residual mismatches and generate error-free cryptographic keys, we developed and tested error management schemes to replace complex ECC, fuzzy extractors, and data helpers. The continuation of this work will implement the algorithms for various applications to optimize security, reduce latencies, and add features specific to each application. We intend to perform an optimization with some of the following multi-factors:

* Length d of the digital file C* that is used for the CRP mechanism. Longer files are desirable to enhance randomness and minimize collisions. Excessive lengths negatively impact latencies. * Number N of challenge-response pairs, and length P of each response. For the subset of response protocol, \(N=256\) or more is needed, and P has to be sufficiently long to avoid collisions, but not so long as to increase latencies. * The acceptable BERs shall be injected in the subset of responses and threshold T shall be set at an acceptable level for the determination of a match. In addition to the experimental work, we are currently developing a comprehensive multi-variate predictive tool. Additional attack vectors are also being investigated with various methods to inject noise and disturb the protocol under consideration. Lastly, the quality of true random number generation (TRNG) is critical to the levels of security of the suggested protocols as well as the actual randomness of the resulting streams of responses. We are performing statistically valid experiments to enable the quantification of randomness with tools developed by NIST, DieHarder, TestU01, and others. Conceptualization, B.C., M.H. and J.H. ; methodology, B.C., M.H. and J.H. ; software, B.C., C.P., M.H. and J.H. ; validation, B.C. ; formal analysis, B.C. ; investigation, B.C. ; resources, B.C. ; data curation, B.C. ; writing--original draft preparation, B.C. ; writing--review and editing, B.C. ; funding acquisition, B.C. All authors have read and agreed to the published version of the manuscript. Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911 NF-23-2-0014. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. Not applicable. The authors declare no conflict of interest. ## Abbreviations

List of acronyms used in this paper: