## 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
Available online: [[https://csrc.nist.gov/projects/post-quantumcryptography/round-3-submissions](https://csrc.nist.gov/projects/post-quantumcryptography/round-3-submissions)]([https://csrc.nist.gov/projects/post-quantumcryptography/round-3-submissions](https://csrc.nist.gov/projects/post-quantumcryptography/round-3-submissions)) (accessed on 29 September 2022). * [PERSON] et al. (2018) [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] CRYSTALS-Dilithium: A lattice-based digital signature scheme. _IACR Trans. Cryptogr. Hardn. Embed. Syst._**2018**, _288_, 238-268. [CrossRef]
* [PERSON] et al. (2021) [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] CRYSTALS-Dilithium: Algorithm Specifications and Supporting Documentation, Submission to NIST's PQC Standardization Process. Available online: [[https://github.com/pq-crystals/dilithium/tree/round3](https://github.com/pq-crystals/dilithium/tree/round3)]([https://github.com/pq-crystals/dilithium/tree/round3](https://github.com/pq-crystals/dilithium/tree/round3)) (accessed on 8 February 2021). * [PERSON] et al. (2020) [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] NTRU Prime: Round 3, Submission to the NIST's Post-Quantum Cryptography Standardization Process. 2020. Available online: [[https://ntruprime.cryp.to/nist/ntruprime-20201007.pdf](https://ntruprime.cryp.to/nist/ntruprime-20201007.pdf)]([https://ntruprime.cryp.to/nist/ntruprime-20201007.pdf](https://ntruprime.cryp.to/nist/ntruprime-20201007.pdf)) (accessed on 24 May 2023). * [PERSON] et al. (2017) [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON] _NIST PQ Submission: NTRU Encrypt a Lattice Based Encryption Algorithm, Submission to the NIST's Post-Quantum Cryptography Standardization Process_; National Institute of Standards and Technology: Gaithersburg, MD, USA, 2017. * [PERSON] et al. (1998) [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON] NTRU: A ring-based public key cryptosystem. In _Algorithmic Number Theory_; [PERSON]: Berlin/Heidelberg, Germany, 1998; pp. 267-288. * [PERSON] et al. (2011) [PERSON]; [PERSON] V.; [PERSON]; [PERSON]; [PERSON] A distinguisher for high rate McEliece cryptosystems. In Proceedings of the IEEE Information Theory Workshop, Paraty, Brazil, 16-20 October 2011; pp. 282-286. [CrossRef]
* [PERSON] et al. (2019) [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON] The SPHINCS+ signature framework. In Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security, CCS'19, New York, NY, USA, 11-15 November 2019; pp. 2129-2146. [CrossRef]
* [PERSON] et al. (2020) [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON] Falcon: Fast-Fourier Lattice-based Compact Signatures over NTRU; Round 3, NIST PQC Standardization Process. 2020. Available online: [[https://www.idi.ens.fr/~prest/Publications/falcon.pdf](https://www.idi.ens.fr/~prest/Publications/falcon.pdf)]([https://www.idi.ens.fr/~prest/Publications/falcon.pdf](https://www.idi.ens.fr/~prest/Publications/falcon.pdf)) (accessed on 29 September 2022). * [PERSON] et al. (2011) [PERSON]; [PERSON]; [PERSON]; [PERSON] [PERSON] The Kecack SHA-3 Submission. Submission to the NIST SHA-3 Competition (Round 3). 2011. Available online: [[http://kececack.noekeon.org/Kecack-submission-3.pdf](http://kececack.noekeon.org/Kecack-submission-3.pdf)]([http://kececack.noekeon.org/Kecack-submission-3.pdf](http://kececack.noekeon.org/Kecack-submission-3.pdf)) (accessed on 14 January 2011). * National Institute of Standards and Technology (2015) National Institute of Standards and Technology.