{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T05:02:34Z","timestamp":1781672554921,"version":"3.54.5"},"reference-count":65,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,18]],"date-time":"2022-01-18T00:00:00Z","timestamp":1642464000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Union","doi-asserted-by":"publisher","award":["826647"],"award-info":[{"award-number":["826647"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In the cybersecurity field, the generation of random numbers is extremely important because they are employed in different applications such as the generation\/derivation of cryptographic keys, nonces, and initialization vectors. The more unpredictable the random sequence, the higher its quality and the lower the probability of recovering the value of those random numbers for an adversary. Cryptographically Secure Pseudo-Random Number Generators (CSPRNGs) are random number generators (RNGs) with specific properties and whose output sequence has such a degree of randomness that it cannot be distinguished from an ideal random sequence. In this work, we designed an all-digital RNG, which includes a Deterministic Random Bit Generator (DRBG) that meets the security requirements for cryptographic applications as CSPRNG, plus an entropy source that showed high portability and a high level of entropy. The proposed design has been intensively tested against both NIST and BSI suites to assess its entropy and randomness, and it is ready to be integrated into the European Processor Initiative (EPI) chip.<\/jats:p>","DOI":"10.3390\/e24020139","type":"journal-article","created":{"date-parts":[[2022,1,18]],"date-time":"2022-01-18T08:09:20Z","timestamp":1642493360000},"page":"139","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Design and Test of an Integrated Random Number Generator with All-Digital Entropy Source"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8504-8203","authenticated-orcid":false,"given":"Luca","family":"Crocetti","sequence":"first","affiliation":[{"name":"Department of Information Engineering, University of Pisa, Via G. Caruso, 16, 56122 Pisa, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5711-432X","authenticated-orcid":false,"given":"Stefano","family":"Di Matteo","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, University of Pisa, Via G. Caruso, 16, 56122 Pisa, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2538-5440","authenticated-orcid":false,"given":"Pietro","family":"Nannipieri","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, University of Pisa, Via G. Caruso, 16, 56122 Pisa, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5426-4974","authenticated-orcid":false,"given":"Luca","family":"Fanucci","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, University of Pisa, Via G. Caruso, 16, 56122 Pisa, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sergio","family":"Saponara","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, University of Pisa, Via G. Caruso, 16, 56122 Pisa, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"015004","DOI":"10.1103\/RevModPhys.89.015004","article-title":"Quantum random number generators","volume":"89","year":"2017","journal-title":"Rev. Mod. Phys."},{"key":"ref_2","unstructured":"Consortium, E. (2021, December 10). EPI Website. Available online: https:\/\/www.european-processor-initiative.eu\/."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Nannipieri, P., Di Matteo, S., Baldanzi, L., Crocetti, L., Zulberti, L., Saponara, S., and Fanucci, L. (2021). VLSI design of Advanced-Features AES CryptoProcessor in the framework of the European Processor Initiative. IEEE Trans. Very Large Scale Integr. (VLSI) Syst., in press.","DOI":"10.1109\/TVLSI.2021.3129107"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Di Matteo, S., Baldanzi, L., Crocetti, L., Nannipieri, P., Fanucci, L., and Saponara, S. (2021). Secure Elliptic Curve Crypto-Processor for Real-Time IoT Applications. Energies, 14.","DOI":"10.3390\/en14154676"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"103444","DOI":"10.1016\/j.micpro.2020.103444","article-title":"SHA2 and SHA-3 Accelerator Design in a 7 nm Technology within the European Processor Initiative","volume":"87","author":"Nannipieri","year":"2020","journal-title":"Microprocess. Microsyst."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Nannipieri, P., Di Matteo, S., Baldanzi, L., Crocetti, L., Belli, J., Fanucci, L., and Saponara, S. (2021). True Random Number Generator Based on Fibonacci-Galois Ring Oscillators for FPGA. Appl. Sci., 11.","DOI":"10.3390\/app11083330"},{"key":"ref_7","first-page":"117","article-title":"Digital Random Number Generator Hardware Accelerator IP-Core for Security Applications","volume":"Volume 627","author":"Baldanzi","year":"2020","journal-title":"Applications in Electronics Pervading Industry, Environment and Society. ApplePies 2019"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Baldanzi, L., Crocetti, L., Falaschi, F., Bertolucci, M., Belli, J., Fanucci, L., and Saponara, S. (2020). Cryptographically Secure Pseudo-Random Number Generator IP-Core Based on SHA2 Algorithm. Sensors, 20.","DOI":"10.3390\/s20071869"},{"key":"ref_9","unstructured":"NIST (2015). Recommendation for Random Number Generation Using Deterministic Random Bit Generators, SP 800-90A Rev. 1."},{"key":"ref_10","unstructured":"NIST (2016). Recommendation for Random Bit Generator (RBG) Constructions, SP 800-90C (Draft)."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/978-3-642-15031-9_24","article-title":"New High Entropy Element for FPGA Based True Random Number Generators","volume":"Volume 6225","author":"Varchola","year":"2010","journal-title":"Cryptographic Hardware and Embedded Systems (CHES) 2010"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1007\/978-3-540-85053-3_11","article-title":"Fast Digital TRNG Based on Metastable Ring Oscillator","volume":"Volume 5154","author":"Vasyltsov","year":"2008","journal-title":"Cryptographic Hardware and Embedded Systems (CHES) 2008"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Schramm, M., Dojen, R., and Heigl, M. (2017, January 5\u20136). Experimental assessment of FIRO- and GARO-based noise sources for digital TRNG designs on FPGAs. Proceedings of the 2017 International Conference on Applied Electronics (AE), Pilsen, Czech Republic.","DOI":"10.23919\/AE.2017.8053618"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Demir, K., and Erg\u00fcn, S. (2020, January 9\u201312). A Comparative Study on Fibonacci-Galois Ring Oscillators for Random Number Generation. Proceedings of the 2020 IEEE 63rd International Midwest Symposium on Circuits and Systems (MWSCAS), Springfield, MA, USA.","DOI":"10.1109\/MWSCAS48704.2020.9184524"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Cao, Y., Ro\u017ei\u0107, V., Yang, B., Balasch, J., and Verbauwhede, I. (2016, January 16\u201319). Exploring active manipulation attacks on the TERO random number generator. Proceedings of the 2016 IEEE 59th International Midwest Symposium on Circuits and Systems (MWSCAS), Abu Dhabi, United Arab Emirates.","DOI":"10.1109\/MWSCAS.2016.7870007"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Li, T., Wu, L., Zhang, X., Wu, X., Zhou, J., and Wang, X. (2017, January 18\u201320). A Novel Transition Effect Ring Oscillator Based True Random Number Generator for a Security SoC. Proceedings of the 2017 International Conference on Electron Devices and Solid-State Circuits (EDSSC), Hsinchu, Taiwan.","DOI":"10.1109\/EDSSC.2017.8126539"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Fujieda, N. (September, January 31). On the Feasibility of TERO-Based True Random Number Generator on Xilinx FPGAs. Proceedings of the 2020 30th International Conference on Field-Programmable Logic and Applications (FPL), Gothenburg, Sweden.","DOI":"10.1109\/FPL50879.2020.00027"},{"key":"ref_18","unstructured":"Kan, W. (2007). Analysis of Underlying Assumptions in NIST DRBGs. IACR Cryptology ePrint Archive, IACR."},{"key":"ref_19","unstructured":"Synopsys (2021, December 10). Design Compiler. Available online: https:\/\/www.synopsys.com\/support\/training\/rtl-synthesis.html."},{"key":"ref_20","unstructured":"Xilinx (2021, December 10). Vivado. Available online: https:\/\/www.xilinx.com\/products\/design-tools\/vivado\/implementation.html."},{"key":"ref_21","unstructured":"Xilinx (2021, December 10). UltraScale+ FPGAs\u2014Product Tables and Product Selection Guide. 2015\u20132021. Available online: https:\/\/www.xilinx.com\/support\/documentation\/selection-guides\/ultrascale-plus-fpga-product-selection-guide.pdf."},{"key":"ref_22","unstructured":"Brown, R. (2021, December 10). Dieharder: A Random Number Test Suite. Version 3.31.1. Available online: https:\/\/webhome.phy.duke.edu\/~rgb\/General\/dieharder.php."},{"key":"ref_23","unstructured":"Walker, J. (2021, December 10). ENT\u2014A Pseudorandom Number Sequence Test Program. Available online: https:\/\/www.fourmilab.ch\/random\/."},{"key":"ref_24","unstructured":"Aggarwal, D., Ghatikar, R., Chennuri, S., and Banerjee, A. (2021). Generation of 1 Gb full entropy random numbers with the enhanced-NRBG method. arXiv."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Sun, Y., and Lo, B. (2018, January 28\u201329). Random number generation using inertial measurement unit signals for on-body IoT devices. Proceedings of the Living in the Internet of Things: Cybersecurity of the IoT-2018, London, UK.","DOI":"10.1049\/cp.2018.0028"},{"key":"ref_26","unstructured":"(2021, December 10). PractRand (Practically Random) C++ Library. Available online: http:\/\/pracrand.sourceforge.net\/."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1134\/S096554252001008X","article-title":"A Practical Approach to Testing Random Number Generators in Computer Algebra Systems","volume":"60","author":"Gevorkyan","year":"2020","journal-title":"Comput. Math. Math. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"24075","DOI":"10.1007\/s11042-020-09108-w","article-title":"TestU01 and Practrand: Tools for a randomness evaluation for famous multimedia ciphers","volume":"79","author":"Sleem","year":"2020","journal-title":"Multimed. Tools Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1268776.1268777","article-title":"TestU01: AC library for empirical testing of random number generators","volume":"33","author":"Simard","year":"2007","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1588","DOI":"10.1109\/JLT.2017.2656866","article-title":"Robust Quantum Random Number Generation with Silicon Nanocrystals Light Source","volume":"35","author":"Bisadi","year":"2017","journal-title":"J. Light. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1628","DOI":"10.1109\/TCSI.2017.2754650","article-title":"CIPRNG: A VLSI Family of Chaotic Iterations Post-Processings for F2-Linear Pseudorandom Number Generation Based on Zynq MPSoC","volume":"65","author":"Bakiri","year":"2018","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2359","DOI":"10.1109\/TCSVT.2017.2703946","article-title":"Design and FPGA-Based Realization of a Chaotic Secure Video Communication System","volume":"28","author":"Chen","year":"2018","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Sharipov, B.R., Perukhin, M.Y., and Mullayanov, B.I. (2021, January 17\u201321). Statistical Analysis of Pseudorandom Sequences and Stegocontainers. Proceedings of the 2021 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), Sochi, Russia.","DOI":"10.1109\/ICIEAM51226.2021.9446328"},{"key":"ref_34","unstructured":"NIST (2010). A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, SP 800-22."},{"key":"ref_35","unstructured":"Killmann, W., and Schindler, W. (2011). A Proposal for: Functionality Classes for Random Number Generators, Version 2.0, Mathematical-Technical Reference of AIS 20\/31."},{"key":"ref_36","unstructured":"BSI (1999). Functionality Classes and Evaluation Methodology for Deterministic Random Number Generators, BSI. Version 1; AIS 20."},{"key":"ref_37","unstructured":"BSI (2001). Functionality Classes and Evaluation Methodology for Physical Random Number Generators, BSI. Version 1; AIS 31."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"012009","DOI":"10.1088\/1742-6596\/1861\/1\/012009","article-title":"Overview of Randomness Test on Cryptographic Algorithms","volume":"1861","author":"Zhang","year":"2021","journal-title":"J. Phys. Conf. Ser. IOP Publ."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Petura, O., Mureddu, U., Bochard, N., Fischer, V., and Bossuet, L. (September, January 29). A Survey of AIS-20\/31 Compliant TRNG Cores Suitable for FPGA Devices. Proceedings of the 2016 26th International Conference on Field Programmable Logic and Applications (FPL), Lausanne, Switzerland.","DOI":"10.1109\/FPL.2016.7577379"},{"key":"ref_40","first-page":"1","article-title":"Statistical testing of cryptographic randomness","volume":"9","author":"Demirhan","year":"2016","journal-title":"\u0130stat. Derg. \u0130stat. Akt\u00fcerya"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Balasch, J., Bernard, F., Fischer, V., Gruji\u0107, M., Laban, M., Petura, O., Ro\u017ei\u0107, V., Van Battum, G., Verbauwhede, I., and Wakker, M. (June, January 28). Design and Testing Methodologies for True Random Number Generators Towards Industry Certification. Proceedings of the 2018 IEEE 23rd European Test Symposium (ETS), Bremen, Germany.","DOI":"10.1109\/ETS.2018.8400697"},{"key":"ref_42","unstructured":"BSI (2021, December 10). Implementation of Test Procedure A and Test Procedure B for AIS 20\/31 Standard. Available online: https:\/\/www.bsi.bund.de\/SharedDocs\/Downloads\/DE\/BSI\/Zertifizierung\/Interpretationen\/AIS_31_testsuit_zip.zip."},{"key":"ref_43","unstructured":"Schindler, W. (1999). AIS 20: Functionality Classes and Evaluation Methodology for Deterministic Random Number Generators, BSI. Version 2.0; Mathematical-Technical Reference of AIS 20."},{"key":"ref_44","unstructured":"Killmann, W., and Schindler, W. (2001). A Proposal for: Functionality Classes and Evaluation Methodology for True (Physical) Random Number Generators, BSI. Version 3.1; Mathematical-Technical Reference of AIS 31."},{"key":"ref_45","unstructured":"NIST (2018). Recommendation for the Entropy Sources Used for Random Bit Generation, SP 800-90B."},{"key":"ref_46","unstructured":"NIST (2021, December 10). SP 800-90B Entropy Assessment Software, Version 1.0, Available online: https:\/\/github.com\/usnistgov\/SP800-90B_EntropyAssessment."},{"key":"ref_47","unstructured":"NIST (2021, December 10). SP 800-22 STS Software, Version 2.1.1, Available online: https:\/\/csrc.nist.gov\/CSRC\/media\/Projects\/Random-Bit-Generation\/documents\/sts-2_1_2.zip."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"3013","DOI":"10.1109\/TIFS.2021.3070424","article-title":"On the Efficient Estimation of Min-Entropy","volume":"16","author":"Kim","year":"2021","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_49","first-page":"373","article-title":"Predictive Models for Min-Entropy Estimation","volume":"Volume 9293","author":"Kelsey","year":"2015","journal-title":"International Workshop on Cryptographic Hardware and Embedded Systems"},{"key":"ref_50","first-page":"18","article-title":"On the Interpretation of Results from the NIST Statistical Test Suite","volume":"18","author":"Riha","year":"2015","journal-title":"Rom. J. Inf. Sci. Technol. (ROMJIST)"},{"key":"ref_51","unstructured":"Intel (2021, December 10). Cyclone V Device Overview. Available online: https:\/\/www.intel.com\/content\/dam\/www\/programmable\/us\/en\/pdfs\/literature\/hb\/cyclone-v\/cv_51001.pdf."},{"key":"ref_52","unstructured":"Xilinx (2017). Spartan-6 FPGAs: Performance, Power, and I\/O Optimized for Cost-Sensitive Applications, Xilinx. Available online: https:\/\/www.xilinx.com\/support\/documentation\/white_papers\/wp396_S6_HV_Perf_Power.pdf."},{"key":"ref_53","unstructured":"Microsemi (2021, December 10). User Guide SmartFusion2 and IGLOO2 FPGA Security and Best Practices (UG0443), Revision 10.0. Available online: https:\/\/www.microsemi.com\/document-portal\/doc_download\/132037-ug0443-smartfusion2-and-igloo2-fpga-security-best-practices-user-guide."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1007\/s00145-010-9089-3","article-title":"On the Security of Oscillator-Based Random Number Generators","volume":"24","author":"Baudet","year":"2011","journal-title":"J. Cryptol."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Kohlbrenner, P., and Gaj, K. (2004, January 22\u201324). An Embedded True Random Number Generator for FPGAs. Proceedings of the 12th International Symposium on Field Programmable Gate Arrays, Monterey, CA, USA.","DOI":"10.1145\/968280.968292"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1109\/TC.2007.250627","article-title":"A Provably Secure True Random Number Generator with Built-In Tolerance to Active Attacks","volume":"56","author":"Sunar","year":"2007","journal-title":"IEEE Trans. Comput."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Wold, K., and Tan, C.H. (2008, January 3\u20135). Analysis and Enhancement of Random Number Generator in FPGA Based on Oscillator Rings. Proceedings of the 2008 International Conference on Reconfigurable Computing and FPGAs, Cancun, Mexico.","DOI":"10.1109\/ReConFig.2008.17"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"879281","DOI":"10.1155\/2010\/879281","article-title":"True-Randomness and Pseudo-Randomness in Ring Oscillator-Based True Random Number Generators","volume":"2010","author":"Bochard","year":"2010","journal-title":"Int. J. Reconfig. Comput."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/3-540-36400-5_30","article-title":"True Random Number Generator Embedded in Reconfigurable Hardware","volume":"Volume 2523","author":"Fischer","year":"2002","journal-title":"Cryptographic Hardware and Embedded Systems (CHES) 2002"},{"key":"ref_60","first-page":"1","article-title":"Mathematical Model of Physical RNGs Based on Coherent Sampling","volume":"45","author":"Bernard","year":"2010","journal-title":"Tatra Mt.-Math. Publ."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/978-3-662-48324-4_18","article-title":"A Physical Approach for Stochastic Modeling of TERO-Based TRNG","volume":"Volume 9293","author":"Haddad","year":"2015","journal-title":"Cryptographic Hardware and Embedded Systems (CHES) 2015"},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Cherkaoui, A., Fischer, V., Aubert, A., and Fesquet, L. (2013, January 19\u201322). A Self-Timed Ring Based True Random Number Generator. Proceedings of the 2013 IEEE 19th International Symposium on Asynchronous Circuits and Systems, Santa Monica, CA, USA.","DOI":"10.1109\/ASYNC.2013.15"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1007\/978-3-642-40349-1_11","article-title":"A Very High Speed True Random Number Generator with Entropy Assessment","volume":"Volume 8086","author":"Cherkaoui","year":"2013","journal-title":"Cryptographic Hardware and Embedded Systems (CHES) 2013"},{"key":"ref_64","unstructured":"Intel (2020). Overview for the Stratix IV Device Family. Stratix IV Device Handbook, Available online: https:\/\/www.intel.com\/content\/dam\/www\/programmable\/us\/en\/pdfs\/literature\/hb\/stratix-iv\/stx4_siv51001.pdf."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Peetermans, A., Rozic, V., and Verbauwhede, I. (2019, January 8\u20139). A Highly-Portable True Random Number Generator Based on Coherent Sampling. Proceedings of the 2019 29th International Conference on Field Programmable Logic and Applications (FPL), Barcelona, Spain.","DOI":"10.1109\/FPL.2019.00041"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/2\/139\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:02:59Z","timestamp":1760133779000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/2\/139"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,18]]},"references-count":65,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["e24020139"],"URL":"https:\/\/doi.org\/10.3390\/e24020139","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,18]]}}}