Gaussian Pseudorandom Number Generator Using Linear Feedback Shift Registers in Extended Fields
A new proposal to generate pseudorandom numbers with Gaussian distribution is presented. The generator is a generalization to the extended field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/5/556 |
| _version_ | 1797413284467441664 |
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| author | Guillermo Cotrina Alberto Peinado Andrés Ortiz |
| author_facet | Guillermo Cotrina Alberto Peinado Andrés Ortiz |
| author_sort | Guillermo Cotrina |
| collection | DOAJ |
| description | A new proposal to generate pseudorandom numbers with Gaussian distribution is presented. The generator is a generalization to the extended field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mi>F</mi><mo>(</mo><msup><mn>2</mn><mi>n</mi></msup><mo>)</mo></mrow></semantics></math></inline-formula> of the one using cyclic rotations of linear feedback shift registers (LFSRs) originally defined in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mi>F</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>. The rotations applied to LFSRs in the binary case are no longer needed in the extended field due to the implicit rotations found in the binary equivalent model of LFSRs in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mi>F</mi><mo>(</mo><msup><mn>2</mn><mi>n</mi></msup><mo>)</mo></mrow></semantics></math></inline-formula>. The new proposal is aligned with the current trend in cryptography of using extended fields as a way to speed up the bitrate of the pseudorandom generators. This proposal allows the use of LFSRs in cryptography to be taken further, from the generation of the classical uniformly distributed sequences to other areas, such as quantum key distribution schemes, in which sequences with Gaussian distribution are needed. The paper contains the statistical analysis of the numbers produced and a comparison with other Gaussian generators. |
| first_indexed | 2024-03-09T05:16:07Z |
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| id | doaj.art-8d9c828f6a264cf0af2fb3c2427d8131 |
| institution | Directory Open Access Journal |
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| language | English |
| last_indexed | 2024-03-09T05:16:07Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8d9c828f6a264cf0af2fb3c2427d81312023-12-03T12:45:49ZengMDPI AGMathematics2227-73902021-03-019555610.3390/math9050556Gaussian Pseudorandom Number Generator Using Linear Feedback Shift Registers in Extended FieldsGuillermo Cotrina0Alberto Peinado1Andrés Ortiz2Department Ingeniería de Comunicaciones, E.T.S. Ingeniería de Telecomunicación, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, SpainDepartment Ingeniería de Comunicaciones, E.T.S. Ingeniería de Telecomunicación, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, SpainDepartment Ingeniería de Comunicaciones, E.T.S. Ingeniería de Telecomunicación, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, SpainA new proposal to generate pseudorandom numbers with Gaussian distribution is presented. The generator is a generalization to the extended field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mi>F</mi><mo>(</mo><msup><mn>2</mn><mi>n</mi></msup><mo>)</mo></mrow></semantics></math></inline-formula> of the one using cyclic rotations of linear feedback shift registers (LFSRs) originally defined in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mi>F</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula>. The rotations applied to LFSRs in the binary case are no longer needed in the extended field due to the implicit rotations found in the binary equivalent model of LFSRs in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mi>F</mi><mo>(</mo><msup><mn>2</mn><mi>n</mi></msup><mo>)</mo></mrow></semantics></math></inline-formula>. The new proposal is aligned with the current trend in cryptography of using extended fields as a way to speed up the bitrate of the pseudorandom generators. This proposal allows the use of LFSRs in cryptography to be taken further, from the generation of the classical uniformly distributed sequences to other areas, such as quantum key distribution schemes, in which sequences with Gaussian distribution are needed. The paper contains the statistical analysis of the numbers produced and a comparison with other Gaussian generators.https://www.mdpi.com/2227-7390/9/5/556LFSRGaussian distributionextended fieldscentral limit theorem |
| spellingShingle | Guillermo Cotrina Alberto Peinado Andrés Ortiz Gaussian Pseudorandom Number Generator Using Linear Feedback Shift Registers in Extended Fields Mathematics LFSR Gaussian distribution extended fields central limit theorem |
| title | Gaussian Pseudorandom Number Generator Using Linear Feedback Shift Registers in Extended Fields |
| title_full | Gaussian Pseudorandom Number Generator Using Linear Feedback Shift Registers in Extended Fields |
| title_fullStr | Gaussian Pseudorandom Number Generator Using Linear Feedback Shift Registers in Extended Fields |
| title_full_unstemmed | Gaussian Pseudorandom Number Generator Using Linear Feedback Shift Registers in Extended Fields |
| title_short | Gaussian Pseudorandom Number Generator Using Linear Feedback Shift Registers in Extended Fields |
| title_sort | gaussian pseudorandom number generator using linear feedback shift registers in extended fields |
| topic | LFSR Gaussian distribution extended fields central limit theorem |
| url | https://www.mdpi.com/2227-7390/9/5/556 |
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