Construction and analysis of resilient five-valued spectra Boolean functions
Boolean functions with five-valued spectra have important applications in code division multiple access (CDMA) communication, coding and cryptography, true random number generators (TRNG), and combinatorial design. An approach based on the Walsh spectral neutralization technique for directly constru...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | zho |
| Published: |
Editorial Department of Journal on Communications
2025-07-01
|
| Series: | Tongxin xuebao |
| Subjects: | |
| Online Access: | http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2025116/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850034066141741056 |
|---|---|
| author | WANG Weiqiong LI Yue LUO Shuyu ZHU Mengrui |
| author_facet | WANG Weiqiong LI Yue LUO Shuyu ZHU Mengrui |
| author_sort | WANG Weiqiong |
| collection | DOAJ |
| description | Boolean functions with five-valued spectra have important applications in code division multiple access (CDMA) communication, coding and cryptography, true random number generators (TRNG), and combinatorial design. An approach based on the Walsh spectral neutralization technique for directly constructing a class of <italic>n</italic>‐variable resilient five-valued spectra Boolean functions was proposed. The nonlinearity of the resulting functions could reach up to <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><msup><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi>n</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo>-</mo><msup><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mfenced open="⌈" close="⌉" separators="|"><mrow><mfrac><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></mfenced></mrow></msup></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/91B2C2BE-4517-4c06-90F2-0DDC989C448C-M006.jpg"><?fx-imagestate width="14.73200035" height="5.84200001"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/91B2C2BE-4517-4c06-90F2-0DDC989C448C-M006c.jpg"><?fx-imagestate width="14.73200035" height="5.84200001"?></graphic></alternatives></inline-formula>, and it was proved that functions achieving this upper bound had the algebraic degree of <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mfenced open="⌊" close="⌋" separators="|"><mrow><mfrac><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></mfenced><mo>+</mo><mn mathvariant="normal">1</mn></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/91B2C2BE-4517-4c06-90F2-0DDC989C448C-M007.jpg"><?fx-imagestate width="10.15999985" height="7.11199999"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/91B2C2BE-4517-4c06-90F2-0DDC989C448C-M007c.jpg"><?fx-imagestate width="10.15999985" height="7.11199999"?></graphic></alternatives></inline-formula>,the resiliency order of approximately <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mfenced open="⌊" close="⌋" separators="|"><mrow><mfrac><mrow><mi>n</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">4</mn></mrow></mfrac></mrow></mfenced></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/91B2C2BE-4517-4c06-90F2-0DDC989C448C-M008.jpg"><?fx-imagestate width="10.15999985" height="7.11199999"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/91B2C2BE-4517-4c06-90F2-0DDC989C448C-M008c.jpg"><?fx-imagestate width="10.15999985" height="7.11199999"?></graphic></alternatives></inline-formula>, and the correction order of <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M9"><mfenced open="⌈" close="⌉" separators="|"><mrow><mfrac><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></mfenced></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/91B2C2BE-4517-4c06-90F2-0DDC989C448C-M009.jpg"><?fx-imagestate width="4.65666676" height="7.11199999"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/91B2C2BE-4517-4c06-90F2-0DDC989C448C-M009c.jpg"><?fx-imagestate width="4.65666676" height="7.11199999"?></graphic></alternatives></inline-formula>. The results demonstrate that the constructed functions achieve a favorable balance among multiple cryptographic properties. |
| format | Article |
| id | doaj-art-cef55ddc0e2749dbb99214af2fc7633c |
| institution | DOAJ |
| issn | 1000-436X |
| language | zho |
| publishDate | 2025-07-01 |
| publisher | Editorial Department of Journal on Communications |
| record_format | Article |
| series | Tongxin xuebao |
| spelling | doaj-art-cef55ddc0e2749dbb99214af2fc7633c2025-08-20T02:57:57ZzhoEditorial Department of Journal on CommunicationsTongxin xuebao1000-436X2025-07-0146145154120191166Construction and analysis of resilient five-valued spectra Boolean functionsWANG WeiqiongLI YueLUO ShuyuZHU MengruiBoolean functions with five-valued spectra have important applications in code division multiple access (CDMA) communication, coding and cryptography, true random number generators (TRNG), and combinatorial design. An approach based on the Walsh spectral neutralization technique for directly constructing a class of <italic>n</italic>‐variable resilient five-valued spectra Boolean functions was proposed. The nonlinearity of the resulting functions could reach up to <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><msup><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mi>n</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mo>-</mo><msup><mrow><mn mathvariant="normal">2</mn></mrow><mrow><mfenced open="⌈" close="⌉" separators="|"><mrow><mfrac><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></mfenced></mrow></msup></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/91B2C2BE-4517-4c06-90F2-0DDC989C448C-M006.jpg"><?fx-imagestate width="14.73200035" height="5.84200001"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/91B2C2BE-4517-4c06-90F2-0DDC989C448C-M006c.jpg"><?fx-imagestate width="14.73200035" height="5.84200001"?></graphic></alternatives></inline-formula>, and it was proved that functions achieving this upper bound had the algebraic degree of <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mfenced open="⌊" close="⌋" separators="|"><mrow><mfrac><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></mfenced><mo>+</mo><mn mathvariant="normal">1</mn></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/91B2C2BE-4517-4c06-90F2-0DDC989C448C-M007.jpg"><?fx-imagestate width="10.15999985" height="7.11199999"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/91B2C2BE-4517-4c06-90F2-0DDC989C448C-M007c.jpg"><?fx-imagestate width="10.15999985" height="7.11199999"?></graphic></alternatives></inline-formula>,the resiliency order of approximately <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mfenced open="⌊" close="⌋" separators="|"><mrow><mfrac><mrow><mi>n</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">4</mn></mrow></mfrac></mrow></mfenced></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/91B2C2BE-4517-4c06-90F2-0DDC989C448C-M008.jpg"><?fx-imagestate width="10.15999985" height="7.11199999"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/91B2C2BE-4517-4c06-90F2-0DDC989C448C-M008c.jpg"><?fx-imagestate width="10.15999985" height="7.11199999"?></graphic></alternatives></inline-formula>, and the correction order of <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M9"><mfenced open="⌈" close="⌉" separators="|"><mrow><mfrac><mrow><mi>n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mrow></mfenced></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/91B2C2BE-4517-4c06-90F2-0DDC989C448C-M009.jpg"><?fx-imagestate width="4.65666676" height="7.11199999"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/91B2C2BE-4517-4c06-90F2-0DDC989C448C-M009c.jpg"><?fx-imagestate width="4.65666676" height="7.11199999"?></graphic></alternatives></inline-formula>. The results demonstrate that the constructed functions achieve a favorable balance among multiple cryptographic properties.http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2025116/Boolean functionfive-valued spectra functionnonlinearityresiliency ordercorrection order |
| spellingShingle | WANG Weiqiong LI Yue LUO Shuyu ZHU Mengrui Construction and analysis of resilient five-valued spectra Boolean functions Tongxin xuebao Boolean function five-valued spectra function nonlinearity resiliency order correction order |
| title | Construction and analysis of resilient five-valued spectra Boolean functions |
| title_full | Construction and analysis of resilient five-valued spectra Boolean functions |
| title_fullStr | Construction and analysis of resilient five-valued spectra Boolean functions |
| title_full_unstemmed | Construction and analysis of resilient five-valued spectra Boolean functions |
| title_short | Construction and analysis of resilient five-valued spectra Boolean functions |
| title_sort | construction and analysis of resilient five valued spectra boolean functions |
| topic | Boolean function five-valued spectra function nonlinearity resiliency order correction order |
| url | http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2025116/ |
| work_keys_str_mv | AT wangweiqiong constructionandanalysisofresilientfivevaluedspectrabooleanfunctions AT liyue constructionandanalysisofresilientfivevaluedspectrabooleanfunctions AT luoshuyu constructionandanalysisofresilientfivevaluedspectrabooleanfunctions AT zhumengrui constructionandanalysisofresilientfivevaluedspectrabooleanfunctions |