{"title":"同态见证加密及其应用","authors":"Yuzhu Wang, Xingbo Wang, Mingwu Zhang","doi":"10.1002/nem.2303","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>In witness encryption (<span>WE</span>), an instance <span></span><math>\n <semantics>\n <mrow>\n <mi>x</mi>\n </mrow>\n <annotation>$$ x $$</annotation>\n </semantics></math> of an <span>NP</span> problem is allowed to be used to encrypt a message, and who holding a witness of the problem can efficiently decrypt the ciphertext. In this work, we put forth the concept of homomorphic witness encryption (<span>HWE</span>), where one can evaluate functions over ciphertexts of the same instance without decrypting them, that is, one can manipulate a set of ciphertexts with messages <span></span><math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <msub>\n <mrow>\n <mi>M</mi>\n </mrow>\n <mrow>\n <mn>1</mn>\n </mrow>\n </msub>\n <mo>,</mo>\n <mo>⋯</mo>\n <mspace></mspace>\n <mo>,</mo>\n <msub>\n <mrow>\n <mi>M</mi>\n </mrow>\n <mrow>\n <mi>n</mi>\n </mrow>\n </msub>\n <mo>)</mo>\n </mrow>\n <annotation>$$ \\left({M}_1,\\cdots, {M}_n\\right) $$</annotation>\n </semantics></math> to obtain the evaluation of <span></span><math>\n <semantics>\n <mrow>\n <mi>f</mi>\n <mo>(</mo>\n <msub>\n <mrow>\n <mi>M</mi>\n </mrow>\n <mrow>\n <mn>1</mn>\n </mrow>\n </msub>\n <mo>,</mo>\n <mo>⋯</mo>\n <mspace></mspace>\n <mo>,</mo>\n <msub>\n <mrow>\n <mi>M</mi>\n </mrow>\n <mrow>\n <mi>n</mi>\n </mrow>\n </msub>\n <mo>)</mo>\n </mrow>\n <annotation>$$ f\\left({M}_1,\\cdots, {M}_n\\right) $$</annotation>\n </semantics></math>, for any function <span></span><math>\n <semantics>\n <mrow>\n <mi>f</mi>\n </mrow>\n <annotation>$$ f $$</annotation>\n </semantics></math>. We declare that such homomorphic witness encryption schemes can be generically constructed from indistinguishable obfuscation (<span></span><math>\n <semantics>\n <mrow>\n <mi>i</mi>\n <mi>O</mi>\n </mrow>\n <annotation>$$ i\\mathcal{O} $$</annotation>\n </semantics></math>) for any classes of functions. Then we propose the instantiate of multiplicatively homomorphic witness encryption (<span>MHWE</span>) and linearly homomorphic witness encryption (<span>LHWE</span>) using an <span></span><math>\n <semantics>\n <mrow>\n <mi>i</mi>\n <mi>O</mi>\n </mrow>\n <annotation>$$ i\\mathcal{O} $$</annotation>\n </semantics></math>, homomorphic encryption for NP problems such as Subset-Sum and a batch-processed <span>GS</span>-proof system, which enables us to evaluate multiplication operations and linear operations over ciphertext. Furthermore, we show the practicality of homomorphic witness encryption by proposing new protocols for applications of interest, such as homomorphic time-lock encryption, multi-party contract signing, and e-voting.</p>\n </div>","PeriodicalId":14154,"journal":{"name":"International Journal of Network Management","volume":"35 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Homomorphic Witness Encryption and Its Applications\",\"authors\":\"Yuzhu Wang, Xingbo Wang, Mingwu Zhang\",\"doi\":\"10.1002/nem.2303\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>In witness encryption (<span>WE</span>), an instance <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>x</mi>\\n </mrow>\\n <annotation>$$ x $$</annotation>\\n </semantics></math> of an <span>NP</span> problem is allowed to be used to encrypt a message, and who holding a witness of the problem can efficiently decrypt the ciphertext. In this work, we put forth the concept of homomorphic witness encryption (<span>HWE</span>), where one can evaluate functions over ciphertexts of the same instance without decrypting them, that is, one can manipulate a set of ciphertexts with messages <span></span><math>\\n <semantics>\\n <mrow>\\n <mo>(</mo>\\n <msub>\\n <mrow>\\n <mi>M</mi>\\n </mrow>\\n <mrow>\\n <mn>1</mn>\\n </mrow>\\n </msub>\\n <mo>,</mo>\\n <mo>⋯</mo>\\n <mspace></mspace>\\n <mo>,</mo>\\n <msub>\\n <mrow>\\n <mi>M</mi>\\n </mrow>\\n <mrow>\\n <mi>n</mi>\\n </mrow>\\n </msub>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$$ \\\\left({M}_1,\\\\cdots, {M}_n\\\\right) $$</annotation>\\n </semantics></math> to obtain the evaluation of <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>f</mi>\\n <mo>(</mo>\\n <msub>\\n <mrow>\\n <mi>M</mi>\\n </mrow>\\n <mrow>\\n <mn>1</mn>\\n </mrow>\\n </msub>\\n <mo>,</mo>\\n <mo>⋯</mo>\\n <mspace></mspace>\\n <mo>,</mo>\\n <msub>\\n <mrow>\\n <mi>M</mi>\\n </mrow>\\n <mrow>\\n <mi>n</mi>\\n </mrow>\\n </msub>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$$ f\\\\left({M}_1,\\\\cdots, {M}_n\\\\right) $$</annotation>\\n </semantics></math>, for any function <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>f</mi>\\n </mrow>\\n <annotation>$$ f $$</annotation>\\n </semantics></math>. We declare that such homomorphic witness encryption schemes can be generically constructed from indistinguishable obfuscation (<span></span><math>\\n <semantics>\\n <mrow>\\n <mi>i</mi>\\n <mi>O</mi>\\n </mrow>\\n <annotation>$$ i\\\\mathcal{O} $$</annotation>\\n </semantics></math>) for any classes of functions. Then we propose the instantiate of multiplicatively homomorphic witness encryption (<span>MHWE</span>) and linearly homomorphic witness encryption (<span>LHWE</span>) using an <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>i</mi>\\n <mi>O</mi>\\n </mrow>\\n <annotation>$$ i\\\\mathcal{O} $$</annotation>\\n </semantics></math>, homomorphic encryption for NP problems such as Subset-Sum and a batch-processed <span>GS</span>-proof system, which enables us to evaluate multiplication operations and linear operations over ciphertext. Furthermore, we show the practicality of homomorphic witness encryption by proposing new protocols for applications of interest, such as homomorphic time-lock encryption, multi-party contract signing, and e-voting.</p>\\n </div>\",\"PeriodicalId\":14154,\"journal\":{\"name\":\"International Journal of Network Management\",\"volume\":\"35 1\",\"pages\":\"\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-09-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Network Management\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/nem.2303\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, INFORMATION SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Network Management","FirstCategoryId":"94","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/nem.2303","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
Homomorphic Witness Encryption and Its Applications
In witness encryption (WE), an instance of an NP problem is allowed to be used to encrypt a message, and who holding a witness of the problem can efficiently decrypt the ciphertext. In this work, we put forth the concept of homomorphic witness encryption (HWE), where one can evaluate functions over ciphertexts of the same instance without decrypting them, that is, one can manipulate a set of ciphertexts with messages to obtain the evaluation of , for any function . We declare that such homomorphic witness encryption schemes can be generically constructed from indistinguishable obfuscation () for any classes of functions. Then we propose the instantiate of multiplicatively homomorphic witness encryption (MHWE) and linearly homomorphic witness encryption (LHWE) using an , homomorphic encryption for NP problems such as Subset-Sum and a batch-processed GS-proof system, which enables us to evaluate multiplication operations and linear operations over ciphertext. Furthermore, we show the practicality of homomorphic witness encryption by proposing new protocols for applications of interest, such as homomorphic time-lock encryption, multi-party contract signing, and e-voting.
期刊介绍：
Modern computer networks and communication systems are increasing in size, scope, and heterogeneity. The promise of a single end-to-end technology has not been realized and likely never will occur. The decreasing cost of bandwidth is increasing the possible applications of computer networks and communication systems to entirely new domains. Problems in integrating heterogeneous wired and wireless technologies, ensuring security and quality of service, and reliably operating large-scale systems including the inclusion of cloud computing have all emerged as important topics. The one constant is the need for network management. Challenges in network management have never been greater than they are today. The International Journal of Network Management is the forum for researchers, developers, and practitioners in network management to present their work to an international audience. The journal is dedicated to the dissemination of information, which will enable improved management, operation, and maintenance of computer networks and communication systems. The journal is peer reviewed and publishes original papers (both theoretical and experimental) by leading researchers, practitioners, and consultants from universities, research laboratories, and companies around the world. Issues with thematic or guest-edited special topics typically occur several times per year. Topic areas for the journal are largely defined by the taxonomy for network and service management developed by IFIP WG6.6, together with IEEE-CNOM, the IRTF-NMRG and the Emanics Network of Excellence.
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