Homomorphic Computation in Reed-Muller Codes and Improvements of Modified pqsigRM ; Reed-Muller 부호의 동형 연산과 Modified pqsigRM의 개선
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| Title: | Homomorphic Computation in Reed-Muller Codes and Improvements of Modified pqsigRM ; Reed-Muller 부호의 동형 연산과 Modified pqsigRM의 개선 |
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| Authors: | 조진규 |
| Contributors: | 노종선, CHO JINKYU, 공과대학 전기·정보공학부 |
| Publisher Information: | 서울대학교 대학원 |
| Publication Year: | 2023 |
| Collection: | Seoul National University: S-Space |
| Subject Terms: | |
| Description: | 학위논문(박사) -- 서울대학교대학원 : 공과대학 전기·정보공학부, 2023. 8. 노종선. ; In this dissertation, two main contributions are given as; i) homomorphic computation in Reed-Muller (RM) codes and ii) improving Modified pqsigRM with the key size and bit-security. First, a method of homomorphic computation in RM codes is proposed. With the ongoing developments in artificial intelligence (AI), big data, and cloud services, fully homomorphic encryption (FHE) is being considered as a solution for preserving privacy and security in machine learning systems. Currently, the most of existing FHE schemes are constructed using lattice-based cryptography. In state-of-the-art algorithms, a huge amount of computational resources are required for homomorphic multiplications and the corresponding bootstrapping that is necessary to refresh the ciphertext for a larger number of operations. Therefore, it is necessary to discover a new innovative approach for FHE that can reduce computational complexity for practical applications. Diverse research works, which are not limited to lattice-based cryptography are also needed. The code-based cryptography can be a new solution for this. In this dissertation, I propose a code-based homomorphic operation scheme in RM codes. It is known that the linear codes are closed under the addition, however, achieving multiplicative homomorphic operations with linear codes has been impossible until now. I strive to solve this problem by proposing a fully homomorphic code scheme that can support both addition and multiplication simultaneously using the RM codes. This can be considered as a preceding step for constructing code-based FHE schemes. I restrict this to the computation of the first order of RM codes. As the order of RM codes increases after multiplication, a bootstrapping technique is required to reduce the order of intermediate RM codes to accomplish a large number of operations. I propose a bootstrapping technique to preserve the order of RM codes after the addition or multiplication by proposing three consecutive ... |
| Document Type: | doctoral or postdoctoral thesis |
| File Description: | ix, 80 |
| Language: | Korean |
| ISBN: | 978-0-00-000000-2 0-00-000000-0 |
| Relation: | 000000178587; https://hdl.handle.net/10371/196433; https://dcollection.snu.ac.kr/common/orgView/000000178587; 000000000050▲000000000058▲000000178587▲ |
| Availability: | https://hdl.handle.net/10371/196433 https://dcollection.snu.ac.kr/common/orgView/000000178587 |
| Accession Number: | edsbas.D4DF1FFD |
| Database: | BASE |
Nájsť tento článok vo Web of Science | Abstract: | 학위논문(박사) -- 서울대학교대학원 : 공과대학 전기·정보공학부, 2023. 8. 노종선. ; In this dissertation, two main contributions are given as; i) homomorphic computation in Reed-Muller (RM) codes and ii) improving Modified pqsigRM with the key size and bit-security. First, a method of homomorphic computation in RM codes is proposed. With the ongoing developments in artificial intelligence (AI), big data, and cloud services, fully homomorphic encryption (FHE) is being considered as a solution for preserving privacy and security in machine learning systems. Currently, the most of existing FHE schemes are constructed using lattice-based cryptography. In state-of-the-art algorithms, a huge amount of computational resources are required for homomorphic multiplications and the corresponding bootstrapping that is necessary to refresh the ciphertext for a larger number of operations. Therefore, it is necessary to discover a new innovative approach for FHE that can reduce computational complexity for practical applications. Diverse research works, which are not limited to lattice-based cryptography are also needed. The code-based cryptography can be a new solution for this. In this dissertation, I propose a code-based homomorphic operation scheme in RM codes. It is known that the linear codes are closed under the addition, however, achieving multiplicative homomorphic operations with linear codes has been impossible until now. I strive to solve this problem by proposing a fully homomorphic code scheme that can support both addition and multiplication simultaneously using the RM codes. This can be considered as a preceding step for constructing code-based FHE schemes. I restrict this to the computation of the first order of RM codes. As the order of RM codes increases after multiplication, a bootstrapping technique is required to reduce the order of intermediate RM codes to accomplish a large number of operations. I propose a bootstrapping technique to preserve the order of RM codes after the addition or multiplication by proposing three consecutive ... |
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| ISBN: | 9780000000002 0000000000 |