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| Title: | 基於同源密碼學之簽章方案相關研究
Supersingular Isogeny-Based Signatures: A survey |
| Authors: | 李立瑜
Lee, Li-Yu |
| Contributors: | 蔡炎龍
Tsai, Yen-lung
李立瑜
Lee, Li-Yu |
| Keywords: | 後量子密碼學
同源密碼學
橢圓曲線
數位簽章
Post-quantum Cryptography
Isogeny Based Cryptography
elliptic curve
signature schemes |
| Date: | 2023 |
| Issue Date: | 2023-09-01 15:26:23 (UTC+8) |
| Abstract: | 自2016年起，美國國家標準與技術局(NIST)提出了後量子密碼學標準化競賽，公開徵求面對量子電腦時代的公鑰加密和數位簽章系統。隨著競賽尾聲的來臨，特別是公鑰加密方案的標準化清單釋出和二次徵求數位簽章系統方案，後量子密碼學的研究重心逐漸轉向數位簽章方案的制定和安全性分析。基於同源性的密碼學，作為後量子密碼學中最新穎的分支，運用了大量的代數和橢圓曲線知識，與其他領域方案相比，極小的金鑰大小是一大優勢，且使用方法與現行的橢圓曲線密碼學相似。
本研究旨在透過基於同源性的後量子數位簽章方案的調查，從NIST PQC競賽的現況出發，介紹基礎密碼學的數學背景、同源密碼學所需的數學知識，並分析這些數位簽章方案的內容、安全性和實作效能考量，期望能促使更多人投入同源密碼學的研究。
Since 2016, the U.S. National Institute of Standards and Technology (NIST) initiated the post-quantum cryptography standardization competition, publicly soliciting public key encryption and digital signature systems for the quantum computing era. As the competition draws to a close, especially with the release of the standardization list for public key encryption schemes and the second call for digital signature system proposals, the research focus of post-quantum cryptography has gradually shifted to the formulation and security analysis of digital signature schemes. Isogeny-based cryptography, as the most novel branch in post-quantum cryptography, employs a wealth of algebraic and elliptic curve knowledge. Compared to schemes from other domains, its extremely small key size is a significant advantage, and its usage is similar to current elliptic curve cryptography.
This study aims to investigate post-quantum digital signature schemes based on isogenies. Starting from the current status of the NIST PQC competition, we introduce the mathematical background of basic cryptography, the mathematical knowledge required for isogeny-based cryptography, and analyze the content, security, and implementation performance considerations of these digital signature schemes. We hope to encourage more people to delve into research in this field. |
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| Description: | 碩士
國立政治大學
應用數學系
110751007 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0110751007 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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