Multivariate Public Key Cryptosystems
暫譯: 多變量公鑰密碼系統

Ding, Jintai, Petzoldt, Albrecht, Schmidt, Dieter S.

  • 出版商: Springer
  • 出版日期: 2020-10-01
  • 售價: $7,100
  • 貴賓價: 9.5$6,745
  • 語言: 英文
  • 頁數: 300
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1071609858
  • ISBN-13: 9781071609859
  • 海外代購書籍(需單獨結帳)

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商品描述

This second edition book discusses the current research on public key cryptosystems, and begins with an introduction including the basic concepts of multivariate cryptography and the history of this field. The authors provide a detailed description and security analysis of the most important multivariate public key schemes, including the four multivariate signature schemes participating as second round candidates in the NIST standardization process for post-quantum cryptosystems. Furthermore, this book covers the Simple Matrix encryption scheme, which is currently the most promising multivariate public key encryption scheme. This book also covers the current state of security analysis methods for multivariate public key cryptosystems including the algorithms and theory of solving systems of multivariate polynomial equations over finite fields. Through the book's website, interested readers can find source code to the algorithms handled in this book.

In 1994, Dr. Peter Shor from Bell Laboratories proposed a quantum algorithm solving the Integer Factorization and the Discrete Logarithm problem in polynomial time, thus making all of the currently used public key cryptosystems, such as RSA and ECC insecure. Therefore, there is an urgent need for alternative public key schemes which are resistant against quantum computer attacks. Researchers worldwide, as well as companies and governmental organizations have put a tremendous effort into the development of post-quantum public key cryptosystems to meet this challenge. One of the most promising candidates for this are Multivariate Public Key Cryptosystems (MPKCs). The public key of an MPKC is a set of multivariate polynomials over a small finite field. Especially for digital signatures, numerous well-studied multivariate schemes offering very short signatures and high efficiency exist. The fact that these schemes work over small finite fields, makes them suitable not only for interconnected computer systems, but also for small devices with limited resources, which are used in ubiquitous computing.

This book gives a systematic introduction into the field of multivariate public key cryptosystems (MPKC), and presents the most promising multivariate schemes for digital signatures and encryption. Although, this book was written more from a computational perspective, the authors try to provide the necessary mathematical background. Therefore, this book is suitable for a broad audience. This would include researchers working in either computer science or mathematics interested in this exciting new field, or as a secondary textbook for a course in MPKC suitable for beginning graduate students in mathematics or computer science. Information security experts in industry, computer scientists and mathematicians would also find this book valuable as a guide for understanding the basic mathematical structures necessary to implement multivariate cryptosystems for practical applications.

商品描述(中文翻譯)

這本第二版的書籍討論了當前公共金鑰密碼系統的研究,並以介紹開始,包括多變量密碼學的基本概念及其歷史。作者提供了對最重要的多變量公共金鑰方案的詳細描述和安全性分析,包括四個參與NIST後量子密碼系統標準化過程的多變量簽名方案,這些方案是第二輪候選者。此外,本書還涵蓋了簡單矩陣加密方案,這是目前最有前景的多變量公共金鑰加密方案。本書還討論了多變量公共金鑰密碼系統的安全性分析方法的現狀,包括在有限域上解決多變量多項式方程組的算法和理論。通過本書的網站,感興趣的讀者可以找到本書中處理的算法的源代碼。

1994年,來自貝爾實驗室的彼得·肖爾(Peter Shor)博士提出了一種量子算法,可以在多項式時間內解決整數因式分解和離散對數問題,從而使目前使用的所有公共金鑰密碼系統(如RSA和ECC)變得不安全。因此,迫切需要能抵抗量子計算機攻擊的替代公共金鑰方案。全球的研究人員、公司和政府組織都在為開發後量子公共金鑰密碼系統而付出巨大努力,以應對這一挑戰。其中最有前景的候選者之一是多變量公共金鑰密碼系統(MPKC)。MPKC的公共金鑰是一組在小有限域上的多變量多項式。特別是對於數字簽名,存在許多經過充分研究的多變量方案,提供非常短的簽名和高效率。這些方案在小有限域上運作,使它們不僅適用於互聯計算機系統,還適用於在無處不在計算中使用的資源有限的小型設備。

本書對多變量公共金鑰密碼系統(MPKC)領域進行了系統的介紹,並展示了最有前景的數字簽名和加密的多變量方案。雖然本書更多是從計算的角度撰寫,但作者試圖提供必要的數學背景。因此,本書適合廣泛的讀者群體,包括對這一令人興奮的新領域感興趣的計算機科學或數學研究人員,或作為適合數學或計算機科學研究生的MPKC課程的輔助教材。行業中的信息安全專家、計算機科學家和數學家也會發現本書對於理解實現多變量密碼系統所需的基本數學結構非常有價值。

作者簡介

Jintai Ding is a Charles Phelps Taft professor at the Department of Mathematical Sciences at the University of Cincinnati. He received B.A. from Xian Jiao tong University in 1988, M.A. from the University of Science and Technology of China in 1990 and PhD from Yale in 1995. He was a lecturer at the Research Institute of Mathematical Sciences of Kyoto University from 1995 to 1998. He has been at the University of Cincinnati since 1998. In 2006-2007, he was a visiting professor and Alexander von Humboldt Fellow at TU Darmstadt. He received the Zhong Jia Qing Prize from the Chinese Mathematical Society in 1990 for his Master Thesis on proving a conjecture by C. L. Siegel. His research was originally in quantum affine algebras and its representation theory, where he was credited for the invention of the Ding-Iohara-Miki algebra. His current interest is in post-quantum cryptography, in particular, multivariate cryptography, latticed-based cryptography and quantum-proof blockchain. He was a co-chair of the 2nd, 10th and 11th international conference on post-quantum cryptography. He and his colleagues developed the Rainbow signature, the GUI HFEv- signature, the Simple Matrix encryption and the LWE-based key exchange schemes. Rainbow is a second round candidate for the NIST post-quantum standardization process. He and his students completely broke a NIST second round post-quantum signature candidate LUOV.
Albrecht Petzoldt received a diploma in mathematics in 2009 from FAU Erlangen-Nuremberg and a PhD in Computer Science in 2013 from Technische Universität Darmstadt / Germany. Since then he worked for several academic and non academic institutions, including Kyushu University / Japan and the National Institute of Standards and Technology (NIST) / USA. Currently, he works as a lecturer at FAU Erlangen-Nuremberg / Germany.His main research interests are located in the field of multivariate cryptography, and in particular in the development and improvement of multivariate signature schemes such as UOV and Rainbow.
In 1966 Dieter Schmidt received his "Diplom in Mathematik" from the Technische Hochschule Stuttgart, Germany. He then went to the University of Minnesota, where he received his PhD in Mathematics in 1970. During that time he also worked for Univac and gained valuable experience in computer programming. After an initial appointment at the University of Maryland, he accepted a position in the Department of Mathematical Sciences at the University of Cincinnati. The department started offering courses in Computer Science in the late 1970's. It was natural for him to teach some of these courses and then to join the Department of Computer Science when it was formed in 1984. In 2002 he started his collaboration with Jintai Ding. He offered his expertise in programming in order to create the software for cryptographic schemes or the code to attack them. Although Dieter Schmidt retired from the University of Cincinnati in 2011, he has continued the collaboration with Jintai Ding.

作者簡介(中文翻譯)

丁金泰(Jintai Ding)是辛辛那提大學數學科學系的查爾斯·菲爾普斯·塔夫特教授。他於1988年獲得西安交通大學的學士學位,1990年獲得中國科學技術大學的碩士學位,1995年獲得耶魯大學的博士學位。他於1995年至1998年擔任京都大學數學科學研究所的講師。自1998年以來,他一直在辛辛那提大學任教。在2006至2007年期間,他擔任達姆施塔特工業大學的訪問教授及亞歷山大·馮·洪堡獎學金得主。他於1990年因其碩士論文中證明C. L. Siegel的猜想而獲得中國數學會的鍾家卿獎。最初他的研究集中在量子仿射代數及其表示理論上,他因發明丁-伊奧哈拉-三木代數而受到認可。他目前的研究興趣在於後量子密碼學,特別是多變量密碼學、基於格的密碼學和量子安全區塊鏈。他曾擔任第二屆、第十屆和第十一屆國際後量子密碼學會議的共同主席。他和他的同事們開發了Rainbow簽名、GUI HFEv-簽名、簡單矩陣加密和基於LWE的密鑰交換方案。Rainbow是NIST後量子標準化過程的第二輪候選者。他和他的學生們完全破解了一個NIST第二輪後量子簽名候選者LUOV。

阿爾布雷希特·佩茲奧爾特(Albrecht Petzoldt)於2009年在法爾茲大學(FAU Erlangen-Nuremberg)獲得數學文憑,並於2013年在德國達姆施塔特工業大學獲得計算機科學博士學位。自那時以來,他在多個學術和非學術機構工作,包括九州大學(Kyushu University)和美國國家標準與技術研究所(NIST)。目前,他在德國法爾茲大學擔任講師。他的主要研究興趣集中在多變量密碼學領域,特別是在UOV和Rainbow等多變量簽名方案的開發和改進上。

迪特·施密特(Dieter Schmidt)於1966年在德國斯圖加特工業大學獲得數學文憑,隨後前往明尼蘇達大學,於1970年獲得數學博士學位。在此期間,他也曾在Univac工作,獲得了寶貴的計算機編程經驗。在馬里蘭大學的初始任職後,他接受了辛辛那提大學數學科學系的職位。該系在1970年代末開始提供計算機科學課程。他自然地教授這些課程,並在1984年計算機科學系成立時加入該系。2002年,他開始與丁金泰合作。他提供編程專業知識,以創建密碼學方案的軟體或攻擊它們的代碼。儘管迪特·施密特於2011年從辛辛那提大學退休,但他仍然與丁金泰保持合作。