学位论文详细信息
On Efficient Polynomial Multiplication and Its Impact on Curve based Cryptosystems
Elliptic Curve Cryptography;Hyperelliptic Curve Cryptography;Pairing;Polynomial Multiplication;Modular Arithmetic;Software Realization;Cyptography;Public Key Cryptography;Karatsuba Multiplication;Three Way Multiplication;Cryptographic Computations;Electrical and Computer Engineering
Alrefai, Ahmad Salam
University of Waterloo
关键词: Elliptic Curve Cryptography;    Hyperelliptic Curve Cryptography;    Pairing;    Polynomial Multiplication;    Modular Arithmetic;    Software Realization;    Cyptography;    Public Key Cryptography;    Karatsuba Multiplication;    Three Way Multiplication;    Cryptographic Computations;    Electrical and Computer Engineering;   
Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/8083/3/Alrefai_Ahmad_Salam.pdf
瑞士|英语
来源: UWSPACE Waterloo Institutional Repository
PDF
【 摘 要 】

Secure communication is critical to many applications. To this end, various security goals can be achieved using elliptic/hyperelliptic curve and pairing based cryptography. Polynomial multiplication is used in the underlying operations of these protocols. Therefore, as part of this thesis different recursive algorithms are studied; these algorithms include Karatsuba, Toom, and Bernstein. In this thesis, we investigate algorithms and implementation techniques to improve the performance of the cryptographic protocols. Common factors present in explicit formulae in elliptic curves operations are utilized such that two multiplications are replaced by a single multiplication in a higher field. Moreover, we utilize the idea based on common factor used in elliptic curves and generate new explicit formulae for hyperelliptic curves and pairing. In the case of hyperelliptic curves, the common factor method is applied to the fastest known even characteristic hyperelliptic curve operations, i.e. divisor addition and divisor doubling. Similarly, in pairing we observe the presence of common factors inside the Miller loop of Eta pairing and the theoretical results show significant improvement when applying the idea based on common factor method. This has a great advantage for applications that require higher speed.

【 预 览 】
附件列表
Files Size Format View
On Efficient Polynomial Multiplication and Its Impact on Curve based Cryptosystems 3788KB PDF download
  文献评价指标  
  下载次数:13次 浏览次数:28次