Fast Exponentiation Using Data Compression
نویسنده
چکیده
We present the first exponentiation algorithm that uses the entropy of the source of the exponent to improve on existing exponentiation algorithms when the entropy is smaller than (1 + w(S)/l(S)), where w(S) is the Hamming weight of the exponent, and l(S) is its length. For entropy 1 it is comparable to the best-known general purpose exponentiation algorithms.
منابع مشابه
Fast and Constant-Time Implementation of Modular Exponentiation
Modular exponentiation is an important operation which requires a vast amount of computations. Therefore, it is crucial to build fast exponentiation schemes. Since Cache and data-dependent branching behavior can alter the runtime of an algorithm significantly, it is also important to build an exponentiation scheme with constant run-time. However, such approaches have traditionally added signifi...
متن کاملHow to Maximize the Potential of FPGA Resources for Modular Exponentiation
This paper describes a modular exponentiation processing method and circuit architecture that can exhibit the maximum performance of FPGA resources. The modular exponentiation architecture proposed by us comprises three main techniques. The first technique is to improve the Montgomery multiplication algorithm in order to maximize the performance of the multiplication unit in FPGA. The second te...
متن کاملDouble-Exponentiation in Factor-4 Groups and Its Applications
In previous work we showed how to compress certain prime-order subgroups of the cyclotomic subgroups of orders 22m + 1 of the multiplicative groups of F∗ 24m by a factor of 4. We also showed that single-exponentiation can be efficiently performed using compressed representations. In this paper we show that double-exponentiation can be efficiently performed using factor-4 compressed representati...
متن کاملFast Software Exponentiation in GF(2^k)
We present a new algorithm for computing a e where a 2 GF2 k and e is a positive integer. The proposed algorithm is more suitable for implementation in software , and relies on the Montgomery multiplication in GF2 k. The speed of the exponentiation algorithm largely depends on the availability of a fast method for multiplying two polynomials of length w deened over GF2. The theoretical analysis...
متن کاملA Survey of Fast Exponentiation Methods
Public-key cryptographic systems often involve raising elements of some group (e.g. GF (2n), Z/NZ, or elliptic curves) to large powers. An important question is how fast this exponentiation can be done, which often determines whether a given system is practical. The best method for exponentiation depends strongly on the group being used, the hardware the system is implemented on, and whether on...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Comput.
دوره 28 شماره
صفحات -
تاریخ انتشار 1998