Analysis of Sliding Window Techniques for Exponentiation

نویسنده

  • etin Kaya Ko
چکیده

The m-ary method for computing x E partitions the bits of the integer E into words of constant length, and then performs as many multiplications as there are nonzero words. Variable length partitioning strategies have been suggested to reduce the number of nonzero words, and thus, the total numb e r o f m ultiplications. Algorithms for exponentiation using such partitioning strategies are termed sliding window techniques. In this paper, we give algorithmic descriptions of two recently proposed sliding window techniques, and calculate the average numberofmultiplications by modeling the partitioning process as a Markov chain. We tabulate the optimal values of the partitioning parameters, and show that the sliding window algorithms require up to 8 fewer multiplications than the m-ary method.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Improved Techniques for Fast Exponentiation

We present improvements to algorithms for efficient exponentiation. The fractional window technique is a generalization of the sliding window and window NAF approach; it can be used to improve performance in devices with limited storage. Window NAF splitting is an efficient technique for exponentiation with precomputation for fixed bases in groups where inversion is easy (e.g. elliptic curves).

متن کامل

Comparative Investigation of Methods of Modular Exponentiation

Main parameters of evaluation of modern information protection systems that implement RSA encryption algorithm are performance, RAM consumption and stability of algorithm of used method of modular exponentiation to the attacks on implementation, particularly in the temporal analysis. Methods of modular exponentiation (binary method, method and sliding window method) are characterized by the dep...

متن کامل

Iterative sliding window method for shorter number of operations in modular exponentiation and scalar multiplication

Cryptography via public key cryptosystems (PKC) has been widely used for providing services such as confidentiality, authentication, integrity and non-repudiation. Other than security, computational efficiency is another major issue of concern. And for PKC, it is largely controlled by either modular exponentiation or scalar multiplication operations such that found in RSA and elliptic curve cry...

متن کامل

Stealing Keys from PCs by Radio: Cheap Electromagnetic Attacks on Windowed Exponentiation (extended version)

We present new side-channel attacks on implementations of RSA and ElGamal encryption. The attacks can extract secret keys using a very low measurement bandwidth (a frequency band of less than 100 kHz, residing under 2 MHz) even when attacking multi-GHz CPUs. They targets implementation that use the popular sliding-window and fixed-window (m-ary) modular exponentiation. We demonstrate the attack...

متن کامل

Adaptive Modular Exponentiation Methods v.s. Python's Power Function

In this paper we use Python to implement two efficient modular exponentiation methods: the adaptive m-ary method and the adaptive sliding-window method of window size k, where both m’s are adaptively chosen based on the length of exponent. We also conduct the benchmark for both methods. Evaluation results show that compared to the industry-standard efficient implementations of modular power fun...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1995