Optimal Left-to-Right Binary Signed-Digit Recoding
نویسندگان
چکیده
This paper describes new methods for producing optimal binary signed-digit representations. This can be useful in the fast computation of exponentiations. Contrary to existing algorithms, the digits are scanned from left to right (i.e., from the most significant position to the least significant position). This may lead to better performances in both hardware and software.
منابع مشابه
A Note on the Signed Sliding Window Integer Recoding and a Left-to-Right Analogue
Addition-subtraction-chains obtained from signed digit recodings of integers are a common tool for computing multiples of random elements of a group where the computation of inverses is a fast operation. Cohen and Solinas independently described one such recoding, the w-NAF. For scalars of the size commonly used in cryptographic applications, it leads to the current scalar multiplication algori...
متن کاملSigned Binary Representations Revisited
The most common method for computing exponentiation of random elements in Abelian groups are sliding window schemes, which enhance the efficiency of the binary method at the expense of some precomputation. In groups where inversion is easy (e.g. elliptic curves), signed representations of the exponent are meaningful because they decrease the amount of required precomputation. The asymptotic bes...
متن کاملParallel Canonical Recoding
We introduce a parallel algorithm for generating the canonical signed-digit expansion of an n-bit number in Olog n time using On gates. The algorithm is similar to the computation of the carries in a carry look-ahead circuit. We also prove that if the binary number x + bx=2c is given, then the canonical signed-digit recoding of x can be computed in O1 time using On gates.
متن کاملImprovement on Ha-Moon Randomized Exponentiation Algorithm
Randomized recoding on the exponent of an exponentiation computation into a signed-digit representation has been a well known countermeasure against some side-channel attacks. However, this category of countermeasures can only be applicable to those cryptosystems with fixed parameters on the base integer when evaluating exponentiation or to some classes of cryptosystems such that the inversion ...
متن کاملDistribution results for low-weight binary representations for pairs of integers
Abstract. We discuss an optimal method for the computation of linear combinations of elements of Abelian groups, which uses signed digit expansions. This has applications in elliptic curve cryptography. We compute the expected number of operations asymptotically (including a periodically oscillating second order term) and prove a central limit theorem. Apart from the usual right-to-left (i.e., ...
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:
- IEEE Trans. Computers
دوره 49 شماره
صفحات -
تاریخ انتشار 2000