Analysis of sliding window techniques for exponentiation
نویسندگان
چکیده
منابع مشابه
Analysis of Sliding Window Techniques for Exponentiation
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 terme...
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Let E be an (additive) monoid and suppose we want to compute nP where n ∈ N and P ∈ E. The obvious way, summing n copies of P , is not very efficient: it requires n − 1 additions. For example, 12P = 2 ( 2(2P +P ) ) uses only one addition and three doublings, rather that eleven additions. The problem of computing a scalar multiple (or the exponent, in a multiplicative setting) using few addition...
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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...
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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).
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1995
ISSN: 0898-1221
DOI: 10.1016/0898-1221(95)00153-p