Abstract
Efficient implementations of cryptosystems are important in order to conserve resources, memory, power, etc., which will enable resource-limited devices to compute necessary cryptographic operations. One technique that successfully reduces the number of necessary operations is the use of a signed digit representation for the key, because it reduces the nonzero density of the representation. One such signed digit representation is the non-adjacent form or NAF. Moreover, one can make more reductions in the number of nonzero symbols of the key by expressing the key with a w-ary NAF or wNAF form. A drawback is that one needs to parse the key twice, once to construct the wNAF representation and the second time to perform the necessary cryptographic operation. At Crypto 2004 [10], Okeya et. al. introduced a w-ary representation wMOF, which possess the same nonzero density as wNAF, as well as an algorithm that computes wMOF in a left-to-right manner utilizing very little memory (“memory-less”). At that time, the authors noted that a left-to-right “memory-less” algorithm that computes wNAF is an open problem. In this work, we define wNAF *, a generalization of wNAF. Further, we construct a left-to-right “memory-less” algorithm that computes the w-ary wNAF * representation of a key and demonstrate that wNAF * is as efficient as wNAF. Our work will demonstrate that the left-to-right wNAF * recoding algorithm closely resembles the right-to-left wNAF recoding algorithm.
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King, B. (2008). wNAF*, an Efficient Left-to-Right Signed Digit Recoding Algorithm. In: Bellovin, S.M., Gennaro, R., Keromytis, A., Yung, M. (eds) Applied Cryptography and Network Security. ACNS 2008. Lecture Notes in Computer Science, vol 5037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68914-0_26
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DOI: https://doi.org/10.1007/978-3-540-68914-0_26
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