Some Explicit Formulae of NAF and its Left-to-Right Analogue Based on Booth Encoding

Provided by: Science & Engineering Research Support soCiety (SERSC)
Topic: Enterprise Software
Format: PDF
In some exponentiation-based public-key cryptosystems including RSA and Elliptic Curve Cryptosystems (ECCs), a binary representation of a given integer (which may be a secret in most cases) is commonly used as a standard technique. Non-Adjacent Form (NAF) is a canonical form of signed binary representation of integers. The author proposed a left-to-right analogue of NAF (FAN). It is known that NAF and FAN can be generated by applying a sliding window method with width-2 to the Booth encoding in right-to-left and left-to-right direction, respectively. In this paper, the authors derive some properties of Booth encoding such as pattern, classification, extension, adjacency and length.

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