Journal of Mathematical Cryptology
Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran
Editorial Board: Blackburn, Simon R. / Blundo, Carlo / Burmester, Mike / Cramer, Ronald / Dawson, Ed / Gilman, Robert / Gonzalez Vasco, Maria Isabel / Grosek, Otokar / Helleseth, Tor / Kim, Kwangjo / Koblitz, Neal / Kurosawa, Kaoru / Lauter, Kristin / Lange, Tanja / Menezes, Alfred / Nguyen, Phong Q. / Pieprzyk, Josef / Rötteler, Martin / Safavi-Naini, Rei / Shparlinski, Igor E. / Stinson, Doug / Takagi, Tsuyoshi / Williams, Hugh C. / Yung, Moti
4 Issues per year
CiteScore 2016: 0.74
SCImago Journal Rank (SJR) 2016: 0.463
Source Normalized Impact per Paper (SNIP) 2016: 0.778
Mathematical Citation Quotient (MCQ) 2016: 0.16
Minimal weight expansions in Pisot bases
For applications to cryptography, it is important to represent numbers with a small number of non-zero digits (Hamming weight) or with small absolute sum of digits. The problem of finding representations with minimal weight has been solved for integer bases, e.g. by the non-adjacent form in base 2. In this paper, we consider numeration systems with respect to real bases β which are Pisot numbers and prove that the expansions with minimal absolute sum of digits are recognizable by finite automata. When β is the Golden Ratio, the Tribonacci number or the smallest Pisot number, we determine expansions with minimal number of digits ±1 and give explicitely the finite automata recognizing all these expansions. The average weight is lower than for the non-adjacent form.
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