Citations: Optimal Left-to-Right Binary Signed-Digit Recoding

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M. Joye and S.-M. Yen, "Optimal left-to-right binary signed-digit recoding," IEEE Trans. Computers, vol. 49, pp. 740--748, 2000.

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Analysis of DPA Countermeasures Based on Randomizing the.. - Ebeid, Hasan (2003) (Correct)

....and k # i for the di#erent possible values of k i 1 , k i and c i . By carefully examining the assignments in (12) we discover that Reitwiesner s approach computes k # by computing 3k = 2k k, subtacts k using a new rule for subtraction, namely 1 = 1 and then discards the least significant 0 [5, 14]. In fact, if 3k = k 0 s i 2 then the conventional pencil and paper method to add nonnegative integers [16, p. 251] gives s i = c i k i k i 1 ) mod 2 = c i k i k i 1 2#(c i k i k i 1 ) 2# where c i is the carry in. Since the carry out can be expressed as c i 1 = #(c i k ....

....2 k 1 k 0 ) 2 2k = k # n k # n 1 k # n 2 k # n 3 . k # 1 k # 0 0 ) NAF Therefore, if the length of the binary representation of the integer k is n bits, the length of its canonical form may be at most n 1 trits. This is because if 0 k 2 , then 3k 3 2 n 2 . Joye and Yen [14] have given both an intuitive and a formal proof that Reitwiesner s algorithm uses the same transformation as in (10) Reitwiesner s recoding algorithm can be represented with the state diagram illustrated in Figure 4. The value of both k i and c i determines the current state. The value of k i 1 ....

M. Joye and S.-M. Yen. Optimal left-to-right binary signed-digit recoding. IEEE Transactions on Computers, 49(7):740--748, July 2000.

On Multi-Exponentiation In Cryptography - Avanzi (2002) (7 citations) (Correct)

....Remark 4.3 As already mentioned, the algorithms of Reitwiesner and Solinas recode the exponents right to left, so extra storage must be reserved for the recoded representations. There exists an alternative to the NAF with the same Hamming weight and which can be computed from left to right [17] by a simple algorithm. However this representation dispenses with the non adjacency property, which has a very negative impact on memory usage. For instance for w = d = 2 the set of precomputations E consists of the values g 2 with either 0 a 3 and 3 b 3, at least one of a; b odd or ....

M. Joye and S.-M. Yen, Optimal left-to-right binary signed-digit recoding. IEEE Transactions on Computers (49) 7, 740--748 (2000).

Improved ZDN-Arithmetic for Fast Modulo Multiplication - Ploog, Flügel, Timmermann (Correct)

....additional borrowsignal bc is required to indicate if a 1 chain or a 0 chain is skipped. Table 1 summarizes all possible cases. The inputs are the next three bits of B to be analyzed and the current bc. The outputs are the corresponding d and the next value for bc, called bc . Joye and Yen [4] proved that usage of Table 1 produces optimal recoded SD numbers with the same (minimal) Hamming weight as the corresponding canonical SD numbers. The algorithm itself requires a leading and two trailing zeros. The algorithm starts with bc=0 and b n =0. b i b i 1 b i 2 d bc bc=0 0 0 X 0 0 0 1 0 ....

M. Joye and S.-M. Yen, "Optimal Left-to-Right Binary Signed-Digit Recoding", IEEE Transactions on Computers, Vol. 49, No. 7, July 2000

Compact Encoding of Non-Adjacent Forms with Applications to.. - Joye, al. (2001) (2 citations) Self-citation (Joye) (Correct)

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M. Joye and S.-M. Yen, "Optimal left-to-right binary signed-digit recoding," IEEE Trans. Computers, vol. 49, pp. 740--748, 2000.

Compact Encoding of Non-Adjacent Forms with Applications to.. - Joye, al. (2001) (2 citations) Self-citation (Joye) (Correct)

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M. Joye and S.-M. Yen, "Optimal left-to-right binary signed-digit recoding," IEEE Trans. Computers, vol. 49, pp. 740--748, 2000.

New Minimal Modified Radix-r Representation with Applications to .. - Joye, al. (2002) (2 citations) Self-citation (Joye Yen) (Correct)