Francois Morain and Jorge Olivos. Speeding up the computations on an elliptic curve using addition-subtraction chains. Theoretical Informatics and Applications, 24:531--543, 1990. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
First 50 documents Next 50
Distribution Results for Low-Weight Binary.. - Grabner, Heuberger, al. (2003) (Correct)
....n in binary notation, the ones correspond to these addition operations. In our context the subtraction of P is not more costly than the addition of P . This leads to the concept of redundant expansions (cf. 3] Now, the possible digits are corresponds to a subtraction of P , see, e.g. [4]. The representation is no longer unique, and the goal is to find a representation with as many zeros as possible, in order to have low complexity. This Canonical Sparse Form was independently discovered by many authors, and we refer to [5] for a historic account. It is sometimes called ....
F. Morain, J. Olivos, Speeding up the computations on an elliptic curve using addition-subtraction chains, RAIRO Inform. Theor. Appl. 24 (1990) 531--543.
Analysis of DPA Countermeasures Based on Randomizing the.. - Ebeid, Hasan (2003) (Correct)
....was presented by the authors and we confirm the results using grammatical specification method. The report is organized as follows. In section 2, we briefly present the binary algorithms for EC scalar multiplication. Section 3 is an overview of the speedup algorithms proposed by Morain and Olivos [24]. Section 4 discusses the DPA countermeasure proposed by Oswald and Aigner [27] and its complexity analysis. In section 5, we present Reitwiesner s canonical recoding approach and its application to EC scalar multiplication. In section 6, we discuss the DPA countermeasure proposed by Ha and Moon ....
....[4, 9, 16, 26, 30] Finding the best addition chain is impractical, but we can find near optimal ones. Some good algorithms exist, among which the binary algorithm (see Section 2) and some of its variations (see [16] and the implementation of the 2 method in [6] Morain and Olivos, in [24], have studied briefly the so called addition subtraction chains. These are defined as in (6) but with v, w l such that k i = v kw (7) They pointed out that addition subtraction chains are mainly important in EC based computations where the inverse of a point is obtained at no extra ....
[Article contains additional citation context not shown here]
F. Morain and J. Olivos. Speeding up the computations on an elliptic curve using addition-subtraction chains. Informatique theorique et Applications/Theoritical Informatics and Applications, 24(6):531--544, 1990.
Weierstraß Elliptic Curves and Side-Channel Attacks - Brier, Joye (2002) (Correct)
No context found.
Francois Morain and Jorge Olivos. Speeding up the computations on an elliptic curve using addition-subtraction chains. Theoretical Informatics and Applications, 24:531--543, 1990.
Compact Encoding of Non-Adjacent Forms with Applications to.. - Joye, al. (2001) (2 citations) (Correct)
No context found.
F. Morain and J. Olivos, "Speeding up the computations on an elliptic curve using addition-subtraction chains," Theoretical Informatics and Applications, vol. 24, pp. 531--543, 1990.
Resistance against Differential Power Analysis for Elliptic Curve.. - Coron (1999) (9 citations) (Correct)
No context found.
F. Morain, J. Olivos. Speeding up the computation of an elliptic curve using addition-subtraction chains, Inform. Theory Appl. 24 (1990), 531-543.
Compact Encoding of Non-Adjacent Forms with Applications to.. - Joye, al. (2001) (2 citations) (Correct)
No context found.
F. Morain and J. Olivos, "Speeding up the computations on an elliptic curve using addition-subtraction chains," Theoretical Informatics and Applications, vol. 24, pp. 531--543, 1990.
An Analysis of Double Base Number Systems - And Sublinear Scalar (Correct)
No context found.
F. Morain and J. Olivos. Speeding up the Computations on an Elliptic Curve using Addition-Subtraction Chains. Inform. Theor. Appl., 24:531--543, 1990.
Resistance against Differential Power Analysis for Elliptic Curve.. - Coron (1999) (9 citations) (Correct)
No context found.
F. Morain, J. Olivos. Speeding up the computation of an elliptic curve using addition-subtraction chains, Inform. Theory Appl. 24 (1990), 531-543.
Optimal Left-to-right Binary Signed-Digit Recoding - Joye, Yen (2000) (7 citations) (Correct)
No context found.
F. Morain and J. Olivos, "Speeding up the computations on an elliptic curve using addition-subtraction chains," Theoretical Informatics and Applications, vol. 24, pp. 531--543, 1990.
New Minimal Modified Radix-r Representation with Applications to .. - Joye, al. (2002) (2 citations) (Correct)
No context found.
F. Morain and J. Olivos, Speeding up the computations on an elliptic curve using addition-subtraction chains, Theoretical Informatics and Applications 24 (1990), 531--543.
An Analysis of Double Base Number Systems - And Sublinear Scalar (Correct)
No context found.
F. Morain and J. Olivos. Speeding up the Computations on an Elliptic Curve using Addition-Subtraction Chains. Inform. Theor. Appl., 24:531--543, 1990.
Recovering Lost Efficiency of Exponentiation Algorithms on Smart.. - Joye (2002) (2 citations) (Correct)
No context found.
Francois Morain and Jorge Olivos. Speeding up the computations on an elliptic curve using addition-subtraction chains. Theoretical Informatics and Applications 24:531-543, 1990.
Optimal Left-to-right Binary Signed-Digit Recoding - Joye, Yen (2000) (7 citations) (Correct)
No context found.
F. Morain and J. Olivos, "Speeding up the computations on an elliptic curve using addition-subtraction chains," Theoretical Informatics and Applications, vol. 24, pp. 531--543, 1990.
Weierstraß Elliptic Curves and Side-Channel Attacks - Brier, Joye (2002) (Correct)
No context found.
Francois Morain and Jorge Olivos. Speeding up the computations on an elliptic curve using addition-subtraction chains. Theoretical Informatics and Applications, 24:531--543, 1990.
New Minimal Modified Radix-r Representation with Applications to .. - Joye, Yen (2002) (2 citations) (Correct)
No context found.
F. Morain and J. Olivos, Speeding up the computations on an elliptic curve using addition-subtraction chains, Theoretical Informatics and Applications 24 (1990), 531--543.
Stern Polynomials - Klavzar, Milutinovic, Petr (Correct)
No context found.
F. Morain, J. Olivos, Speeding up the computations on an elliptic curve using addition-subtraction chains, RAIRO Inform. Theor. Appl. 24 (1990) 531--543. 10
Recovering Lost Efficiency of Exponentiation Algorithms on Smart.. - Joye (2002) (2 citations) (Correct)
No context found.
Francois Morain and Jorge Olivos. Speeding up the computations on an elliptic curve using addition-subtraction chains. Theoretical Informatics and Applications 24:531--543, 1990.
Stern Polynomials - Klavzar, Milutinovic, Petr (Correct)
No context found.
F. Morain, J. Olivos, Speeding up the computations on an elliptic curve using addition-subtraction chains, RAIRO Inform. Theor. Appl. 24 (1990) 531--543. 10
Analysis of Some Efficient Window Methods and their.. - Schmidt-Samoa, Semay, .. (2004) (Correct)
No context found.
F. Morain and J. Olivos. Speeding up the computations on an elliptic curve using addition-subtraction chains. RAIRO Theoretical Informatics and Applications, 24:531-543, 1990.
Signed Binary Representations Revisited - Okeya, Schmidt-Samoa, Spahn.. (2004) (Correct)
No context found.
Morain, F., Olivos, J., Speeding Up the Computations on an Elliptic Curve using Addition-Subtraction Chains, RAIRO Theoretical Informatics and Applications , 24, (1990), pp.531-543.
Sign Change Fault Attacks on Elliptic Curve Cryptosystems - Blömer, Otto, Seifert (2004) (Correct)
No context found.
F. Morain and J. Olivos, Speeding up the computations on an elliptic curve using addition-subtractions chains, Theoretical Informatics and Applications (1990), no. 24, 531--543.
Optimal Left-to-right Binary Signed-Digit Recoding - Joye, Yen (2000) (7 citations) (Correct)
No context found.
F. Morain and J. Olivos, "Speeding up the computations on an elliptic curve using addition-subtraction chains," Theoretical Informatics and Applications, vol. 24, pp. 531--543, 1990.
New Minimal Modified Radix-r Representation with Applications to .. - Joye, Yen (2002) (2 citations) (Correct)
No context found.
F. Morain and J. Olivos, Speeding up the computations on an elliptic curve using addition-subtraction chains, Theoretical Informatics and Applications 24 (1990), 531--543.
Recovering Lost Efficiency of Exponentiation Algorithms on Smart.. - Joye (2002) (2 citations) (Correct)
No context found.
Francois Morain and Jorge Olivos. Speeding up the computations on an elliptic curve using addition-subtraction chains. Theoretical Informatics and Applications 24:531-543, 1990.
Weierstraß Elliptic Curves and Side-Channel Attacks - Brier, Joye (2002) (Correct)
No context found.
Francois Morain and Jorge Olivos. Speeding up the computations on an elliptic curve using addition-subtraction chains. Theoretical Informatics and Applications, 24:531--543, 1990.
Fast Algorithms for Elliptic Curve Cryptosystems over Binary.. - Han, al. (1999) (Correct)
No context found.
Francois Morain et J. Olivos, "Speeding up the Computation on an Elliptic Curve using Addition-Subtraction Chains", RAIRO Informatique Theorique Et Applications - Theoretical Informatics and Applications, 24,6, p. 531-543, 1990.
Fast Generation of Pairs (k, [k]P) for Koblitz Elliptic Curves - Coron, al. (2001) (Correct)
No context found.
F. Morain and J. Olivos. Speeding up the computation of an elliptic curve using addition-subtraction chains. Inform. Theory Appl., 24:531--543, 1990.
Compact Encoding of Non-Adjacent Forms with Applications to.. - Joye, al. (2001) (2 citations) (Correct)
No context found.
F. Morain and J. Olivos, "Speeding up the computations on an elliptic curve using addition-subtraction chains," Theoretical Informatics and Applications, vol. 24, pp. 531--543, 1990.
Resistance against Differential Power Analysis for Elliptic Curve.. - Coron (1999) (9 citations) (Correct)
No context found.
F. Morain, J. Olivos. Speeding up the computation of an elliptic curve using addition-subtraction chains, Inform. Theory Appl. 24 (1990), 531-543.
New Minimal Modified Radix-r Representation with Applications to .. - Joye, Yen (2002) (2 citations) (Correct)
No context found.
F. Morain and J. Olivos, Speeding up the computations on an elliptic curve using addition-subtraction chains, Theoretical Informatics and Applications 24 (1990), 531--543.
Fast Generation of Pairs (k, [k]P) for Koblitz Elliptic Curves - Coron, al. (2001) (Correct)
No context found.
F. Morain and J. Olivos. Speeding up the computation of an elliptic curve using addition-subtraction chains. Inform. Theory Appl., 24:531--543, 1990.
Compact Encoding of Non-Adjacent Forms with Applications to.. - Joye, Tymen (2001) (2 citations) (Correct)
No context found.
F. Morain and J. Olivos, "Speeding up the computations on an elliptic curve using addition-subtraction chains," Theoretical Informatics and Applications, vol. 24, pp. 531--543, 1990.
Resistance against Differential Power Analysis for Elliptic Curve.. - Coron (1999) (9 citations) (Correct)
No context found.
F. Morain, J. Olivos. Speeding up the computation of an elliptic curve using addition-subtraction chains, Inform. Theory Appl. 24 (1990), 531-543.
Recovering Lost Efficiency of Exponentiation Algorithms on Smart.. - Joye (2002) (2 citations) (Correct)
No context found.
Francois Morain and Jorge Olivos. Speeding up the computations on an elliptic curve using addition-subtraction chains. Theoretical Informatics and Applications 24:531-543, 1990.
Fast Algorithms for Elliptic Curve Cryptosystems over Binary.. - Han, al. (1999) (Correct)
No context found.
Francois Morain et J. Olivos, "Speeding up the Computation on an Elliptic Curve using Addition-Subtraction Chains", RAIRO Informatique Theorique Et Applications - Theoretical Informatics and Applications, 24,6, p. 531-543, 1990.
Fast Exponentiation with Precomputation: Algorithms.. - Brickell, Gordon.. (1995) (9 citations) (Correct)
No context found.
F. Morain and J. Olivos, Speeding up the computations on an elliptic curve using addition-subtraction chains, Inform. Theor. Appl., 24 (1990), pp. 531--543. 20
New Minimal Modified Radix-r Representation with Applications to .. - Joye, Yen (2002) (2 citations) (Correct)
No context found.
F. Morain and J. Olivos, Speeding up the computations on an elliptic curve using addition-subtraction chains, Theoretical Informatics and Applications 24 (1990), 531--543.
Optimal Left-to-right Binary Signed-Digit Recoding - Joye, Yen (2000) (7 citations) (Correct)
No context found.
F. Morain and J. Olivos, "Speeding up the computations on an elliptic curve using addition-subtraction chains," Theoretical Informatics and Applications, vol. 24, pp. 531--543, 1990.
Recovering Lost Efficiency of Exponentiation Algorithms on Smart.. - Joye (2002) (2 citations) (Correct)
No context found.
Francois Morain and Jorge Olivos. Speeding up the computations on an elliptic curve using addition-subtraction chains. Theoretical Informatics and Applications 24:531--543, 1990.
Fast Algorithms for Elliptic Curve Cryptosystems over Binary.. - Han, al. (1999) (Correct)
No context found.
Francois Morain et J. Olivos, "Speeding up the Computation on an Elliptic Curve using Addition-Subtraction Chains", RAIRO Informatique Theorique Et Applications - Theoretical Informatics and Applications, 24,6, p. 531-543, 1990.
Weierstraß Elliptic Curves and Side-Channel Attacks - Brier, Joye (2002) (Correct)
No context found.
Francois Morain and Jorge Olivos. Speeding up the computations on an elliptic curve using addition-subtraction chains. Theoretical Informatics and Applications, 24:531--543, 1990.
Fast Generation of Pairs (k, [k]P) for Koblitz Elliptic Curves - Coron, al. (2001) (Correct)
No context found.
F. Morain and J. Olivos. Speeding up the computation of an elliptic curve using addition-subtraction chains. Inform. Theory Appl., 24:531--543, 1990.
Compact Encoding of Non-Adjacent Forms with Applications to.. - Joye, Tymen (2001) (2 citations) (Correct)
No context found.
F. Morain and J. Olivos, "Speeding up the computations on an elliptic curve using addition-subtraction chains," Theoretical Informatics and Applications, vol. 24, pp. 531--543, 1990.
Optimal Left-to-right Binary Signed-Digit Recoding - Joye, Yen (2000) (7 citations) (Correct)
No context found.
F. Morain and J. Olivos, "Speeding up the computations on an elliptic curve using addition-subtraction chains," Theoretical Informatics and Applications, vol. 24, pp. 531--543, 1990.
Resistance against Differential Power Analysis for Elliptic Curve.. - Coron (1999) (9 citations) (Correct)
No context found.
F. Morain, J. Olivos. Speeding up the computation of an elliptic curve using addition-subtraction chains, Inform. Theory Appl. 24 (1990), 531-543.
Weierstraß Elliptic Curves and Side-Channel Attacks - Brier, Joye (2002) (Correct)
No context found.
Francois Morain and Jorge Olivos. Speeding up the computations on an elliptic curve using addition-subtraction chains. Theoretical Informatics and Applications, 24:531--543, 1990.
Alternative Digit Sets for Nonadjacent Representations - Muir, Stinson (2003) (Correct)
No context found.
F. Morain and J. Olivos. Speeding up the Computations on an Elliptic Curve using Addition-Subtraction Chains, RAIRO Theoretical Informatics and Applications 24 (1990), 531--543.
Alternative Digit Sets for Nonadjacent Representations - Muir, Stinson (2003) (Correct)
No context found.
F. Morain and J. Olivos. Speeding up the Computations on an Elliptic Curve using Addition-Subtraction Chains, RAIRO Theoretical Informatics and Applications 24 (1990), 531--543.
Weierstraß Elliptic Curves and Side-Channel Attacks - Brier, Joye (2002) (Correct)
No context found.
Francois Morain and Jorge Olivos. Speeding up the computations on an elliptic curve using addition-subtraction chains. Theoretical Informatics and Applications, 24:531--543, 1990.
New Minimal Modified Radix-r Representation with Applications to .. - Joye, Yen (2002) (2 citations) (Correct)
No context found.
F. Morain and J. Olivos, Speeding up the computations on an elliptic curve using addition-subtraction chains, Theoretical Informatics and Applications 24 (1990), 531--543.
First 50 documents Next 50
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC