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Efficient and secure elliptic curve point multiplication using doublebase chains
 In Advances in Cryptology  ASIACRYPT 2005, Lecture Notes in Computer Science 3788
, 2005
"... Abstract. In this paper, we propose a efficient and secure point multiplication algorithm, based on doublebase chains. This is achieved by taking advantage of the sparseness and the ternary nature of the socalled doublebase number system (DBNS). The speedups are the results of fewer point additio ..."
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Cited by 36 (8 self)
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Abstract. In this paper, we propose a efficient and secure point multiplication algorithm, based on doublebase chains. This is achieved by taking advantage of the sparseness and the ternary nature of the socalled doublebase number system (DBNS). The speedups are the results of fewer point additions and improved formulæ for point triplings and quadruplings in both even and odd characteristic. Our algorithms can be protected against simple and differential sidechannel analysis by using sidechannel atomicity and classical randomization techniques. Our numerical experiments show that our approach leads to speedups compared to windowing methods, even with window size equal to 4, and other SCA resistant algorithms. 1
The Doublebase Number System and its Application to Elliptic Curve Cryptography
 in Mathematics of Computation
, 2008
"... Abstract. We describe an algorithm for point multiplication on generic elliptic curves, based on a representation of the scalar as a sum of mixed powers of 2 and 3. The sparseness of this socalled doublebase number system, combined with some efficient point tripling formulae, lead to efficient poi ..."
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Cited by 9 (2 self)
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Abstract. We describe an algorithm for point multiplication on generic elliptic curves, based on a representation of the scalar as a sum of mixed powers of 2 and 3. The sparseness of this socalled doublebase number system, combined with some efficient point tripling formulae, lead to efficient point multiplication algorithms for curves defined over both prime and binary fields. Sidechannel resistance is provided thanks to sidechannel atomicity.
Multiplication by a constant is sublinear
 In 18th Symposium on Computer Arithmetic. IEEE
, 2007
"... Abstract — This paper explores the use of the doublebase number system (DBNS) for constant integer multiplication. The DBNS recoding scheme represents integers – in this case constants – in a multipleradix way in the hope of minimizing the number of additions to be performed during constant multip ..."
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Cited by 7 (0 self)
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Abstract — This paper explores the use of the doublebase number system (DBNS) for constant integer multiplication. The DBNS recoding scheme represents integers – in this case constants – in a multipleradix way in the hope of minimizing the number of additions to be performed during constant multiplication. On the theoretical side, we propose a formal proof which shows that our recoding technique diminishes the number of additions in a sublinear way. Therefore, we prove Lefèvre’s conjecture that the multiplication by an integer constant is achievable in sublinear time. In a second part, we investigate various strategies and we provide numerical data showcasing the potential interest of our approach. I.
Fast Elliptic Curve Point Multiplication using DoubleBase Chains
, 2005
"... Among the various arithmetic operations required in implementing public key cryptographic algorithms, the elliptic curve point multiplication has probably received the maximum attention from the research community in the last decade. Many methods for e#cient and secure implementation of point mul ..."
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Cited by 7 (2 self)
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Among the various arithmetic operations required in implementing public key cryptographic algorithms, the elliptic curve point multiplication has probably received the maximum attention from the research community in the last decade. Many methods for e#cient and secure implementation of point multiplication have been proposed. The e#ciency of these methods mainly depends on the representation one uses for the scalar multiplier. In the current work we propose an e#cient algorithm based on the socalled doublebase number system. We introduce the new concept of doublebase chains which, if manipulated with care, can significantly reduce the complexity of scalar multiplication on elliptic curves. Besides we have adopted some other measures to further reduce the operation count. Our algorithm compares favorably against classical and other similar approaches.
Approximate Constructions In Finite Fields
"... this paper are new, we do not give complete detailed proofs but indicate the underlying ideas. Here we present a list of possible applications (which is certainly incomplete). We start from pointing out some general purpose applications: ffl Coding Theory : AP1, AP3, AP6 ..."
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Cited by 1 (1 self)
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this paper are new, we do not give complete detailed proofs but indicate the underlying ideas. Here we present a list of possible applications (which is certainly incomplete). We start from pointing out some general purpose applications: ffl Coding Theory : AP1, AP3, AP6
unknown title
"... ABSTRACT: We analyze the problem of constructing a network which will have a fixed routing and which will be highly fault tolerant. A construction is presented which forms a "product route graph " from two or more constituent "route graphs. " The analysis involv ..."
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ABSTRACT: We analyze the problem of constructing a network which will have a fixed routing and which will be highly fault tolerant. A construction is presented which forms a &quot;product route graph &quot; from two or more constituent &quot;route graphs. &quot; The analysis involves the surviving route graph, which consists of all nonfaulty nodes in the network with two nodes being connected by a directed edge iff the route from the first to the second is still intact after a set of component failures. The diameter of the surviving route graph, that is, the maximum distance between any pair of nodes, is a measure of the worstcase performance degradation caused by the faults. The number of faults tolerated, the diameter, and the degree of the product graph are related in a simple way to the corresponding parameters of the constituent graphs. In addition, there is a &quot;padding theorem &quot; which allows one to add
SOME DIOPHANTINE PROPERTIES OF THE SEQUENCE OF SUNITS
"... Integers having no prime factors outside a fixed set of primes play important role and are heavily investigated in several parts of number theory. For example, they play special role in diophantine number theory; see e.g. the classical survey paper of Evertse, Győry, Stewart and Tijdeman [1] or ..."
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Integers having no prime factors outside a fixed set of primes play important role and are heavily investigated in several parts of number theory. For example, they play special role in diophantine number theory; see e.g. the classical survey paper of Evertse, Győry, Stewart and Tijdeman [1] or