Theory and applications of the double-base number system

Dimitrov, Vassil S.; Jullien, G.A.; Miller, William C.

doi:10.1109/12.805158

Cited by 92 publications

(47 citation statements)

References 15 publications

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“…Another recoding solution was proposed with the use of multiple-radix representations and especially with the double-base number system (DBNS) [14]. In this solution, the authors use both radices 2 and 3 simultaneously, i.e., the values are expressed by a ¼ P i;j a i;j 2 i 3 j with a i;j 2 f0; 1g.…”

Section: Direct Recoding Methodsmentioning

confidence: 99%

Some optimizations of hardware multiplication by constant matrices

Boullis

Tisserand

16th IEEE Symposium on Computer Arithmetic, 2003. Proceedings.

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Abstract-This paper presents some improvements on the optimization of hardware multiplication by constant matrices. We focus on the automatic generation of circuits that involve constant matrix multiplication, i.e., multiplication of a vector by a constant matrix. The proposed method, based on number recoding and dedicated common subexpression factorization algorithms, was implemented in a VHDL generator. Our algorithms and generator have been extended to the case of some digital filters based on multiplication by a constant matrix and delay operations. The obtained results on several applications have been implemented on FPGAs and compared to previous solutions. Up to 40 percent area and speed savings are achieved.

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Section: Direct Recoding Methodsmentioning

confidence: 99%

Some optimizations of hardware multiplication by constant matrices

Boullis

Tisserand

16th IEEE Symposium on Computer Arithmetic, 2003. Proceedings.

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“…The double base number system (DBNS) simultaneously uses two bases for representing numbers [6]. In this work, we use bases 2 and 3.…”

Section: Double Base Number System (Dbns)mentioning

confidence: 99%

Hardware implementation of DBNS recoding for ECC processor

Chabrier

Pamula

Tisserand

2010

2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers

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Abstract-The paper presents arithmetic level protections for ECC processor against some side channel attacks. The proposed protection is based on random recodings of the secret key in the double base number system (DBNS). DBNS is a highly redundant and sparse number system. Here, the high redundancy level of DBNS is used to randomly modify on-the-fly the ki digits during the scalar multiplication [k]P . The proposed solution leads to random numbers and orders of curve level operations (point addition, doubling and tripling) during the computation of [k]P operations. Our random recoding method provides [k]P computation time comparable to the best w-NAF recoding methods. But standard w-NAF recodings are deterministic ones while our solution is a random one.

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“…The double-base number system (DBNS) [10] is a representation scheme in which every positive integer k is represented as the sum or difference of {2, 3}-integers (i.e., numbers of the form 2…”

Section: Double-base Number Systemmentioning

confidence: 99%

Efficient and Secure Elliptic Curve Point Multiplication Using Double-Base Chains

Dimitrov

Imbert

Mishra

2005

Lecture Notes in Computer Science

105

133

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Abstract. In this paper, we propose a efficient and secure point multiplication algorithm, based on double-base chains. This is achieved by taking advantage of the sparseness and the ternary nature of the socalled double-base number system (DBNS). The speed-ups are the results of fewer point additions and improved formulae for point triplings and quadruplings in both even and odd characteristic. Our algorithms can be protected against simple and differential side-channel analysis by using side-channel atomicity and classical randomization techniques. Our numerical experiments show that our approach leads to speed-ups compared to windowing methods, even with window size equal to 4, and other SCA resistant algorithms.

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Theory and applications of the double-base number system

Cited by 92 publications

References 15 publications

Some optimizations of hardware multiplication by constant matrices

Some optimizations of hardware multiplication by constant matrices

Hardware implementation of DBNS recoding for ECC processor

Efficient and Secure Elliptic Curve Point Multiplication Using Double-Base Chains

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