Logical Design with Molecular Components

Santis, Filomena De; Iaccarino, Gennaro

doi:10.1007/3-540-32392-9_56

Cited by 1 publication

(5 citation statements)

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“…[6,7]). The result (line 16) is a set of test tubes containing the recursive sum of α, left and cyclically shifted at the positions where βi = 1.…”

Section: Fast Parallel Multiplier Algorithmmentioning

confidence: 99%

“…Line 2 uses the procedure AddPosition(Ti, EcoRI) described by the algorithm 4 to move all the bits in Ti of 1 place, by increasing their offsets. Lines 3 and 4 check for bit-overflow (lemma 1 ensures that strands with offset greater than r are easily traceable by gel electrophoresis -see also procedures in [6,7]). Lines 5-10 provide the molecules SiX k Y r E (that become Si+1X k Y r E) with the transition from T [α]i to T [α]i+1.…”

Section: Pcr(t W)mentioning

confidence: 99%

“…By dividing α into m (m ≤ n) test tubes (packages) T [α]m...T [α]1 containing all the integers X[α] [7], the DNA strand wi encoding a generic integer i, with 1 ≥ i ≥ n, will look like:…”

Section: Encoding Binary Numbersmentioning

confidence: 99%

“…On the other side, the parallel adder described in [15] works in O(n) and the length of every strand increases linearly with n, O(n). The multiplication is done by successively adding β times the cyclic left shifted α value [7], that is:…”

Section: Fast Parallel Adder Complexitymentioning

confidence: 99%

“…storing information at nano level. DNA computer resulted not only to be faster and smaller than any other computer built so far [7], but also to be able to guarantee high parallelism levels in their molecular computations. Roughly speaking, their computing power is somehow commensurate to the number of bits (approximately 10 18 ) efficiently manipulated.…”

Section: Introductionmentioning

confidence: 96%

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Fastest parallel molecular algorithms for the elliptic curve discrete logarithm problem over GF(2n)

Iaccarino

Mazza

2009

Proceedings of the 2009 Workshop on Bio-Inspired Algorithms for Distributed Systems

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Cryptography based on Elliptic Curves (ECC) has emerged as an effective alternative to the existing public-key cryptosystems (RSA and DSA). Its success was due both to the fact that no fast algorithms were known to break it and that exceptional security levels could be obtained by using short keys. The Elliptic Curve Discrete Logarithm (ECDL) problem is the cornerstone of much of present-day ECCs. It was classified as a computationally intractable problem and, consequently, as a reliable and unbreakable cryptosystem. In a recent work, Li et al. built a molecular computer designed to solve it over GF (2 n ). It was based on two DNA-inspired algorithms: a parallel adder and a parallel multiplier, working in O(n) and O(n 2 ) respectively, where n is the input size. In this paper, we first present two faster biological implementations, working in O(log(n)) and O(n · log(n)) respectively (worst case). Then, we propose our model as a reference parallel solution of the ECDL problem and finally we highlight the computational power of such nature-inspired paradigm.

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“…[6,7]). The result (line 16) is a set of test tubes containing the recursive sum of α, left and cyclically shifted at the positions where βi = 1.…”

Section: Fast Parallel Multiplier Algorithmmentioning

confidence: 99%

Section: Pcr(t W)mentioning

confidence: 99%

Section: Encoding Binary Numbersmentioning

confidence: 99%

Section: Fast Parallel Adder Complexitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%