Post-processing is indispensable in quantum key distribution （QKD）, which is aimed at sharing secret keys between two distant parties. It mainly consists of key reconciliation and privacy amplification, which is use...
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Post-processing is indispensable in quantum key distribution （QKD）, which is aimed at sharing secret keys between two distant parties. It mainly consists of key reconciliation and privacy amplification, which is used for sharing the same keys and for distilling unconditional secret keys. In this paper, we focus on speeding up the privacy amplification process by choosing a simple multiplicative universal class of hash functions. By constructing an optimal multiplication algorithm based on four basic multiplication algorithms, we give a fast software implementation of length-adaptive privacy amplification. ＂Length-adaptive＂ indicates that the implementation of privacy amplification automatically adapts to different lengths of input blocks. When the lengths of the input blocks are 1 Mbit and 10 Mbit, the speed of privacy amplification can be as fast as 14.86 Mbps and 10.88 Mbps, respectively. Thus, it is practical for GHz or even higher repetition frequency QKD systems.
Let n, l be positive integers with l <= 2n - 1. Let R be an arbitrary nontrivial ring, not necessarily commutative and not necessarily having a multiplicative identity and R[x] be the polynomial ring over R. In thi...
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Let n, l be positive integers with l <= 2n - 1. Let R be an arbitrary nontrivial ring, not necessarily commutative and not necessarily having a multiplicative identity and R[x] be the polynomial ring over R. In this paper, we give improved upper bounds on the minimum number of multiplications needed to multiply two arbitrary polynomials of degree at most (n - 1) modulo x(n) over R. Moreover, we introduce a new complexity notion, the minimum number of multiplications needed to multiply two arbitrary polynomials of degree at most (n - 1) modulo x(l) over R. This new complexity notion provides improved bounds on the minimum number of multiplications needed to multiply two arbitrary polynomials of degree at most (n - 1) modulo x(n) over R. (C) 2011 Elsevier B.V. All rights reserved.
Operations in finite fields find diverse applications. Circuits have been designed for carrying out such operations. In the paper, two circuits that carry out multiplication in GF(2p) have been presented. These circui...
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Operations in finite fields find diverse applications. Circuits have been designed for carrying out such operations. In the paper, two circuits that carry out multiplication in GF(2p) have been presented. These circuits are suitable for implementation using VLSI techniques, and are simpler than existing circuits. The architecture used here is that of systolic arrays and consists of regular interconnection of simple cells.
In this correspondence the problem of performing the multiplication by recoding the multiplier is considered. A special recoding for fractional numbers in two"s complement form is presented, that generates a clas...
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In this correspondence the problem of performing the multiplication by recoding the multiplier is considered. A special recoding for fractional numbers in two"s complement form is presented, that generates a class of uniform shift multiplication algorithms having the property that every partial product is always in the open interval (-1,1). Both the scan of the multiplier from the least to the most significant bit and the scan in the opposite direction are considered.
Although integrated-circuit technology promises to reduce the cost of logic, there are still situations where low-cost multiplication and/or division algorithms must be implemented in today"s technology. This can...
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Although integrated-circuit technology promises to reduce the cost of logic, there are still situations where low-cost multiplication and/or division algorithms must be implemented in today"s technology. This can be accomplished by the algorithms presented here: repetitive addition (subtraction) algorithms for multiplication (division), employing a right shift. The result of the operation is truncated, which limits the accurqcy but reduces significantly the amount of intermediate storage required. The degree of accuracy is quite adequate for selected applications.
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