scholarly journals Order-Preserving and Efficient One-to-Many Search on Encrypted Data

2020 ◽  
Author(s):  
Dongping Hu ◽  
Aihua Yin ◽  
Huaying Yan ◽  
Tao Long
Keyword(s):  
Keyword Search ◽  
Linear Time ◽  
Range Query ◽  
Binary Search ◽  
Hypergeometric Distribution ◽  
Encryption Algorithm ◽  
A Value ◽  
Data Volume ◽  
Negative Hypergeometric Distribution ◽  
The Given

Order-preserving encryption (OPE) is an useful tool in cloud computing as it allows untrustworthy server to execute range query or exact keyword search directly on the ciphertexts. It only requires sub-linear time in the data size while the queries are occurred. This advantage is very suitable in the cloud where the data volume is huge. However, the order-preserving encryption is deterministic and it leaks the plaintexts’ order and its distribution. In this paper, we propose an one-to-many OPE by taking into account the security and the efficiency. For a given plaintext, the encryption algorithm firstly determines the corresponding ciphertext gap by performing binary search on ciphertext space and plaintext space at the same time. An exact sample algorithm for negative hypergeometric distribution is used to fix the size of the gap. Lastly a value in the gap is randomly chosen as the mapping of the given plaintext. It is proven that our scheme is more secure than deterministic OPE with realizing efficient search. In particular, a practical and exact sampling algorithm for the negative hypergeometric distribution (NHGD) is first proposed.

A Note for Order-Preserving Encryption Based on Negative Hypergeometric Distribution

2014 ◽  
Vol 926-930 ◽  
pp. 2478-2481
Author(s):  
Dong Ping Hu ◽  
Yuan Ping Zhu ◽  
Ai Hua Yin
Keyword(s):  
Security Analysis ◽  
Hypergeometric Distribution ◽  
Encryption Algorithm ◽  
Encryption Scheme ◽  
Symmetric Encryption ◽  
Sampling Algorithm ◽  
Negative Hypergeometric Distribution ◽  
Proof Procedure

Order-preserving encryption (OPE) scheme is a deterministic symmetric encryption scheme whose encryption algorithm produces ciphertexts that preserves numerical ordering of the plaintexts. The cryptographic study of OPE was initiated by Boldyreva, Chenette, Lee, and ONeill [1]. They proposed an OPE scheme based on a sampling algorithm for the negative hypergeometric distribution (NHGD). In this paper, we present the security analysis of NHGD-based OPE and the proof procedure of efficiency.

Battleship and the negative hypergeometric distribution

2018 ◽  
Vol 41 (1) ◽  
pp. 3-7 ◽  
Author(s):  
Melanie A. Autin ◽  
Natasha E. Gerstenschlager
Keyword(s):  
Hypergeometric Distribution ◽  
Negative Hypergeometric Distribution

scholarly journals Splaying a search tree in preorder takes linear time

1990 ◽  
Vol 13 (1) ◽  
pp. 186-186
Author(s):  
R. Chaudhuri ◽  
H. Höft
Keyword(s):  
Linear Time ◽  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Splay Tree ◽  
Tree Traversal ◽  
Special Case

In this paper we prove that if the nodes of an arbitraryn-node binary search treeTare splayed according to the preorder sequence ofTthen the total time isO(n). This is a special case of the splay tree traversal conjecture of Sleator and Tarjan [1].

Optical Investigation of Electronic Properties in Bulk and Surface Region of Sublimation-Grown 3C-SiC Crystals

2009 ◽  
Vol 615-617 ◽  
pp. 303-306 ◽  
Author(s):  
Georgios Manolis ◽  
Kęstutis Jarašiūnas ◽  
Irina G. Galben-Sandulache ◽  
Didier Chaussende
Keyword(s):  
Carrier Density ◽  
Defect Density ◽  
Surface Region ◽  
Carrier Dynamics ◽  
Optical Investigation ◽  
Extended Defects ◽  
A Value ◽  
Continuous Feed ◽  
The Given

We applied a picosecond dynamic grating technique for studies of nonequilibrium carrier dynamics in a 0.8 mm thick bulk 3C-SiC crystal grown by the continuous feed physical vapor transport (CF-PVT) on 6H-SiC (0001) substrate. Investigation of carrier dynamics at surface or bulk excitation conditions was performed for excess carrier density in range from ~ 1017 cm-3 to ~ 1020 cm3 using for excitation weakly or strongly absorbed illumination. In DPBs free domains, the bipolar diffusion coefficient and carrier lifetime value at 300K were found gradually increasing with carrier density. The bipolar mobility vs. temperature dependence, μ. ~ T -k, provided a value k = 1.2 - 2 in range T < 100 K, thus indicating a negligible scattering by point and extended defects. These data indicated strong contribution of the carrier-density dependent but not defect-density governed scattering mechanisms, thus indicating high quality of the CF-PVT grown bulk cubic SiC. These studies were found in good correlation with the structural and photoluminescence characterization of the given crystal.

Functional Pearls: The Minout problem

1991 ◽  
Vol 1 (1) ◽  
pp. 121-124
Author(s):  
Richard S. Bird
Keyword(s):  
Natural Number ◽  
Linear Time ◽  
Constant Time ◽  
Natural Numbers ◽  
Free Object ◽  
Functional Program ◽  
Practical Applications ◽  
The World ◽  
The Given ◽  
Easy Solution

The problem of computing the smallest natural number not contained in a given set of natural numbers has a number of practical applications. Typically, the given set represents the indices of a class of objects ‘in use’ and it is required to find a ‘free’ object with smallest index. Our purpose in this article is to derive a linear-time functional program for the problem. There is an easy solution if arrays capable of being accessed and updated in constant time are available, but we aim for an algorithm that employs only standard lists. Noteworthy is the fact that, although an algorithm using lists is the result, the derivation is carried out almost entirely in the world of sets.

FUNCTIONAL PEARL On building trees with minimum height

1997 ◽  
Vol 7 (4) ◽  
pp. 441-445 ◽  
Author(s):  
RICHARD S. BIRD
Keyword(s):  
Binary Tree ◽  
Linear Time ◽  
Internal Node ◽  
The Other ◽  
Top Down ◽  
Functional Program ◽  
Size Information ◽  
Common Solution ◽  
Minimum Height ◽  
The Given

A common solution to the problem of handling list indexing efficiently in a functional program is to build a binary tree. The tree has the given list as frontier and is of minimum height. Each internal node of the tree stores size information (actually, the size of its left subtree) to direct the search for an element at a given position in the frontier. One application was considered in my previous pearl (Bird, 1997). There are two complementary methods for building such a tree, both of which can be implemented in linear time. One method is ‘recursive’, or top down, and works by splitting the list into two equal halves, recursively building a tree for each half, and then combining the two results. The other method is ‘iterative’, or bottom up, and works by first creating a list of singleton trees, and then repeatedly combining the trees in pairs until just one tree remains. The two methods lead to different trees, but in each case the result is a tree with smallest possible height.

Approximating Convex Polyhedra with Axis-Parallel Boxes

1997 ◽  
Vol 07 (03) ◽  
pp. 253-267 ◽  
Author(s):  
Binhai Zhu
Keyword(s):  
Hausdorff Distance ◽  
Convex Polyhedron ◽  
Linear Time ◽  
Time Algorithm ◽  
Convex Polyhedra ◽  
Linear Time Algorithm ◽  
Brute Force ◽  
Axis Parallel ◽  
The Given ◽  
Fixed Center

In this paper, we present an O(n4 log 2n) time algorithm to compute an approximate discrete axis-parallel box of a given n-vertex convex polyhedron P such that the given polyhedron is minimized. Here, "discrete" means that each plane containing a face of the approximate box passes through a vertex of P (or, more generally, passes through a point of a set of given points). This algorithm is significantly faster than the brute force O(n7) time solution for computing the optimal approximate axis-parallel box A* of P such that the symmetric difference of the volume between P and A* is minimized. We present a linear time algorithm to compute a pseudo-optimal (with factor [Formula: see text] approximate axis-parallel box of a convex polyhedron under the Hausdorff distance criterion. We also present O(n) and O(n7 log n) time algorithms to compute the optimal approximate ball, with or without a fixed center, of a convex polyhedron under the Hausdorff distance criterion.

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