Secure Merge with O(n log log n) Secure Operations

Data-oblivious algorithms are a key component of many secure computation protocols. In this work, we show that advances in secure multiparty shuffling algorithms can be used to increase the efficiency of several key cryptographic tools. The key observation is that many secure computation protocols rely heavily on secure shuffles. The best data-oblivious shuffling algorithms require $O(n \log n)$, operations, but in the two-party or multiparty setting, secure shuffling can be achieved with only $O(n)$ communication. Leveraging the efficiency of secure multiparty shuffling, we give novel algorithms that improve the efficiency of securely sorting sparse lists, secure stable compaction, and securely merging two sorted lists. Securely sorting private lists is a key component of many larger secure computation protocols. The best data-oblivious sorting algorithms for sorting a list of $n$ elements require $O(n \log n)$ comparisons. Using black-box access to a linear-communication secure shuffle, we give a secure algorithm for sorting a list of length $n$ with $t \ll n$ nonzero elements with communication $O(t \log^2 n + n)$, which beats the best oblivious algorithms when the number of nonzero elements, $t$, satisfies $t < n/\log^2 n$. Secure compaction is the problem of removing dummy elements from a list, and is essentially equivalent to sorting on 1-bit keys. The best oblivious compaction algorithms run in $O(n)$-time, but they are unstable, i.e., the order of the remaining elements is not preserved. Using black-box access to a linear-communication secure shuffle, we give a stable compaction algorithm with only $O(n)$ communication. Our main result is a novel secure merge protocol. The best previous algorithms for securely merging two sorted lists into a sorted whole required $O(n \log n)$ secure operations. Using black-box access to an $O(n)$-communication secure shuffle, we give the first secure merge algorithm that requires only $O(n \log \log n)$ communication. Our algorithm takes as input $n$ secret-shared values, and outputs a secret-sharing of the sorted list. All our algorithms are generic, i.e., they can be implemented using generic secure computations techniques and make black-box access to a secure shuffle. Our techniques extend naturally to the multiparty situation (with a constant number of parties) as well as to handle malicious adversaries without changing the asymptotic efficiency. These algorithm have applications to securely computing database joins and order statistics on private data as well as multiparty Oblivious RAM protocols

Performance Analysis of Security Protocols

Security is critical to a wide range of applications and services. Numerous security mechanisms and protocols have been developed and are widely used with today’s Internet. These protocols, which provide secrecy, authentication, and integrity control, are essential to protecting electronic information. There are many types of security protocols and mechanisms, such as symmetric key algorithms, asymmetric key algorithms, message digests, digital certificates, and secure socket layer (SSL) communication. Symmetric and asymmetric key algorithms provide secrecy. Message digests are used for authentication. SSL communication provides a secure connection between two sockets. The purpose of this graduate project was to do performance analysis on various security protocols. These are performance comparisons of symmetric key algorithms DES (Data Encryption Standard), 3DES (Triple DES), AES (Advanced Encryption Standard), and RC4; of public-private key algorithms RSA and ElGamal; of digital certificates using message digests SHA1 (Secure Hash Algorithm) and MD5; and of SSL (Secure Sockets Layer) communication using security algorithms 3DES with SHA1 and RC4 with MD5

Secure Transmission in Amplify-and-Forward Diamond Networks with a Single Eavesdropper

Unicast communication over a network of $M$-parallel relays in the presence of an eavesdropper is considered. The relay nodes, operating under individual power constraints, amplify and forward the signals received at their inputs. The problem of the maximum secrecy rate achievable with AF relaying is addressed. Previous work on this problem provides iterative algorithms based on semidefinite relaxation. However, those algorithms result in suboptimal performance without any performance and convergence guarantees. We address this problem for three specific network models, with real-valued channel gains. We propose a novel transformation that leads to convex optimization problems. Our analysis leads to (i)a polynomial-time algorithm to compute the optimal secure AF rate for two of the models and (ii) a closed-form expression for the optimal secure rate for the other.Comment: 12pt font, 18 pages, 1 figure, conferenc

Efficient And Robust Video Steganography Algorithms For Secure Data Communication

Nowadays, the science of information hiding has gained tremendous significance due to advances in information and communication technology. The performance of any steganography method relies on the imperceptibility, embedding capacity, and robustness against attacks. This research provides solutions for the existing video steganography problems by proposing new and effective methods for digital video steganography. The key objectives of our paper are as follows: 1) a highly secure video steganography algorithm based on error correcting codes (ECC); 2) an increased payload video steganography algorithm in the discrete wavelet domain based on ECC; 3) a novel video steganography algorithm based on Kanade-Lucas-Tomasi (KLT) tracking and ECC; 4) a robust video steganography algorithm in the wavelet domain based on KLT tracking and ECC; and 5) a video steganography algorithm based on multiple object tracking and ECC. The experimental results from our research demonstrate that our proposed algorithms achieve higher embedding capacity as well as better imperceptibility of stego videos. Furthermore, the preprocessing stages increase the security and robustness of the proposed algorithms against attacks when compared to state-of-the-art steganographic methods