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Characterizing bit permutation networks

Gerard J. Chang, Frank K. Hwang, Li-Da Tong
1999 Networks  
In this paper, we studied a more general class of networks, which we call ( m / 1)-stage d-nary bit permutation networks.  ...  We characterize the equivalence of such networks by sequence of positive integers.  ...  INTRODUCTION For a detailed description and notation of bit permutation networks, see Section 2.  ... 
doi:10.1002/(sici)1097-0037(199907)33:4<261::aid-net3>3.0.co;2-q fatcat:fxn6gjkhcna4jimnxz4m265w3a

Characterizing the bit permutation networks obtained from the line digraphs of bit permutation networks

Frank K. Hwang, Chih-Hung Yen
2001 Networks  
By Theorem 2, we say that a bit permutation network N d (n; u, v, f 1 , . . . , f s−1 ) can be characterized by a (s − 1)vector (k 1 , . . . , k s−1 ).  ...  They showed that an s-stage d-nary bit permutation network N with d n inputs (outputs) can be characterized by a (s − 1)-vector (k 1 , . . . , k s−1 ), where k t = j ∈ {1, . . . , n − 1} means that N is  ... 
doi:10.1002/net.1018 fatcat:whntkkaxobgxxhcllw3a6hiiia

Equivalence of buddy networks with arbitrary number of stages

Chiuyuan Chen, Frank K. Hwang, James K. Lan
2005 Networks  
Equivalence of multistage interconnection networks is an important concept because it reduces the number of networks to be studied. Equivalence among the banyan networks has been well studied.  ...  Note that all these abovementioned networks are in the general class of buddy networks. In this article we study equivalence of buddy networks with an arbitrary number of stages.  ...  Such a permutation is called an bit permutation if it can be characterized by a permutation σ i of the n bits. A network is a bit permuting network if each G i corresponds to a σ i .  ... 
doi:10.1002/net.20085 fatcat:kjgs2e5egjh7bjwzh33rwz4cp4

Independent connections: an easy characterization of baseline-equivalent multistage interconnection networks

J.C. Bermond, J.M. Fourneau
1989 Theoretical Computer Science  
Using our graph characterization of networks topologically equivalent to the Baseline network, we show that all the Banyan networks built with independent connections are isomorphic.  ...  As these PIPID are associated with a very simple bit directed routing, they are used to define most of the networks introduced in the literature.  ...  This characterization is difficult to apply if the networks are defined by permutations on the links.  ... 
doi:10.1016/0304-3975(89)90061-3 fatcat:35q5fwye7ja2jh472uqd457jey

A necessary and sufficient closure property for two-stage constructions of switching networks

Ching-Min Lien, Cheng-Shang Chang, Duan-Shin Lee
2015 2015 IEEE International Conference on Communications (ICC)  
Since banyan-type networks are constructed recursively by using two-stage constructions with 2 × 2 switches, we obtain a complete characterization for any realizable permutation of any banyan-type network  ...  Such a necessary and sufficient result provides a complete characterization of the permutations that can be realized by two-stage constructions.  ...  Though there are characterizations of permutations realizable by certain banyantype networks [17] , our characterization seems to be the first complete characterization of the permutations realizable  ... 
doi:10.1109/icc.2015.7249021 dblp:conf/icc/LienCL15 fatcat:6ndxezyiu5goddryebaixfluoy

FAULT‐TOLERANT DESIGN OF BATCHER–BANYAN CLASS ATM SWITCHES

RUI‐FENG (RAYMOND) LIAO, ALBERTO LEON‐GARCIA
1996 International Journal of Communication Systems  
Furthermore, we extend this method to Batcher sorting networks and construct a fault-tolerant Batcher sorter.  ...  Based on the technique developed by D a vis 9 , we propose a general fault-testing technique and verify it for a variety of unique-path self-routing networks.  ...  We rst characterize the self-routing mechanism and construct a new network subset of delta networks | Bit-Permutation class networks.  ... 
doi:10.1002/(sici)1099-1131(199603)9:2<81::aid-dac295>3.3.co;2-1 fatcat:slrfnnzv4bcspmsrqq6xl6ykje

FAULT-TOLERANT DESIGN OF BATCHER-BANYAN CLASS ATM SWITCHES

RUI-FENG (RAYMOND) LIAO, ALBERTO LEON-GARCIA
1996 International Journal of Communication Systems  
Furthermore, we extend this method to Batcher sorting networks and construct a fault-tolerant Batcher sorter.  ...  Based on the technique developed by D a vis 9 , we propose a general fault-testing technique and verify it for a variety of unique-path self-routing networks.  ...  We rst characterize the self-routing mechanism and construct a new network subset of delta networks | Bit-Permutation class networks.  ... 
doi:10.1002/(sici)1099-1131(199603)9:2<81::aid-dac295>3.0.co;2-a fatcat:sswgwkgsazg6zm3dnjnwe3yozu

Channel graphs of bit permutation networks

Li-Da Tong, Frank K. Hwang, Gerard J. Chang
2001 Theoretical Computer Science  
In this paper, we show that a bit permutation network has a unique channel graph if and only if it is connected, and two connected bit permutation networks are isomorphic if and only if their channel graphs  ...  Channel graphs have been widely used in the study of blocking networks.  ...  It was shown [2] that (m + 1)th-stage d-nary bit permutation networks can be characterized by canonical sequences. Proof. Immediate from the deÿnition of N d (n; k 1 ; k 2 ; : : : ; k m ). Proof.  ... 
doi:10.1016/s0304-3975(00)00237-1 fatcat:xxitdmg5hnejzp56wb565ozj6m

Efficient permutation instructions for fast software cryptography

R.B. Lee, Zhijie Shi, Xiiao Yang
2001 IEEE Micro  
While targeted at solving the more difficult problem of permuting n 1-bit elements, we also address the issue of permuting a smaller number of multi-bit subwords packed into an nbit word, a feature needed  ...  This paper introduces four novel permutation instructions and the underlying methodology for performing arbitrary n-bit permutations efficiently in programmable processors.  ...  We characterized the performance of these different permutation methodologies, and the tradeoffs between them.  ... 
doi:10.1109/40.977759 fatcat:4ny2o4khwvglrbw5mvpgen4d7e

Permutations on the Block PRAM

Andrew Chin
1993 Information Processing Letters  
We characterize the Block PRAM complexity of some useful classes of permutations, improving known results.  ...  ., Permutations on the Block PRAM, Information Processing Letters 45 (1993) 69-73.  ...  In this paper, we characterize the complexity of performing specific frequently used permutations on the Block PRAM.  ... 
doi:10.1016/0020-0190(93)90218-x fatcat:25ftrg2qpbc75jff5lqzz6omki

Rearrangeability of bit permutation networks

Xuewen Bao, Frank K. Hwang, Qiao Li
2006 Theoretical Computer Science  
In this paper, we introduce the concept of routing grid as a tool for analyzing realizability of permutations on bit permutation networks (BPNs).  ...  We extend a result by Linial and Tarsi which characterizes permutations realizable on shuffle-exchange networks to any BPNs.  ...  We extended a result by Linial and Tarsi which characterizes permutations realizable on shuffle-exchange networks to any BPNs.  ... 
doi:10.1016/j.tcs.2005.09.077 fatcat:jbsrsfoevzh45gfi5ph4kcygym

Frames: a simple characterization of permutations realized by frequently used networks

H. Cam, J.A.B. Fortes
1995 IEEE transactions on computers  
This paper introduces the concept of frame and shows how iit can be used to characterize all the permutations realized on various multistage inteirconnection networks.  ...  Rearrangeable multistage interconnection networks such as the Benes network realize any permutation, yet their routing algorithms are not cost-effective.  ...  Because the control bits of the rth SB of RAB 1 constitute the set {0,1) and fittherth blockoffl,dl fitsfl. Induction Step: Assume that the thtorem holds for k-1.  ... 
doi:10.1109/12.381954 fatcat:zsuo7kyok5hv3cyd3ey5sldhoi

Implementation of a New Lightweight Encryption Design for Embedded Security

Gaurav Bansod, Nishchal Raval, Narayan Pisharoty
2015 IEEE Transactions on Information Forensics and Security  
In this paper, we present the design of hybrid lightweight encryption system based on bit permutation instruction GRP (group operation) and the S-box of PRESENT.  ...  We have carefully studied the properties and security aspects of bit permutation instructions like GRP [10] .PRESENT is a Substitution Permutation network based on 80 bit or 128 bit key size and 64 bit  ...  PRESENT ALGORITHM In the cryptographic environment, there are two types of instructions, one is the "SP-network" (Substitution Permutation network) like AES, PRESENT etc and other is the "Feistel network  ... 
doi:10.1109/tifs.2014.2365734 fatcat:7o5imbkltncsdexghpedzap2jq

Using the Augmented Data Manipulator Network in PASM

H.J. Siegel, R.J. McMillen
1981 Computer  
network input and output.  ...  The multistage ADM network, on the other hand, generally has multiple paths between a given network input and output.  ...  A partitionable network can be characterized by any limitations on the way in which it can be subdivided.  ... 
doi:10.1109/c-m.1981.220330 fatcat:gs2sbzlvp5fafkw365ziv6ek54

Page 710 of Mathematical Reviews Vol. , Issue 2003A [page]

2003 Mathematical Reviews  
(RC-NCT-AM; Hsinchu) ; Yen, Chih-Hung (RC-NCT-AM; Hsinchu) Characterizing the bit permutation networks obtained from the line digraphs of bit permutation networks.  ...  Tong [Networks 33 (1999), no. 4, 261-267; see MR 2000c:94001] showed that an s-stage d-ary bit permutation net- work N with d” inputs (outputs) can be characterized by an (s — 1)-vector (k, k,_,), where  ... 
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