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On the Duality of Probing and Fault Attacks

JOURNAL OF ELECTRONIC TESTING-theory AND APPLICATIONS 2010年第4期26卷 483-493页

作者： Gammel, Berndt M. Mangard, Stefan Infineon Technol AG Munich Germany

In this work we investigate the problem of simultaneous privacy and integrity protection in cryptographic circuits. We consider a white-box scenario with a powerful, yet limited attacker. A concise metric for the level of probing and fault security is introduced, which is directly related to the capabilities of a realistic attacker. In order to investigate the interrelation of probing and fault security we introduce a common mathematical framework based on the formalism of information and coding theory. The framework unifies the known linear masking schemes. We proof a central theorem about the properties of linear codes which leads to optimal secret sharing schemes. These schemes provide the lower bound for the number of masks needed to counteract an attacker with a given strength. The new formalism reveals an intriguing duality principle between the problems of probing and fault security, and provides a unified view on privacy and integrity protection using error detecting codes. Finally, we introduce a new class of linear tamper-resistant codes. These are eligible to preserve security against an attacker mounting simultaneous probing and fault attacks.

关键词： Probing attacks Fault attacks Side channel attacks coding theory Secret sharing Secure computation

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Design of Memories with Concurrent Error Detection and Correction by Nonlinear SEC-DED Codes

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JOURNAL OF ELECTRONIC TESTING-theory AND APPLICATIONS 2010年第5期26卷 559-580页

作者： Wang, Zhen Karpovsky, Mark Kulikowski, Konrad J. Boston Univ Reliable Comp Lab Boston MA 02215 USA

In this paper we propose memory protection architectures based on nonlinear single-error-correcting, double-error-detecting (SEC-DED) codes. Linear SEC-DED codes widely used for design of reliable memories cannot detect and can miscorrect lots of errors with large Hamming weights. This may be a serious disadvantage for many modern technologies when error distributions are hard to estimate and multi-bit errors are highly probable. The proposed protection architectures have fewer undetectable errors and fewer errors that are miscorrected by all codewords than architectures based on linear codes with the same dimension at the cost of a small increase in the latency penalty, the area overhead and the power consumption. The nonlinear SEC-DED codes are generalized from the existing perfect nonlinear codes (Vasil'ev codes, Probl Kibern 8:375-378, 1962;Phelps codes, SIAM J Algebr Discrete Methods 4:398-403, 1983;and the codes based on one switching constructions, Etzion and Vardy, IEEE Trans Inf theory 40:754-763, 1994). We present the error correcting algorithms, investigate and compare the error detection and correction capabilities of the proposed nonlinear SEC-DED codes to linear extended Hamming codes and show that replacing linear extended Hamming codes by the proposed nonlinear SEC-DED codes results in a drastic improvement in the reliability of the memory systems in the case of repeating errors or high multi-bit error rate. The proposed approach can be applied to RAM, ROM, FLASH and disk memories.

关键词： coding theory Reliable memories SEC-DED Error detection and correction Soft errors Nonlinear codes Robust

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HARDNESS OF RECONSTRUCTING MULTIVARIATE POLYNOMIALS OVER FINITE FIELDS

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SIAM JOURNAL ON COMPUTING 2010年第6期39卷 2598-2621页

作者： Gopalan, Parikshit Khot, Subhash Saket, Rishi Microsoft Res Silicon Valley Mountain View CA 94043 USA Univ Washington Seattle WA 98195 USA Univ Texas Austin Austin TX 78712 USA New York Univ Dept Comp Sci New York NY 10012 USA Georgia Tech Coll Comp Atlanta GA 30332 USA

We study the polynomial reconstruction problem for low-degree multivariate polynomials over finite field F[2]. In this problem, we are given a set of points x is an element of {0, 1}(n) and target values f(x) is an element of {0, 1} for each of these points, with the promise that there is a polynomial over F[2] of degree at most d that agrees with f at 1-epsilon fraction of the points. Our goal is to find a degree d polynomial that has good agreement with f. We show that it is NP-hard to find a polynomial that agrees with f on more than 1-2(-d) + delta fraction of the points for any epsilon, delta > 0. This holds even with the stronger promise that the polynomial that fits the data is in fact linear, whereas the algorithm is allowed to find a polynomial of degree d. Previously the only known hardness of approximation (or even NP-completeness) was for the case when d = 1, which follows from a celebrated result of Hastad [J. ACM, 48 (2001), pp. 798-859]. In the setting of Computational Learning, our result shows the hardness of nonproper agnostic learning of parities, where the learner is allowed a low-degree polynomial over F[2] as a hypothesis. This is the first nonproper hardness result for this central problem in computational learning. Our results can be extended to multivariate polynomial reconstruction over any finite field.

关键词： hardness of approximation polynomials finite fields coding theory computational learning

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Storage coding for Wear Leveling in Flash Memories

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IEEE TRANSACTIONS ON INFORMATION theory 2010年第10期56卷 5290-5299页

作者： Jiang, Anxiao (Andrew) Mateescu, Robert Yaakobi, Eitan Bruck, Jehoshua Siegel, Paul H. Vardy, Alexander Wolf, Jack K. Texas A&M Univ Dept Comp Sci & Engn College Stn TX 77843 USA Microsoft Res Cambridge Cambridge CB3 0FB England Univ Calif San Diego Ctr Magnet Recording Res La Jolla CA 92093 USA CALTECH Dept Elect Engn Pasadena CA 91125 USA Univ Calif San Diego Dept Elect & Comp Engn Dept Comp Sci & Engn La Jolla CA 92093 USA Univ Calif San Diego Dept Math La Jolla CA 92093 USA

Flash memory is a nonvolatile computer memory comprised of blocks of cells, wherein each cell is implemented as either NAND or NOR floating gate. NAND flash is currently the most widely used type of flash memory. In a NAND flash memory, every block of cells consists of numerous pages;rewriting even a single page requires the whole block to be erased and reprogrammed. Block erasures determine both the longevity and the efficiency of a flash memory. Therefore, when data in a NAND flash memory are reorganized, minimizing the total number of block erasures required to achieve the desired data movement is an important goal. This leads to the flash data movement problem studied in this paper. We show that coding can significantly reduce the number of block erasures required for data movement, and present several optimal or nearly optimal data-movement algorithms based upon ideas from coding theory and combinatorics. In particular, we show that the sorting-based (noncoding) schemes require O(n log n) erasures to move data among n blocks, whereas coding-based schemes require only O(n) erasures. Furthermore, coding-based schemes use only one auxiliary block, which is the best possible and achieve a good balance between the number of erasures in each of the n + 1 blocks.

关键词： coding theory combinatorics data storage flash memory graph theory wear leveling

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Rewriting Codes for Joint Information Storage in Flash Memories

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IEEE TRANSACTIONS ON INFORMATION theory 2010年第10期56卷 5300-5313页

作者： Jiang, Anxiao (Andrew) Bohossian, Vasken Bruck, Jehoshua Texas A&M Univ Dept Comp Sci & Engn College Stn TX 77843 USA CALTECH Dept Elect Engn Pasadena CA 91125 USA

Memories whose storage cells transit irreversibly between states have been common since the start of the data storage technology. In recent years, flash memories have become a very important family of such memories. A flash memory cell has q states-state 0, 1, ... , q - 1-and can only transit from a lower state to a higher state before the expensive erasure operation takes place. We study rewriting codes that enable the data stored in a group of cells to be rewritten by only shifting the cells to higher states. Since the considered state transitions are irreversible, the number of rewrites is bounded. Our objective is to maximize the number of times the data can be rewritten. We focus on the joint storage of data in flash memories, and study two rewriting codes for two different scenarios. The first code, called floating code, is for the joint storage of multiple variables, where every rewrite changes one variable. The second code, called buffer code, is for remembering the most recent data in a data stream. Many of the codes presented here are either optimal or asymptotically optimal. We also present bounds to the performance of general codes. The results show that rewriting codes can integrate a flash memory's rewriting capabilities for different variables to a high degree.

关键词： coding theory data storage flash memory

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Weakly-Constrained Codes for Suppression of Patterning Effects in Digital Communications

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IEEE TRANSACTIONS ON COMMUNICATIONS 2010年第10期58卷 2845-2854页

作者： Shafarenko, Alexander Skidin, Anton Turitsyn, Sergei K. Univ Hertfordshire Sch Comp Sci Hatfield AL10 9AB Herts England SB RAS Inst Computat Technol Novosibirsk 630090 Russia Aston Univ Photon Res Grp Birmingham B4 7ET W Midlands England

We propose weakly-constrained stream and block codes with tunable pattern-dependent statistics and demonstrate that the block code capacity at large block sizes is close to the the prediction obtained from a simple Markov model published earlier. We demonstrate the feasibility of the code by presenting original encoding and decoding algorithms with a complexity log-linear in the block size and with modest table memory requirements. We also show that when such codes are used for mitigation of patterning effects in optical fibre communications, a gain of about 0.5dB is possible under realistic conditions, at the expense of small redundancy (approximate to 10%).

关键词： Patterning effects weakly-constrained codes coding theory pre-encoding

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BREAKING THE ε-SOUNDNESS BOUND OF THE LINEARITY TEST OVER GF(2)

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SIAM JOURNAL ON COMPUTING 2010年第5期39卷 1988-2003页

作者： Kaufman, Tali Litsyn, Simon Xie, Ning MIT CSAIL Cambridge MA 02139 USA SUNY Buffalo Buffalo NY 14260 USA Tel Aviv Univ Dept Elect Engn Syst IL-69978 Tel Aviv Israel

For Boolean functions that are epsilon-far from the set of linear functions, we study the lower bound on the rejection probability (denoted by REJ(epsilon)) of the linearity test suggested by Blum, Luby, and Rubinfeld [J. Comput. System Sci., 47 (1993), pp. 549-595]. This problem is arguably the most fundamental and extensively studied problem in property testing of Boolean functions. The previously best bounds for REJ(epsilon) were obtained by Bellare et al. [IEEE Trans. Inform. theory, 42 (1996), pp. 1781-1795]. They used Fourier analysis to show that REJ(epsilon) >= epsilon for every 0 <= epsilon <= 1/2. They also conjectured that this bound might not be tight for epsilon's which are close to 1/2. In this paper we show that this indeed is the case. Specifically, we improve the lower bound of REJ(epsilon) >= epsilon by an additive constant that depends only on epsilon: REJ(epsilon) >= epsilon + min{1376 epsilon(3)(1-2 epsilon)(12), 1/4 epsilon(1-2 epsilon)(4)}, for every 0 <= epsilon <= 1/2. Our analysis is based on a relationship between REJ(epsilon) and the weight distribution of a coset code of the Hadamard code. We use both Fourier analysis and coding theory tools to estimate this weight distribution.

关键词： property testing linearity test coding theory Fourier analysis

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Fast method for precoding and decoding of distributive multi-input multi-output channels in relay-based decode-and-forward cooperative wireless networks

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IET COMMUNICATIONS 2010年第2期4卷 144-153页

作者： Lee, M. H. Matalgah, M. M. Song, W. Chonbuk Natl Univ Inst Informat & Commun Jeonju 561756 South Korea Univ Mississippi Dept Elect Engn Ctr Wireless Commun University MS 38677 USA

It is well-known that the performance of the relay-based decode-and-forward (DF) cooperative networks outperforms the performance of the amplify-and-forward cooperative networks. However, this performance improvement is accomplished at the expense of adding more signal processing complexity (precoding/decoding) at each relay node. In this study, the authors tackle this signal processing complexity issue by proposing a Jacket-based fast method for reducing the precoding/decoding complexity in terms of time computation. Jacket transforms have shown to find applications in signal processing and coding theory. Jacket transforms are defined to be n x n matrices A = (a(jk)) over a field F with the property AA(dagger) nI(n), where A(dagger) is the transpose matrix of the element-wise inverse of A, that is, A(dagger) (a(kj)(-1)), which generalise Hadamard transforms and centre weighted Hadamard transforms. In particular, exploiting the Jacket transform properties, the authors propose a new eigenvalue decomposition (EVD) method with application in precoding and decoding of distributive multi-input multi-output channels in relay-based DF cooperative wireless networks in which the transmission is based on using single-symbol decodable space-time block codes. The authors show that the proposed Jacket-based method of EVD has significant reduction in its computational time as compared to the conventional-based EVD method. Performance in terms of computational time reduction is evaluated quantitatively through mathematical analysis and numerical results.

关键词： coding theory Communication system theory eigenvalue decomposition method Signal processing and detection Codes precoding weighted Hadamard transforms block codes Jacket transforms decoding channel coding Integral transforms in numerical analysis distributive multi-input multi-output channels precoding Hadamard transforms Signal processing theory signal processing complexity relay-based decode-and-forward cooperative networks eigenvalues and eigenfunctions signal processing conventional-based EVD method communication complexity computational time reduction distributive multi-input multi-output channels decoding

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Bounds for General Transmission Systems

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IEEE TRANSACTIONS ON INFORMATION theory 2010年第12期56卷 5943-5944页

作者： Higgs, Russell John Univ Coll Dublin Sch Math Sci Dublin 4 Ireland

We show that the codebook of every general transmission system can also be regarded as a classical code in a natural way. Consequently, using the Hamming metric, bounds on the cardinality of the codebooks of transmiss... 详细信息

关键词： coding theory general transmission system network code

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Projection-forcing multisets of weight changes

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JOURNAL OF COMBINATORIAL theory SERIES A 2010年第8期117卷 1136-1142页

作者： Kramer, Josh Brown Sabalka, Lucas Illinois Wesleyan Univ Bloomington IL 61701 USA SUNY Binghamton Dept Math Sci Binghamton NY 13902 USA

Let F be a finite field. A multiset S of integers is projection-forcing if for every linear function phi : F(n) -> F(m) whose multiset of weight changes is S, phi is a coordinate projection up to permutation and scaling of entries. The MacWilliams Extension Theorem from coding theory says that S = (0, 0, ... , 0) is projection-forcing. We give a (super-polynomial) algorithm to determine whether or not a given S is projection-forcing. We also give a condition that can be checked in polynomial time that implies that S is projection-forcing. This result is a generalization of the MacWilliams Extension Theorem and work by the first author. (C) 2010 Elsevier Inc. All rights reserved.

关键词： MacWilliams Extension Theorem Projections Finite fields coding theory

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