A Survey of Results for Deletion Channels and Related Synchronization Channels

Mitzenmacher, Michael

doi:10.1007/978-3-540-69903-3_1

Cited by 13 publications

(5 citation statements)

References 20 publications

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“…Since their introduction, errorcorrecting codes have received much attention and found countless applications in both theory and practice. There has also been some study of error correction for other families F , such as ones where tampering functions preserve edit distance instead of Hamming distance (see the survey of [58]). However, it is also clear that error correction cannot be achieved for many natural (and simple) function families-such as even the single "zero function" f that maps all values x to the all-zero string.…”

Section: Introductionmentioning

confidence: 99%

Non-Malleable Codes

Dziembowski

Pietrzak

Wichs

2018

J. ACM

181

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We introduce the notion of "non-malleable codes" which relaxes the notion of error correction and error detection. Informally, a code is non-malleable if the message contained in a modified codeword is either the original message, or a completely unrelated value. In contrast to error correction and error detection, nonmalleability can be achieved for very rich classes of modifications. We construct an efficient code that is non-malleable with respect to modifications that affect each bit of the codeword arbitrarily (i.e., leave it untouched, flip it, or set it to either 0 or 1), but independently of the value of the other bits of the codeword. Using the probabilistic method, we also show a very strong and general statement: there exists a non-malleable code for every "small enough" family F of functions via which codewords can be modified. Although this probabilistic method argument does not directly yield efficient constructions, it gives us efficient non-malleable codes in the random-oracle model for very general classes of tampering functions-e.g., functions where every bit in the tampered codeword can depend arbitrarily on any 99% of the bits in the original codeword. As an application of non-malleable codes, we show that they provide an elegant algorithmic solution to the task of protecting functionalities implemented in hardware (e.g., signature cards) against "tampering attacks." In such attacks, the secret state of a physical system is tampered, in the hopes that future interaction with the modified system will reveal some secret information. This problem was previously studied in the work of Gennaro et al. in 2004 under the name "algorithmic tamper proof security" (ATP). We show that nonmalleable codes can be used to achieve important improvements over the prior work. In particular, we show that any functionality can be made secure against a large class of tampering attacks, simply by encoding the secret state with a non-malleable code while it is stored in memory. CCS Concepts: • Mathematics of computing → Coding theory; • Security and privacy → Information-theoretic techniques; Tamper-proof and tamper-resistant designs;

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Section: Introductionmentioning

confidence: 99%

Non-Malleable Codes

Dziembowski

Pietrzak

Wichs

2018

J. ACM

181

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“…As proved by Orlitsky [3], design of optimal protocols for recovery from deletions on forward links implies optimal protocols for recovery from deletions and insertions. Furthermore, such protocols can be implemented as efficient channel codes for communicating over edit channels (see [11], [20], [21], [22]). …”

Section: Discussionmentioning

confidence: 99%

A Deterministic Polynomial-Time Protocol for Synchronizing From Deletions

Yazdi

Dolecek

2014

IEEE Trans. Inform. Theory

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In this paper, we consider a synchronization problem between nodes A and B that are connected through a twoway communication channel. Node A contains a binary file X of length n and node B contains a binary file Y that is generated by randomly deleting bits from X, by a small deletion rate β. The location of deleted bits is not known to either node A or node B. We offer a deterministic synchronization scheme between nodes A and B that needs a total of O(nβ log 1 β ) transmitted bits and reconstructs X at node B with probability of error that is exponentially low in the size of X. Orderwise, the rate of our scheme matches the optimal rate for this channel.This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. 2 have been many improvements over the baseline approach. For example Suel et al. [9] proposed a protocol that in certain cases can save up to 50% of bandwidth over RSYNC. There are also more specialized synchronization tools, such as VSYNC [10], which synchronizes between video files. B. Our ContributionWhile most of the previous work has concentrated on synchronizing from a fixed number of edits between two files X and Y , in this paper we are interested in a more practical scenario, which is synchronizing from a fixed rate of edits between two files. We only study synchronization from deletions, and will discuss possible extensions to the more general case of deletions and insertions at the end of the paper. More specifically, we consider synchronization between node A and node B where node A has a binary string X that is generated by an i.i.d. Bernoulli process of parameter 1 2 . Node B has a binary string Y that is generated from X by randomly and independently deleting bits of X with probability β that is very small. We are interested in an optimal transmission protocol for synchronizing between nodes A and B when n, the length of X, is large.We remark that, throughout the paper, by small β we implicitly mean that there exists β 0 > 0 such that our discussion is valid for all β < β 0 . Furthermore, by large n we implicitly mean that for every β < β 0 there exists a positive integer n β such that our discussion is valid for all n > n β .In order to evaluate a lower bound on the optimal number of transmitted bits between nodes A and B, suppose that node A has access to string Y . Then, the optimal number of transmitted bits to node B, needed for reconstructing X is H(X|Y ), which is the conditional entropy of string X given string Y . Ma et al.[11] considered a more general set-up where the deletion pattern follows a stationary Markov chain. By applying the result of [11] to our model, for small values of β, the entropy H(X|Y ) can be estimated as follows

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“…Classical InsDel codes were initially studied in [Lev66], inspiring a rich line of research into these codes; see surveys [Slo02,Mit08,MBT10] for more information. Recently, kdeletion correcting codes with optimal rate were constructed, answering a long standing open question [SB21].…”

Section: B Related Workmentioning

confidence: 99%

Private and Resource-Bounded Locally Decodable Codes for Insertions and Deletions

Block

Blocki²

2021

2021 IEEE International Symposium on Information Theory (ISIT)

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We revisit computationally relaxed locally decodable codes (crLDCs) (Blocki et al., Trans. Inf. Theory '21) and give two new constructions. Our first construction is a Hamming crLDC that is conceptually simpler than prior constructions, leveraging digital signature schemes and an appropriately chosen Hamming code. Our second construction is an extension of our Hamming crLDC to handle insertion-deletion (InsDel) errors, yielding an InsDel crLDC. This extension crucially relies on the noisy binary search techniques of Block et al. (FSTTCS '20) to handle InsDel errors. Both crLDC constructions have binary codeword alphabets, are resilient to a constant fraction of Hamming and InsDel errors, respectively, and under suitable parameter choices have poly-logarithmic locality and encoding length linear in the message length and polynomial in the security parameter. These parameters compare favorably to prior constructions in the poly-logarithmic locality regime.

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A Survey of Results for Deletion Channels and Related Synchronization Channels

Cited by 13 publications

References 20 publications

Non-Malleable Codes

Non-Malleable Codes

A Deterministic Polynomial-Time Protocol for Synchronizing From Deletions

Private and Resource-Bounded Locally Decodable Codes for Insertions and Deletions

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