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On Lattices, Learning with Errors, Random Linear Codes, and Cryptography
 In STOC
, 2005
"... Our main result is a reduction from worstcase lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the ‘learning from parity with error’ problem to higher moduli. It can also be viewed as the problem of decoding from a random linear co ..."
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Cited by 364 (6 self)
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that all parties share a random bit string of length Õ(n2), the size of the public key can be reduced to Õ(n). 1
Unveiling Turbo Codes: Some Results on Parallel Concatenated Coding Schemes
, 1995
"... A parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver. The input bits to the first encoder are scrambled by the interleaver before entering the second encoder. The codeword of the parallel concatenated code consists of the input bits to ..."
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Cited by 314 (6 self)
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to the first encoder followed by the parity check bits of both encoders. This construction can be generalized to any number of constituent codes. Parallel concatenated schemes employing two convolutional codes as constituent codes, in connection with an iterative decoding algorithm of complexity comparable
Closing the gap in the capacity of wireless networks via percolation theory
 IEEE TRANS. INFORMATION THEORY
, 2007
"... An achievable bit rate per source–destination pair in a wireless network of � randomly located nodes is determined adopting the scaling limit approach of statistical physics. It is shown that randomly scattered nodes can achieve, with high probability, the same Ia � � transmission rate of arbitrari ..."
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Cited by 238 (8 self)
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theory ensures that crossing paths form in the transition region between these two extreme scenarios. Nodes along these paths are used as a backbone, relaying data for other nodes, and can transport the total amount of information generated by all the sources. A lower bound on the achievable bit rate
Randomness Requirements for Security
 BCP 106, RFC 4086
, 2005
"... This document is intended to become a Best Current Practice. Comments should be sent to the authors. Distribution is unlimited. This document is an InternetDraft and is in full conformance with all provisions of Section 10 of RFC 2026. InternetDrafts are working documents of the Internet Engineeri ..."
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Cited by 176 (0 self)
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. It is inappropriate to use InternetDrafts as reference material or to cite them other than as "work in progress. " The list of current InternetDrafts can be accessed at http://www.ietf.org/ietf/1idabstracts.txt The list of InternetDraft Shadow Directories can be accessed at
HMQV: A HighPerformance Secure DiffieHellman Protocol
 Protocol, Advances in Cryptology — CRYPTO ’05, LNCS 3621
, 2005
"... The MQV protocol of Law, Menezes, Qu, Solinas and Vanstone is possibly the most e#cient of all known authenticated Di#eHellman protocols that use publickey authentication. In addition to great performance, the protocol has been designed to achieve a remarkable list of security properties. As a ..."
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Cited by 169 (6 self)
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The MQV protocol of Law, Menezes, Qu, Solinas and Vanstone is possibly the most e#cient of all known authenticated Di#eHellman protocols that use publickey authentication. In addition to great performance, the protocol has been designed to achieve a remarkable list of security properties. As a
Algorithmic results in list decoding
 In Foundations and Trends in Theoretical Computer Science (FnTTCS
"... Errorcorrecting codes are used to cope with the corruption of data by noise during communication or storage. A code uses an encoding procedure that judiciously introduces redundancy into the data to produce an associated codeword. The redundancy built into the codewords enables one to decode the or ..."
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Cited by 15 (3 self)
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Errorcorrecting codes are used to cope with the corruption of data by noise during communication or storage. A code uses an encoding procedure that judiciously introduces redundancy into the data to produce an associated codeword. The redundancy built into the codewords enables one to decode
Approximate listdecoding of direct product . . .
"... Given a message msg ∈ {0, 1} N, its kwise direct product encoding is the sequence of ktuples (msg(i1),..., msg(ik)) over all possible ktuples of indices (i1,..., ik) ∈ {1,..., N} k. We give an efficient randomized algorithm for approximate local listdecoding of direct product codes. That is, gi ..."
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Cited by 33 (8 self)
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Given a message msg ∈ {0, 1} N, its kwise direct product encoding is the sequence of ktuples (msg(i1),..., msg(ik)) over all possible ktuples of indices (i1,..., ik) ∈ {1,..., N} k. We give an efficient randomized algorithm for approximate local listdecoding of direct product codes. That is
The Complexity of Local List Decoding
"... We study the complexity of locally listdecoding binary error correcting codes with good parameters (that are polynomially related to information theoretic bounds). We show that computing majority over Θ(1/ǫ) bits is essentially equivalent to locally listdecoding binary codes from relative distance ..."
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Cited by 4 (1 self)
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1/2 − ǫ with list size at most poly(1/ǫ). That is, a localdecoder for such a code can be used to construct a circuit of roughly the same size and depth that computes majority on Θ(1/ǫ) bits. On the other hand, there is an explicit locally listdecodable code with these parameters that has a very
ListDecodable Codes
"... The field of coding theory is motivated by the problem of communicating reliably over noisy channels — where the data sent over the channel may come out corrupted on the other end, but we nevertheless want the receiver to be able to correct the errors and recover the original message. There is a vas ..."
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. ” In particular, a generalization of the notion of an errorcorrecting code yields a framework that we will use to unify all of the main pseudorandom objects covered in this survey (averaging samplers, expander graphs, randomness extractors, listdecodable codes, pseudorandom generators).
5 ListDecodable Codes
"... The field of coding theory is motivated by the problem of communicating reliably over noisy channels — where the data sent over the channel may come out corrupted on the other end, but we nevertheless want the receiver to be able to correct the errors and recover the original message. There is a vas ..."
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. ” In particular, a generalization of the notion of an errorcorrecting code yields a framework that we will use to unify all of the main pseudorandom objects covered in this survey (averaging samplers, expander graphs, randomness extractors, listdecodable codes, pseudorandom generators).
Results 1  10
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2,274