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2-Xor revisited: satisfiability and probabilities of functions [article]

Élie de Panafieu and Danièle Gardy and Bernhard Gittenberger and Markus Kuba
2015 arXiv   pre-print
The problem 2-Xor-Sat asks for the probability that a random expression, built as a conjunction of clauses x ⊕ y, is satisfiable.  ...  The answers to both problems involve a description of 2-Xor expressions as multigraphs and use classical methods of analytic combinatorics by expressing probabilities through coefficients of generating  ...  We thank Hervé Daudé and Vlady Ravelomanana for fruitful discussions. References  ... 
arXiv:1511.07813v1 fatcat:dqhrrs7cibdr5kkkxuilljrmr4

The circulant hash revisited

Filipe Araujo, Samuel Neves
2020 Journal of Mathematical Cryptology  
AbstractAt ProvSec 2013, Minematsu presented the circulant hash, an almost-xor universal hash using only the xor and rotation operations.  ...  In this paper we revisit the circulant hash and reinterpret it as a multiplication in the polynomial ring 𝔽2[x]/(xn + 1).  ...  Minematsu proved this function is 2/2 n -almost xor universal.  ... 
doi:10.1515/jmc-2018-0054 fatcat:qshkbxzxrrgs5czpvj6ekhos3y

Space compression revisited

S.R. Das, T.F. Barakat, E.M. Petriu, M.H. Assaf, K. Chakrabarty
2000 IEEE Transactions on Instrumentation and Measurement  
The techniques utilize the concepts of Hamming distance and sequence weights along with failure probabilities of errors in the selection of specific gates for merger of pairs of output streams from the  ...  The concept is extended to establish generalized mergeability criteria for merging an arbitrary number of output bit streams under conditions of both stochastic independence and dependence of line errors  ...  ACKNOWLEDGMENT The authors are extremely grateful to the anonymous referees and to the Guest Editor Dr.  ... 
doi:10.1109/19.850416 fatcat:7iowgwaiqfhslibopm7jmmdn6q

And/Or Trees Revisited

B. CHAUVIN, P. FLAJOLET, D. GARDY, B. GITTENBERGER
2004 Combinatorics, probability & computing  
We also consider the relationship between the probability P (f ) and the complexity L(f ) of a boolean function f .  ...  The existence of a limiting probability distribution P (.) on the set of and/or trees was shown by Lefmann and Savicky [8] .  ...  Enumerating functions and limit distribution for and/or trees We recall that the generating function for binary trees, counted by the number of (internal and external) nodes, satisfies the equation b(z  ... 
doi:10.1017/s0963548304006273 fatcat:p4h4anl4hngzdad26vmvq6m7ty

Aliasing-free compaction revisited

S.R. Das, A. Hossain, S. Biswas, E.M. Petriu
2008 IET Circuits, Devices & Systems  
The authors revisit the general problem of designing zero-aliasing (or aliasing-free) space compression hardware in relation to embedded cores-based SOC for single stuck-line faults in particular, extending  ...  The design of space-efficient support hardware for built-in self-testing is of immense significance in the synthesis of present day very large-scale integration circuits and systems, particularly in the  ...  Thanks are also due to the guest editor and to Ms Ann Thompson of the IET Editorial office for their immense help and kind understanding.  ... 
doi:10.1049/iet-cds:20070119 fatcat:xo2zjiri2revxmx6lsjnhkq6he

Information Distance Revisited

Bruno Bauwens, Markus Bläser, Christophe Paul
2020 Symposium on Theoretical Aspects of Computer Science  
We consider the notion of information distance between two objects x and y introduced by Bennett, Gács, Li, Vitanyi, and Zurek [C. H.  ...  ., 1998] as the minimal length of a program that computes x from y as well as computing y from x, and study different versions of this notion.  ...  There are two upper semicomputable symmetric functions E 1 , E 2 that both satisfy the condition ( * ) and the triangle inequality, such that no function that is bounded both by E 1 and E 2 can satisfy  ... 
doi:10.4230/lipics.stacs.2020.46 dblp:conf/stacs/Bauwens20 fatcat:546xyd3txrh5nbjnhnhxbxbdi4

Revisiting LFSMs [article]

François Arnault and Thierry Berger and Marine Minier and Benjamin Pousse
2011 arXiv   pre-print
In a second part, a new design criterion called diffusion delay for LFSRs is introduced and well compared with existing related notions. This criterion represents the diffusion capacity of an LFSR.  ...  We present some examples of LFSRs generated using our algorithm to show the relevance of our approach.  ...  It is satisfied if, whenever a single input bit is complemented, each of the output bits changes with a 50% probability [28] .  ... 
arXiv:1004.4806v3 fatcat:aynqlsobz5e7jlvtgtcmdgtszu

F2 Lanczos revisited

Michael Peterson, Chris Monico
2008 Linear Algebra and its Applications  
We present a new variant of the block Lanczos algorithm for finding vectors in the kernel of a symmetric matrix over F 2 . Our algorithm is at least as efficient as that of Montgomery [Peter L.  ...  Namely, our W i satisfy W T i W j = 0 for i / = j as opposed to W T i AW j = 0 in [6].  ...  . , W n−1 } have been computed satisfying the first three hypotheses of Proposition 4.2 and W n is to be computed.  ... 
doi:10.1016/j.laa.2007.09.016 fatcat:dftvigznlzdh5jf6ppr7nqjjkq

Revisiting AES related-key differential attacks with constraint programming

David Gérault, Pascal Lafourcade, Marine Minier, Christine Solnon
2018 Information Processing Letters  
In particular, we improve the best related-key differential for the whole AES-256 and give the best related-key differential on 10 rounds of AES-192, which is the differential trail with the longest path  ...  The Advanced Encryption Standard (AES) is one of the most studied symmetric encryption schemes. During the last years, several attacks have been discovered in different adversary models.  ...  states: 22 with probability 2 −6 and 1 with probability 2 −7 .  ... 
doi:10.1016/j.ipl.2018.07.001 fatcat:vngdrjgezvaqhax7hwfrpk5etq

Dining Cryptographers Revisited [chapter]

Philippe Golle, Ari Juels
2004 Lecture Notes in Computer Science  
We present new DC-net constructions that simultaneously achieve noninteractivity and high-probability detection and identification of cheating players.  ...  Suppose that each pair of players (P i , P j ) shares a set of keys k i,j (w) for i, j, w ∈ {1, 2, . . . , n}, where k i,j (w) = k j,i (w).  ...  Using the terminology of [5] , the function paramgen is a parameter generator that satisfies the DBDH assumption.  ... 
doi:10.1007/978-3-540-24676-3_27 fatcat:szfzn3dydng3nh77ewc3kv6tza

PTHash: Revisiting FCH Minimal Perfect Hashing [article]

Giulio Ermanno Pibiri, Roberto Trani
2021 arXiv   pre-print
We conduct an extensive experimental assessment and show that the algorithm finds functions that are competitive in space with state-of-the art techniques and provide 2-4× better lookup time.  ...  Algorithms that find such functions when n is large and retain constant evaluation time are of practical interest; for instance, search engines and databases typically use minimal perfect hash functions  ...  The result was achieved via a careful revisitation of the framework introduced by Fox, Chen, and Heath [15] (FCH) in 1992.  ... 
arXiv:2104.10402v1 fatcat:s5dvbkhkezf75lo3jn6evruz64

LT Codes For Efficient and Reliable Distributed Storage Systems Revisited [article]

Yongge Wang
2012 arXiv   pre-print
By employing the underlying ideas of efficient Belief Propagation (BP) decoding process in LT codes, this paper introduces two classes of codes called flat BP-XOR codes and array BP-XOR codes (which can  ...  However, Plank and Thomason's experimental results show that LDPC code performs well only asymptotically when the number of data fragments increases and it has the worst performance for small number of  ...  Doug Stinson and Yvo Desmedt, for some discussions on edge-colored graphs, Hamiltonian circuit, and factorization of complete graphs.  ... 
arXiv:1207.5542v1 fatcat:l74zsf5gavgvpdsfs7bw62vqpi

Functional Graph Revisited: Updates on (Second) Preimage Attacks on Hash Combiners [chapter]

Zhenzhen Bao, Lei Wang, Jian Guo, Dawu Gu
2017 Lecture Notes in Computer Science  
By exploiting more properties of cyclic nodes of functional graph, we find an improved preimage attack against the XOR combiner with a complexity of 2 5n/8 , while the previous best-known complexity is  ...  Moreover, we find the first generic second-preimage attack on Zipper hash with an optimal complexity of 2 3n/5 .  ...  The authors would like to thank the anonymous reviewers of CRYPTO 2017 and Itai Dinur for their valuable comments and suggestions.  ... 
doi:10.1007/978-3-319-63715-0_14 fatcat:aa5zjsel6jbetgluwlkhdswiku

Anonymous Signatures Revisited [chapter]

Vishal Saraswat, Aaram Yun
2009 Lecture Notes in Computer Science  
We revisit the notion of the anonymous signature, first formalized by Yang, Wong, Deng and Wang [12], and then further developed by Fischlin [6] and Zhang and Imai [13] .  ...  We present a new formalism of anonymous signature, where instead of the message, a part of the signature is withheld to maintain anonymity.  ...  Acknowledgements We thank anonymous reviewers for many constructive and helpful comments. Especially, we revised notions of the unpretendability, following criticisms on our previous definition.  ... 
doi:10.1007/978-3-642-04642-1_13 fatcat:6bab63dcqffshbqfbmmseyzawi

Revisiting Alphabet Reduction in Dinur's PCP

Venkatesan Guruswami, Jakub Opršal, Sai Sandeep, Raghu Meka, Jarosław Byrka
2020 International Workshop on Approximation Algorithms for Combinatorial Optimization  
size), and a composition step that brings back the alphabet size to an absolute constant (at the expense of a fixed constant factor loss in the soundness gap).  ...  Our composition step thus bypasses the concept of Assignment Testers from Dinur's proof, and we believe it is more intuitive - it is just a gadget reduction.  ...  . (13) The probability that our decoding satisfies edge e of Label Cover is at least i,j:π(i)=σ(j)f (i) 2ĝ (j) 2 = 1 − α,β |α|>1, or |β|>1, or α={i} and β={j} and π(i) =σ(j)f (α) 2ĝ (β) 2 (14) ≥ 1 − α  ... 
doi:10.4230/lipics.approx/random.2020.34 dblp:conf/approx/GuruswamiOS20 fatcat:acxlmcck7rbvxe6ssqeymlcgdm
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