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On the Construction of Pseudorandom Permutations: Luby—Rackoff Revisited

Moni Naor, Omer Reingold
1999 Journal of Cryptology  
The method is based on composing four (or three for weakened security) so called Feistel permutations, each of which requires the evaluation of a pseudo-random function.  ...  Luby and Racko 27] showed a method for constructing a pseudo-random permutation from a pseudo-random function.  ...  We thank the anonymous referees for their many helpful comments. It is di cult to overestimate Oded's contribution to the presentation of this paper.  ... 
doi:10.1007/pl00003817 fatcat:phcmfv5lobepthj6423hcctaha

Luby–Rackoff Revisited: On the Use of Permutations as Inner Functions of a Feistel Scheme

Gilles Piret
2006 Designs, Codes and Cryptography  
In this paper we are dealing with the security of the Feistel structure in the Luby-Rackoff model when the round functions are replaced by permutations.  ...  It is why we revisit Luby-Rackoff's proofs [6] in this specific case.  ...  In their seminal paper [6] , Luby and Rackoff introduced a model that permits the assessment of the security of some block cipher constructions.  ... 
doi:10.1007/s10623-005-3562-2 fatcat:ujnn5ihvs5fbfodmwrugoeetoy

On the XOR of Multiple Random Permutations [chapter]

Bart Mennink, Bart Preneel
2015 Lecture Notes in Computer Science  
A straightforward way of constructing an n-bit pseudorandom function is to XOR two or more pseudorandom permutations: p1 ⊕ . . . ⊕ p k .  ...  This XOR construction has gained broad attention over the last two decades. In this work, we revisit the security of this well-established construction.  ...  They named the problem "Luby-Rackoff backwards", referring to the celebrated result by Luby and Rackoff who showed how to construct a PRP from a PRF [21] .  ... 
doi:10.1007/978-3-319-28166-7_30 fatcat:wd7zux6cyfeoxpbazrg6qmtawq

How to Generate Pseudorandom Permutations Over Other Groups: Even-Mansour and Feistel Revisited [article]

Hector Bjoljahn Hougaard
2017 arXiv   pre-print
We show that Even and Mansour's original notions of secrecy are obtained on a one-key, group variant of the Even-Mansour cipher.  ...  We generalize the result by Kilian and Rogaway, that the Even-Mansour cipher is pseudorandom, to super pseudorandomness, also in the one-key, group case.  ...  As another consideration of block ciphers, the Feistel cipher construction of Luby and Rackoff [LR88] showed how to build pseudorandom permutations from pseudorandom functions.  ... 
arXiv:1707.01699v2 fatcat:btl7ikrsqbcsjotgrj3xqjitpy

Page 8338 of Mathematical Reviews Vol. , Issue 2000k [page]

2000 Mathematical Reviews  
of pseudorandom permutations: Luby-Rackoff revisited.  ...  Luby and C. W. Rackoff [SIAM J. Comput. 17 (1988), no. 2, 373-386; MR 89i:68025] showed a method for constructing a pseudorandom permutation from a pseudorandom function.  ... 

Public-Seed Pseudorandom Permutations [chapter]

Pratik Soni, Stefano Tessaro
2017 Lecture Notes in Computer Science  
This paper initiates the study of standard-model assumptions on permutations -or more precisely, on families of permutations indexed by a public seed.  ...  We introduce the notion of a public-seed pseudorandom permutation (psPRP), which is inspired by the UCE notion by Bellare, Hoang, and Keelveedhi (CRYPTO '13).  ...  Acknowledgments We wish to thank John Retterer-Moore for his involvement in an earlier stage of this project. We also thank the EUROCRYPT '17 anonymous reviewers for their insightful feedback.  ... 
doi:10.1007/978-3-319-56614-6_14 fatcat:2d7xhdjlnfedzcsdq22pcqyt24

An Algebraic System for Constructing Cryptographic Permutations over Finite Fields [article]

Arnab Roy, Matthias Steiner
2022 arXiv   pre-print
In addition, we prove a general upper bound on the differential uniformity of the GTDS.  ...  In view of these efforts, in this work we build an algebraic framework that allows the systematic exploration of viable and efficient design strategies for constructing symmetric-key (iterative) permutations  ...  result let's shortly revisit the notion of (KAC).  ... 
arXiv:2204.01802v2 fatcat:qkkx2ky7vfeotjuta74qsccx6m

The Related-Key Analysis of Feistel Constructions [chapter]

Manuel Barbosa, Pooya Farshim
2015 Lecture Notes in Computer Science  
However, irrespective of the number of rounds, no Feistel construction can resist related-key attacks where the keys can be offset by a constant.  ...  It is well known that the classical three-and four-round Feistel constructions are provably secure under chosen-plaintext and chosen-ciphertext attacks, respectively.  ...  Pooya Farshim was supported by grant Fi 940/4-1 of the German Research Foundation (DFG).  ... 
doi:10.1007/978-3-662-46706-0_14 fatcat:gg7huflgxvebdns7mcphyuma5u

Pseudorandomness of Basic Structures in the Block Cipher KASUMI

Ju-Sung Kang, Bart Preneel, Heuisu Ryu, Kyo Il Chung, Chee Hang Park
2003 ETRI Journal  
Thus, we cannot straightforwardly apply the Luby-Rackoff result to KASUMI.  ...  Based on the pseudorandomness of the FI function, we prove that the threeround KASUMI-like structure is not a pseudorandom permutation, but a four-round KASUMI-like structure is a pseudorandom permutation  ...  ACKNOWLEDGEMENTS Thanks to Tetsu Iwata for pointing out some flaws in the proof of Theorem 1 of [12] . We also appreciate the anonymous referees' valuable comments.  ... 
doi:10.4218/etrij.03.0102.0210 fatcat:ei45bb3zrzawnms2s6oyeupupe

On the Optimality of Non-Linear Computations of Length-Preserving Encryption Schemes [chapter]

Mridul Nandi
2015 Lecture Notes in Computer Science  
It is well known that three and four rounds of balanced Feistel cipher or Luby-Rackoff (LR) encryption for two blocks messages are pseudorandom permutation (PRP) and strong pseudorandom permutation (SPRP  ...  Motivating with these observations, we consider the following questions in this paper: What is the minimum number of invocations of block-functions required to achieve PRP or SPRP security over blocks  ...  The author would like to thank Lear Bahack who found an error of the SPRP distinguisher in one of the sub-cases.  ... 
doi:10.1007/978-3-662-48800-3_5 fatcat:tonruoea75hgremznrvcibqx5i

On Lai–Massey and quasi-Feistel ciphers

Aaram Yun, Je Hong Park, Jooyoung Lee
2010 Designs, Codes and Cryptography  
From this, we give a new proof for Vaudenay's theorems on the security of the Lai-Massey cipher, and also we introduce for Lai-Massey a new construction of pseudorandom permutation, analoguous to the construction  ...  We show that most of the works on the Feistel cipher can be naturally extended to the quasi-Feistel cipher.  ...  In theoretical cryptography, the result of Luby and Rackoff implies that pseudorandom permutations exist, if pseudorandom functions exist (which in turn is true, if one-way functions exist).  ... 
doi:10.1007/s10623-010-9386-8 fatcat:ar73otms5rdslavxcadi7kbu5m

How to Construct an Ideal Cipher from a Small Set of Public Permutations [chapter]

Rodolphe Lampe, Yannick Seurin
2013 Lecture Notes in Computer Science  
We show how to construct an ideal cipher with n-bit blocks and n-bit keys (i.e. a set of 2 n public n-bit permutations) from a small constant number of n-bit random public permutations.  ...  We analyze this construction in the plain indifferentiability framework of Maurer, Renner, and Holenstein (TCC 2004), and show that twelve rounds are sufficient to achieve indifferentiability from an ideal  ...  This must be contrasted with the classical Luby-Rackoff result stating that the 4-round Feistel construction with pseudorandom round functions yield a SPRP.  ... 
doi:10.1007/978-3-642-42033-7_23 fatcat:ayc6xcehrrhpblpg6wqy67gddm

On the Power of the Randomized Iterate

Iftach Haitner, Danny Harnik, Omer Reingold
2011 SIAM journal on computing (Print)  
This technique was used in [GKL93] to give a construction of pseudorandom generators from regular one-way functions.  ...  We consider two of the most fundamental theorems in Cryptography. The first, due to Håstad et al. [HILL99] , is that pseudorandom generators can be constructed from any one-way function.  ...  We also thank Tal Moran and Ariel Gabizon for reading a preliminary version of this manuscript.  ... 
doi:10.1137/080721820 fatcat:6hod36jhebellbeiaoyrz6xb6a

On the Power of the Randomized Iterate [chapter]

Iftach Haitner, Danny Harnik, Omer Reingold
2006 Lecture Notes in Computer Science  
This technique was used in [GKL93] to give a construction of pseudorandom generators from regular one-way functions.  ...  We consider two of the most fundamental theorems in Cryptography. The first, due to Håstad et al. [HILL99] , is that pseudorandom generators can be constructed from any one-way function.  ...  We also thank Tal Moran and Ariel Gabizon for reading a preliminary version of this manuscript.  ... 
doi:10.1007/11818175_2 fatcat:iut5gr2sjrfb5k77vgv6bey2pq

Applications of H-Technique: Revisiting Symmetric Key Security Analysis [article]

Ashwin Jha, Mridul Nandi
2018 IACR Cryptology ePrint Archive  
In this systematization of knowledge (SoK) paper, we aim to provide a brief survey on the H-technique.  ...  The SoK is in four parts: First, we redevelop the necessary nomenclatures and tools required to study the security of any symmetric key design, especially in the H-technique setting.  ...  Figure 6 . 1 : 61 Figure 6.1: The 3-round Luby-Rackoff or LR3 construction. Figure 6 . 2 : 62 Figure 6.2: The 3-round TPRP-based Luby-Rackoff or TLR3 construction.  ... 
dblp:journals/iacr/JhaN18 fatcat:znobnjw6pjbwtein3ebsofrbyu
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