---
_id: '3210'
abstract:
- lang: eng
text: 'Luby and Rackoff showed how to construct a (super-)pseudo-random permutation
{0,1}2n→ {0,1}2n from some number r of pseudo-random functions {0,1}n → {0,1}n.
Their construction, motivated by DES, consists of a cascade of r Feistel permutations.
A Feistel permutation 1for a pseudo-random function f is defined as (L, R) → (R,L
⊕ f (R)), where L and R are the left and right part of the input and ⊕ denotes
bitwise XOR or, in this paper, any other group operation on {0,1}n. The only non-trivial
step of the security proof consists of proving that the cascade of r Feistel permutations
with independent uniform random functions {0,1}n → {0,1}n, denoted Ψ2nr is indistinguishable
from a uniform random permutation {0,1}2n → {0,1}2n by any computationally unbounded
adaptive distinguisher making at most O(2cn) combined chosen plaintext/ciphertext
queries for any c < α, where a is a security parameter. Luby and Rackoff proved
α = 1/2 for r = 4. A natural problem, proposed by Pieprzyk is to improve on α
for larger r. The best known result, α = 3/4 for r = 6, is due to Patarin. In
this paper we prove a = 1 -O(1/r), i.e., the trivial upper bound α = 1 can be
approached. The proof uses some new techniques that can be of independent interest. '
alternative_title:
- LNCS
author:
- first_name: Ueli
full_name: Maurer, Ueli M
last_name: Maurer
- first_name: Krzysztof Z
full_name: Krzysztof Pietrzak
id: 3E04A7AA-F248-11E8-B48F-1D18A9856A87
last_name: Pietrzak
orcid: 0000-0002-9139-1654
citation:
ama: 'Maurer U, Pietrzak KZ. The security of many round Luby Rackoff pseudo random
permutations. In: Vol 2656. Springer; 2003:544-561. doi:10.1007/3-540-39200-9_34'
apa: 'Maurer, U., & Pietrzak, K. Z. (2003). The security of many round Luby
Rackoff pseudo random permutations (Vol. 2656, pp. 544–561). Presented at the
EUROCRYPT: Theory and Applications of Cryptographic Techniques, Springer. https://doi.org/10.1007/3-540-39200-9_34'
chicago: Maurer, Ueli, and Krzysztof Z Pietrzak. “The Security of Many Round Luby
Rackoff Pseudo Random Permutations,” 2656:544–61. Springer, 2003. https://doi.org/10.1007/3-540-39200-9_34.
ieee: 'U. Maurer and K. Z. Pietrzak, “The security of many round Luby Rackoff pseudo
random permutations,” presented at the EUROCRYPT: Theory and Applications of Cryptographic
Techniques, 2003, vol. 2656, pp. 544–561.'
ista: 'Maurer U, Pietrzak KZ. 2003. The security of many round Luby Rackoff pseudo
random permutations. EUROCRYPT: Theory and Applications of Cryptographic Techniques,
LNCS, vol. 2656, 544–561.'
mla: Maurer, Ueli, and Krzysztof Z. Pietrzak. *The Security of Many Round Luby
Rackoff Pseudo Random Permutations*. Vol. 2656, Springer, 2003, pp. 544–61,
doi:10.1007/3-540-39200-9_34.
short: U. Maurer, K.Z. Pietrzak, in:, Springer, 2003, pp. 544–561.
conference:
name: 'EUROCRYPT: Theory and Applications of Cryptographic Techniques'
date_created: 2018-12-11T12:02:02Z
date_published: 2003-06-04T00:00:00Z
date_updated: 2021-01-12T07:41:49Z
day: '04'
doi: 10.1007/3-540-39200-9_34
extern: 1
intvolume: ' 2656'
month: '06'
page: 544 - 561
publication_status: published
publisher: Springer
publist_id: '3473'
quality_controlled: 0
status: public
title: The security of many round Luby Rackoff pseudo random permutations
type: conference
volume: 2656
year: '2003'
...