In cryptography, a pseudorandom permutation (PRP) is a function that cannot be distinguished from a random permutation (that is, a permutation selected at random with uniform probability, from the family of all permutations on the function's domain) with practical effort.
Let F be a mapping . F is a PRP if and only if
For any , is a bijection from to , where .
For any , there is an "efficient" algorithm to evaluate for any ,.
For all probabilistic polynomial-time distinguishers : , where is chosen uniformly at random and is chosen uniformly at random from the set of permutations on n-bit strings.
A pseudorandom permutation family is a collection of pseudorandom permutations, where a specific permutation may be chosen using a key.
The idealized abstraction of a (keyed) block cipher is a truly random permutation on the mappings between plaintext and ciphertext. If a distinguishing algorithm exists that achieves significant advantage with less effort than specified by the block cipher's security parameter (this usually means the effort required should be about the same as a brute force search through the cipher's key space), then the cipher is considered broken at least in a certificational sense, even if such a break doesn't immediately lead to a practical security failure.
Modern ciphers are expected to have super pseudorandomness.
That is, the cipher should be indistinguishable from a randomly chosen permutation on the same message space, even if the adversary has black-box access to the forward and inverse directions of the cipher.
Michael Luby and Charles Rackoff showed that a "strong" pseudorandom permutation can be built from a pseudorandom function using a Luby–Rackoff construction which is built using a Feistel cipher.
An unpredictable permutation (UP) Fk is a permutation whose values cannot be predicted by a fast randomized algorithm. Unpredictable permutations may be used as a cryptographic primitive, a building block for cryptographic systems with more complex properties.
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This course introduces the basics of cryptography. We review several types of cryptographic primitives, when it is safe to use them and how to select the appropriate security parameters. We detail how
In cryptography, a Feistel cipher (also known as Luby–Rackoff block cipher) is a symmetric structure used in the construction of block ciphers, named after the German-born physicist and cryptographer Horst Feistel, who did pioneering research while working for IBM; it is also commonly known as a Feistel network. A large proportion of block ciphers use the scheme, including the US Data Encryption Standard, the Soviet/Russian GOST and the more recent Blowfish and Twofish ciphers.
Explores the power of interaction in cryptographic primitives and conventional cryptanalysis techniques.
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Four recent trends have emerged in the evolution of authenticated encryption schemes: (1) Regarding simplicity, the adoption of public permutations as primitives allows for sparing a key schedule and the need for storing round keys; (2) using the sums of p ...
In this paper we characterize all 2n-bit-to-n-bit Pseudorandom Functions (PRFs) constructed with the minimum number of calls to n-bit-to-n-bit PRFs and arbitrary number of linear functions. First, we show that all two-round constructions are either classic ...
In this paper, we study the security of the Key-Alternating Feistel (KAF) ciphers, a class of key alternating ciphers with the Feistel structure, where each round of the cipher is instantiated with n-bit public round permutation Pi\documentclass[12pt]{mini ...