F Functions Research Articles

On Generalized Feistel Structures Using the Diffusion Switching Mechanism

To design secure blockciphers, estimating immunity against differential attack and linear attack is essential. Recently, Diffusion Switching Mechanism (DSM) is proposed as a design framework to enhance the immunity of Feistel structure against differential attack and linear attack. In this paper, we give novel results on the effect of DSM on three generalized Feistel structures, i.e. Type-I, Type-II and Nyberg's structures. We first show a method for roughly estimating lower bounds of a number of active S-boxes in Type-I and Type-II structures using DSM. Then we propose an improved search algorithm to find lower bounds for generalized structures efficiently. Experimental results obtained by the improved algorithm show that DSM raises lower bounds for all of the structures, and also show that Nyberg's structure has the slowest diffusion effect among them when SP-type F-functions are used.

Improved Feistel-based ciphers for wireless sensor network security

Wireless sensor networks (WSNs) are exposed to a variety of attacks. The quality and complexity of attacks are rising day by day. The proposed work aims at showing how the complexity of modern attacks is growing accordingly, leading to a similar rise in methods of resistance. Limitations in computational and battery power in sensor nodes are constraints on the diversity of security mechanisms. We must apply only suitable mechanisms to WSN where our approach was motivated by the application of an improved Feistel scheme. The modified accelerated-cipher design uses data-dependent permutations, and can be used for fast hardware, firmware, software and WSN encryption systems. The approach presented showed that ciphers using this approach are less likely to suffer intrusion of differential cryptanalysis than currently used popular WSN ciphers like DES, Camellia and so on.

Differential fault analysis on the contracting UFN structure, with application to SMS4 and MacGuffin

The contracting unbalanced Feistel networks (UFN) is a particular structure in the block ciphers, where the “left half” and the “right half” are not of equal size, and the size of the domain of one half is larger than that of the range. This paper studies the security of the contracting UFN structure against differential fault analysis (DFA). We propose two basic byte-oriented fault models and two corresponding attacking methods. Then we implement the attack on two instances of the contracting UFN structure, the block ciphers SMS4 and MacGuffin. The experiments require 20 and 4 faulty ciphertexts to recover the 128-bit secret key of SMS4 in the two fault models, respectively. Under similar hypothesis, MacGuffin is breakable with 355 and 165 faulty ciphertexts, respectively. So our work not only builds up a general model of DFA on the contracting UFN structure and ciphers, but also provides a new reference for fault analysis on other block ciphers.

Confidential Communication Through Chaos Encryption in Wireless Sensor Network

Abstract A new byte block cipher algorithm with discrete chaos and Feistel structure has been studied for confidential communication in wireless sensor network to improve security. After permutation, the byte block was encrypted through a Feistel structure in multiple turns and afterwards replaced again. The child keys are the composite sequence of discrete chaos and linear congruence sequences. Both the plain text and cipher text are of 8 bits. The number of keys is alterable. A nonlinear encryption function in the Feistel structure with chaos was constructed. The cipher algorithm was realized in the Micaz node, and the confidential communication experiment in wireless sensor network was completed successfully. Additional ROM memory required for the cipher algorithm is 4144 bytes and an additional RAM memory 61 bytes. The cipher algorithm is nonlinear chaos and the Feistel structure holds the best of the RC6, DES and SKIPJACK cipher algorithms.The result shows that the algorithm needs a little memory and is safe at a high level.

Tamper Proofing by Design Using Generalized Involution-Based Concurrent Error Detection for Involutional Substitution Permutation and Feistel Networks

Secure operation of cryptographic algorithms is critical to the success of secure transactions. Fault-based attacks that recover secret keys by deliberately introducing fault(s) in cipher implementations and analyzing the faulty outputs have been proven to be extremely powerful. Substitution Permutation Networks (SPN) and Feistel Networks (FN) are the two important classes of Symmetric Block Ciphers. Some SPN ciphers and all FN Ciphers satisfy the involution property. A function F is an involution if F(F(x)) = x. In this paper, we investigate tamper proofing techniques that use low cost involution-based time redundancy concurrent error detection (CED) schemes for involutional SPN and FN symmetric block ciphers. We incorporated this tamper proofing by design technique in a hardware implementation of the 128-bit ANUBIS SPN cipher (an involution variant of the Advanced Encryption Standard (AES)) and the 128-bit TwoFish FN cipher (an AES finalist). We performed fault simulation at both the algorithm and the gate level to show that the low-cost involution-based CED schemes, in addition to detecting all transient faults, can detect all single-bit permanent faults and > 99 percent of all multiple-bit permanent faults. Consequently, this low cost CED technique can protect the crypto device against Differential Fault Analysis (DFA) attacks.

Applying evolutionary computation methods for the cryptanalysis of Feistel ciphers

In this contribution instances of a problem introduced by the differential cryptanalysis of Feistel cryptosystems are formulated as optimization tasks. The performance of Evolutionary Computation methods on these tasks is studied for a representative Feistel cryptosystem, the Data Encryption Standard. The results indicate that the proposed methodology is efficient in handling this type of problems and furthermore, that its effectiveness depends mainly on the construction of the objective function. This approach is applicable to all Feistel cryptosystems that are amenable to differential cryptanalysis.

Chaotic block ciphers: from theory to practical algorithms

Digital chaotic ciphers have been investigated for more than a decade. However, their overall performance in terms of the tradeoff between security and speed, as well as the connection between chaos and cryptography, has not been sufficiently addressed. We propose a chaotic Feistel cipher and a chaotic uniform cipher. Our plan is to examine crypto components from both dynamical-system and cryptographical points of view, thus to explore connection between these two fields. In the due course, we also apply dynamical system theory to create cryptographically secure transformations and evaluate cryptographical security measures

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

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. There is a priori no reason to think that the security bounds remain the same in this case, as illustrated by Knudsen's attack [5]. It is why we revisit Luby---Rackoff's proofs [6] in this specific case. The conclusion is that when the inner functions are random permutations, a 3-round (resp. 4-round) Feistel scheme remains secure against pseudorandom (resp. superpseudorandom) distinguishers as long as m 2n/2 (with m the number of queries and 2n the block size).

On the application of wide-trail strategy to improve an extended feistel cryptosystem

In this paper, we discuss a wide-trail-strategy-based method able to enhance the security offered by an encryption scheme developed in the University of Ferrara and based on an extended Feistel structure. By adding a new diffusion layer to the basic round transformation of the original system, we are able to increase the amount of active transformations, improving both the strength of the scheme against linear and differential attacks and the whole cipher performance by considerably reducing the system decoding time.

Linear provable security for a class of unbalanced feistel network

A structure iterated by the unbalanced Feistel networks is introduced. It is showed that this structure is provable resistant against linear attack. The main result of this paper is that the upper bound of r-round (r⩾2m) linear hull probabilities are bounded by q 2 when around function F is bjective and the maximal linear hull probabilities of round function F is q. Application of this structure to block cipher designs brings out the provable security against linear attack with the upper bounds of probabilities.

Software performance characterisation of block cipher structures using S-boxes and linear mappings

A new framework is presented for evaluating the performance characteristics of block cipher structures composed of S-boxes and maximum distance separable (MDS) mappings. In particular, a novel performance metric is introduced and applied to nested substitution-permutation networks and Feistel networks with round functions composed of S-boxes and MDS mappings. Within each cipher structure, many cases are considered based on two types of S-boxes (4×4 and 8×8) and parameterised MDS mappings. In the study of each case, the performance is analysed based on a table lookup implementation. Although this implementation method is the typical approach used for software realisation, it may also be applicable to hardware realisation in some instances. Cipher security, in the form of resistance to differential and linear attacks, is applied as a basis which is used to normalise the performance in the analysis. Because the discussed structures are similar to many existing ciphers such as AES and Camellia, the analysis provides a meaningful mechanism for seeking efficient ciphers through a wide comparison of security, performance, and implementation methods.

Decorrelation: A Theory for Block Cipher Security

Pseudorandomness is a classical model for the security of block ciphers. In this paper we propose convenient tools in order to study it in connection with the Shannon Theory, the Carter–Wegman universal hash functions paradigm, and the Luby–Rackoff approach. This enables the construction of new ciphers with security proofs under specific models. We show how to ensure security against basic differential and linear cryptanalysis and even more general attacks. We propose practical construction schemes.

Distinguishing attack on five-round Feistel networks

Recently it was shown (by J. Patarin) how to distinguish a general five-round Feistel network from a random permutation using (23n/2) chosen plaintexts or (27n/4) known plaintexts. The present authors report improvement of these results and a distinguisher is presented which uses roughly 2n chosen plaintexts or roughly 23n/2 known plaintexts.

The Security of Feistel Ciphers with Six Rounds or Less

This paper considers the security of Feistel networks where the round func- tions are chosen at random from a family of 2 k randomly chosen functions for any k. Also considered are the networks where the round functions are themselves permuta- tions, since these have applications in practice. The constructions are attacked under the assumption that a key-recovery attack on one round function itself requires an exhaus- tive search over all 2 k possible functions. Attacks are given on all three-, four-, five-, and six-round Feistel constructions and interesting bounds on their security level are obtained. In a chosen text scenario the key recovery attacks on the four-round construc- tions, the analogue to the super pseudorandom permutations in the Luby and Rackoff model, take roughly only the time of an exhaustive search for the key of one round. A side result of the presented attacks is that some constructions, which have been proved super pseudorandom in the model of Luby and Rackoff, do not seem to offer more security in our model than constructions which are not super pseudorandom.

On Decorrelated Fast Cipher

Decorrelated Fast Cipher(DFC) is a candidate for the Advanced Encryption Standard (AES). It is shown that the cryptographic properties of the confusion permutation of DFC are weak in this paper. With the same F-function of DFC, a Feistel cipher VDFC which has no resistance against differential cryptanalysis is constructed. This demonstrates the importance of the key addition into DFC sufficiently. As a result, DFC may not be qualified candidate for the AES.

On the Construction of Pseudorandom Permutations: Luby—Rackoff Revisited

Luby and Rackoff [26] showed a method for constructing a pseudorandom permutation from a pseudorandom function. The method is based on composing four (or three for weakened security) so-called Feistel permutations, each of which requires the evaluation of a pseudorandom function. We reduce somewhat the complexity of the construction and simplify its proof of security by showing that two Feistel permutations are sufficient together with initial and final pairwise independent permutations. The revised construction and proof provide a framework in which similar constructions may be brought up and their security can be easily proved. We demonstrate this by presenting some additional adjustments of the construction that achieve the following: ? Reduce the success probability of the adversary. ? Provide a construction of pseudorandom permutations with large input-length using pseudorandom functions with small input-length.

Developments in generalised Feistel networks

Nyberg (1996) obtained an upper bound on the maximum average of differential probability for a generalised Feistel network. A counter-example to this result is given.

On Weaknesses of Non–surjective Round Functions

We propose a new attack on Feistel ciphers with a non-surjective round function such as the CAST cipher family and LOKI91. We extend the attack towards block ciphers that use a non-uniformly distributed round function and apply the extended attack to the CAST family. This attack demonstrates that the round function of a Feistel cipher with six to eight rounds needs to be surjective and sufficiently uniform.

Block Ciphers: Analysis, Design and Applications

In this thesis we study cryptanalysis, applications and design of secret key block ciphers. In particular, the important class of <em> Feistel ciphers</em> is studied, which has a number of rounds, where in each round one applies a cryptographically weak function.

Practically Secure Feistel Ciphers

In this paper we give necessary design principles to be used, when constructing secure Feistel ciphers. We introducee a new concept, <strong> practical security</strong> against linear and differential attacks on Feistel ciphers. We give examples of such Feistel ciphers (practically) resistant to differential attacks, linear attacks and other attacks.