Pseudorandom Permutation Research Articles

Some applications of IFS based on square symmetries

This paper describes a fractal based method for generating the pseudorandom permutations. We construct an Iterated Function System (IFS) belonging to the class of square symmetries and simulate the pseudorandom walk on a square. In this way some families of key based permutations are generated. The cardinalities of generated families are analysed.

A robust and secure chaotic standard map based pseudorandom permutation-substitution scheme for image encryption

A novel and robust chaos-based pseudorandom permutation–substitution scheme for image encryption is proposed. It is a loss-less symmetric block cipher and specifically designed for the color images but may also be used for the gray scale images. A secret key of 161-bit, comprising of the initial conditions and system parameter of the chaotic map (the standard map), number of iterations and number of rounds, is used in the algorithm. The whole encryption process is the sequential execution of a preliminary permutation and a fix number of rounds (as specified in the secret key) of substitution and main permutation of the 2D matrix obtained from the 3D image matrix. To increase the speed of encryption all three processes: preliminary permutation, substitution and main permutation are done row-by-row and column-by-column instead of pixel-by-pixel. All the permutation processes are made dependent on the input image matrix and controlled through the pseudo random number sequences (PRNS) generated from the discretization of chaotic standard map which result in both key sensitivity and plaintext sensitivity. However each substitution process is initiated with the initial vectors (different for rows and columns) generated using the secret key and chaotic standard map and then the properties of rows and column pixels of input matrix are mixed with the PRNS generated from the standard map. The security and performance analysis of the proposed image encryption has been performed using the histograms, correlation coefficients, information entropy, key sensitivity analysis, differential analysis, key space analysis, encryption/decryption rate analysis etc. Results suggest that the proposed image encryption technique is robust and secure and can be used for the secure image and video communication applications.

Lossy Compression and Iterative Reconstruction for Encrypted Image

This work proposes a novel scheme for lossy compression of an encrypted image with flexible compression ratio. A pseudorandom permutation is used to encrypt an original image, and the encrypted data are efficiently compressed by discarding the excessively rough and fine information of coefficients generated from orthogonal transform. After receiving the compressed data, with the aid of spatial correlation in natural image, a receiver can reconstruct the principal content of the original image by iteratively updating the values of coefficients. This way, the higher the compression ratio and the smoother the original image, the better the quality of the reconstructed image.

Reconfigurable Hardware Implementations of Tweakable Enciphering Schemes

Tweakable enciphering schemes are length-preserving block cipher modes of operation that provide a strong pseudorandom permutation. It has been suggested that these schemes can be used as the main building blocks for achieving in-place disk encryption. In the past few years, there has been an intense research activity toward constructing secure and efficient tweakable enciphering schemes. But actual experimental performance data of these newly proposed schemes are yet to be reported. In this paper, we present optimized FPGA implementations of six tweakable enciphering schemes, namely, HCH, HCTR, XCB, EME, HEH, and TET, using a 128-bit AES core as the underlying block cipher. We report the performance timings of these modes when using both pipelined and sequential AES structures. The universal polynomial hash function included in the specification of HCH, HCHfp (a variant of HCH), HCTR, XCB, TET, and HEH was implemented using a Karatsuba multiplier as the main building block. We provide detailed algorithm analysis of each of the schemes trying to exploit their inherent parallelism as much as possible. Our experiments show that a sequential AES core is not an attractive option for the design of these modes as it leads to rather poor throughput. In contrast, according to our place-and-route results on a Xilinx Virtex 4 FPGA, our designs achieve a throughput of 3.95 Gbps for HEH when using an encryption/decryption pipelined AES core, and a throughput of 5.71 Gbps for EME when using a encryption-only pipeline AES core. The performance results reported in this paper provide experimental evidence that hardware implementations of tweakable enciphering schemes can actually match and even outperform the data rates achieved by state-of-the-art disk controllers, thus showing that they might be used for achieving provably secure in-place hard disk encryption.

Power of a Public Random Permutation and Its Application to Authenticated Encryption

This paper shows that many independent pseudorandom permutations over {0,1} <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> can be obtained from a single public random permutation and secret n bits. It is then proved that a slightly modified IAPM (an authenticated-encryption scheme) is secure even if the underlying block cipher F is publicly accessible (as a blackbox). A similar result is derived for OCB mode, too. The security proofs are based on our first result, and they are extremely simple. Finally, it is shown that our security bound is tight within a constant factor.

Notions and relations for RKA-secure permutation and function families

The theory of designing block ciphers is mature, having seen significant progress since the early 1990s for over two decades, especially during the AES development effort. Nevertheless, interesting directions exist, in particular in the study of the provable security of block ciphers along similar veins as public-key primitives, i.e. the notion of pseudorandomness (PRP) and indistinguishability (IND). Furthermore, recent cryptanalytic progress has shown that block ciphers well designed against known cryptanalysis techniques including related-key attacks (RKA) may turn out to be less secure against RKA than expected. The notion of provable security of block ciphers against RKA was initiated by Bellare and Kohno, and subsequently treated by Lucks. Concrete block cipher constructions were proposed therein with provable security guarantees. In this paper, we are interested in the security notions for RKA-secure block ciphers. In the first part of the paper, we show that secure tweakable permutation families in the sense of strong pseudorandom permutation (SPRP) can be transformed into secure permutation families in the sense of SPRP against some classes of RKA (SPRP–RKA). This fact allows us to construct a secure SPRP–RKA cipher which is faster than the Bellare–Kohno PRP–RKA cipher. We also show that function families of a certain form secure in the sense of a pseudorandom function (PRF) can be transformed into secure permutation families in the sense of PRP against some classes of RKA (PRP–RKA). We can exploit it to get various constructions secure against some classes of RKA from known MAC algorithms. Furthermore, we discuss how the key recovery (KR) security of the Bellare–Kohno PRP–RKA, the Lucks PRP–RKA and our SPRP–RKA ciphers relates to existing types of attacks on block ciphers like meet-in-the-middle and slide attacks. In the second part of the paper, we define other security notions for RKA-secure block ciphers, namely in the sense of indistinguishability (IND) and non-malleability, and show the relations between these security notions. In particular, we show that secure tweakable permutation families in the sense of IND (resp. non-malleability) can be transformed into RKA-secure permutation families in the sense of IND (resp. non-malleability).

On Lai–Massey and quasi-Feistel ciphers

We introduce a new notion called a quasi-Feistel cipher, which is a generalization of the Feistel cipher, and contains the Lai---Massey cipher as an instance. We show that most of the works on the Feistel cipher can be naturally extended to the quasi-Feistel cipher. 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 of Naor---Reingold using pairwise independent permutations. Also, we prove the birthday security of (2b?1)- and (3b?2)-round unbalanced quasi-Feistel ciphers with b branches against CPA and CPCA attacks, respectively.

An image encryption scheme with a pseudorandom permutation based on chaotic maps

Many research efforts for image encryption schemes have elaborated for designing nonlinear functions since security of these schemes closely depends on inherent characteristics of nonlinear functions. It is commonly believed that a chaotic map can be used as a good candidate of a nonlinear component for image encryption schemes. We propose a new image encryption algorithm using a large pseudorandom permutation which is combinatorially generated from small permutation matrices based on chaotic maps. The random-like nature of chaos is effectively spread into encrypted images by using the permutation matrix. The experimental results show that the proposed encryption scheme provides comparable security with that of the conventional image encryption schemes based on Baker map or Logistic map.

Tweakable Pseudorandom Permutation from Generalized Feistel Structure

Tweakable pseudorandom permutations have wide applications such as the disk sector encryption, and the underlying primitive for efficient MACs and authenticated encryption schemes. Goldenberg et al. showed constructions of a tweakable pseudorandom permutation based on the Feistel structure. In this paper, we explore the possibility of designing tweakable pseudorandom permutations based on the Generalized Feistel Structure. We show that tweakable pseudorandom permutations can be obtained without increasing the number of rounds compared to the non-tweakable versions. We also present designs that take multiple tweaks as input.

Security of the Misty Structure Using Involutions as Round Functions

In this paper, we study the security of the Misty structure, where each round function is chosen at random from the set of involutions. Based on the game-playing framework, we prove the pseudorandomness of the 3-round R-Misty structure and the 4-round L-Misty structure as well as the super-pseudorandomness of the 5-round R-Misty structure for m « 2n/2, where m denotes the number of queries and 2n denotes the block size. We also give similar results for the Misty structures such that each round function is chosen at random from the set of involutions with a constant number of fixed points. Our results generalize the results of [10] giving the first construction of a (strong) pseudorandom permutation based on random involutions (without any restriction on the number of fixed points), and suggest a new criterion for design of block ciphers in an involutional Misty structure that each round function should have a constant number of fixed points.

Efficient Tweakable Enciphering Schemes From (Block-Wise) Universal Hash Functions

This paper describes several constructions of tweakable strong pseudorandom permutations (SPRPs) built from different modes of operations of a block cipher and suitable universal hash functions. For the electronic codebook (ECB) mode based construction, an invertible blockwise universal hash function is required. We simplify an earlier construction of such a function described by Naor and Reingold. The other modes of operations considered are the output feedback (OFB) mode and a counter-like mode. All the constructions make the same number of block cipher calls and the same number of multiplications. Combined with a class of polynomials defined by Bernstein, the new constructions provide the currently best known algorithms for the important practical problem of disk encryption.

Efficient Pseudorandom-Function Modes of a Block-Cipher-Based Hash Function

SUMMARY This article discusses the provable security of pseudorandom-function (PRF) modes of an iterated hash function using a block cipher. The iterated hash function uses the Matyas-Meyer-Oseas (MMO) mode for the compression function and the Merkle-Damgard with a permutation (MDP) for the domain extension transform. It is shown that the keyed-via-IV mode and the key-prefix mode of the iterated hash function are pseudorandom functions if the underlying block cipher is a pseudorandom permutation under a related-key attack with respect to the permutation used in MDP. More precisely, the key-prefix mode also requires that EIV(K) ⊕ K is pseudoramdom, where E is the underlying block cipher, IV is the fixed initial value of the hash function, and K is a secret key. It is also confirmed that the MMO compression function is the best choice with MDP among the block-cipher-based compression functions in the PreneelGovaerts-Vandewalle model in terms of the provable security.

A general mixing strategy for the ECB-Mix-ECB mode of operation

EME is an important mode of operation of a block cipher. It converts an n-bit block cipher into a strong pseudo-random permutation which works on longer length strings. In this short note, we generalize the mixing layer of EME. The generalization is done using a linear map ψ from F 2 n to itself, where n is the block size of the underlying block cipher. A possible instantiation of ψ is using word oriented LFSRs. For n = 128 , this implementation of ψ results in the mixing layer being processed about twice as fast as that in the original EME mode of operation.

Performance of Two-Disk Failure-Tolerant Disk Arrays

RAID5 disk arrays use the rebuild process to reconstruct the contents of a failed disk on a spare disk, but this process is unsuccessful if latent sector failures are encountered or a second disk failure occurs. The high cost of data loss has led to two-disk failure-tolerant (2DFT) arrays: RAID6, EVENODD, row-diagonal parity (RDP), and RM2. RAID6 uses Reed-Solomon (RS) codes, whereas the latter three use parity encoding. This paper is concerned with the performance from the viewpoint of disk accesses, which, with an appropriate choice of symbol sizes, is the same for RAID6, EVENODD, and RDP, rather than the computational cost (number of XOR operations). We compare the performance of 2DFTs with each other, as well as RAIDO and RAID5 in normal and degraded operating modes. We derive cost functions for processing discrete disk accesses. The mean response time can be obtained analytically with Poisson arrivals and first-come, first-served (FCFS) scheduling. A simulation is used for validation, calibrating the approximate fork-join response analysis, and shortest-access-time-first (SATF) scheduling. The response time for read requests in RAID6 and RM2 is higher than RAID5 and RAIDO and increases with the fraction of write requests. When there is a single disk failure, RM2 outperforms RAID6 since it has a smaller parity group size than RAID6, but RAID6 outperforms RM2 with two disk failures because of its costlier recovery process. Disk loads in RM2 and RAID6 in degraded mode are unbalanced, and a solution based on pseudorandom permutations is proposed for this purpose

A Parallelizable Message Authentication Code

This paper defines and analyzes a fully deterministic parallelizable block-cipher mode of operation for message authentication— DPMAC (deterministic parallelizable message authentication code). DPMAC is constructed based on a 128-bit block cipher, works for strings of any bit length, and employs a single block-cipher key. Its security is proved, using the Game-Playing technique to quantify an adversary's forgery probability in terms of the quality of the block cipher as a pseudo-random permutation.

Plaintext Simulatability

We propose a new security class, called plaintext simulatability, defined over the public-key encryption schemes. The notion of plaintext simulatability (denoted PS) is similar to the notion of plaintext awareness (denoted PA) defined in [3], but it is properly a weaker security class for public-key encryption. It is known that PA implies the class of CCA2-secure encryption (denoted IND-CCA2) but not vice versa. In most cases, PA is unnecessarily strong---In such cases, PA is only used to study that the public-key encryption scheme involved meets IND-CCA2, because it looks much easier to treat the membership of PA than to do directly the membership of IND-CCA2. We show that PS also implies IND-CCA2, while preserving such a technical advantage as well as PA. We present two novel CCA2-secure public-key encryption schemes, which should have been provided with more complicated security analyses. One is a random-oracle version of Dolev-Dwork-Naor's encryption scheme [9]. Unlike the original scheme, this construction is efficient. The other is a public-key encryption scheme based on a strong pseudo-random permutation family [16] which provides the optimal ciphertext lengths for verifying the validity of ciphertexts, i.e., (ciphertext size) = (message size) + (randomness size). According to [19], such a construction remains open. Both schemes meet PS but not PA.

Systematic Recursive Construction of LDPC Codes

This letter presents a systematic and recursive method to construct good low-density parity-check (LDPC) codes, especially those with high rate. The proposed method uses a parity check matrix of a quasi-cyclic LDPC code with given row and column weights as a core upon which the larger code is recursively constructed with extensive use of pseudorandom permutation matrices. This construction preserves the minimum distance and girth properties of the core matrix and can generate either regular, or irregular LDPC codes. The method provides a unique representation of the code in compact notation.

OCB

We describe a parallelizable block-cipher mode of operation that simultaneously provides privacy and authenticity. OCB encrypts-and-authenticates a nonempty string M ∈ {0, 1}* using ⌈| M |/ n ⌉ + 2 block-cipher invocations, where n is the block length of the underlying block cipher. Additional overhead is small. OCB refines a scheme, IAPM, suggested by Charanjit Jutla. Desirable properties of OCB include the ability to encrypt a bit string of arbitrary length into a ciphertext of minimal length, cheap offset calculations, cheap key setup, a single underlying cryptographic key, no extended-precision addition, a nearly optimal number of block-cipher calls, and no requirement for a random IV. We prove OCB secure, quantifying the adversary's ability to violate the mode's privacy or authenticity in terms of the quality of its block cipher as a pseudorandom permutation (PRP) or as a strong PRP, respectively.

3GPP 무결성 알고리즘 f9의 증명가능 안전성

3GPP의 비동기식 IMT-2000 시스템의 보안 구조에는 표준 무결성 알고리즘 f9가 있다. f9는 비동기식(W-CDMA) IMT-2000의 무선 구간에서 데이터 무결성과 시그널링 데이터의 출처를 인증하기 위한 메시지 인증 코드(MAC)를 계산하는 알고리즘으로 블록 암호 KASUMI에 기반한 CBC-MAC의 변형이다. 이 논문은 f9의 증명 가능한 안전성을 제공한다. 기반이 되는 블록 암호가 유사 랜덤 순열이면 어떤 공격자에 대해서도 f9가 안전함을 증명한다. Within the security architecture of the 3GPP system there is a standardised integrity algorithm f9. The integrity algorithm f9 computes a MAC to authenticate the data integrity and data origin of signalling data over a radio access link of W-CDMA IMT-2000. f9 is a variant of the standard CBC MAC based on the block cipher KASUMI. In this paper we provide the provable security of f9 We prove that f9 is secure by giving concrete bound on an adversary's inability to forge in terms of her inability to distinguish the underlying block cipher from a pseudorandom permutation.

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.