Pseudorandom Permutation Research Articles

Exposing the most match parity bit approach (MMPB-A) for data concealment in digital images

Steganography was originally developed to hide and transmit sensitive information. One major advancement in this field is the ability to hide data within digital images. Significant progress has been made, demonstrating effective methods for concealing data. Various techniques have been used, including statistical steganography, distortion techniques, and the Discrete Cosine Transform (DCT). However, the Least Significant Bit (LSB) method is particularly important and remains the most widely used. Researchers have developed methods based on these principles, such as pseudorandom permutation. This paper introduces the Most Match Parity Bit Approach (MMPB-A), which is based on the LSB method. MMPB-A strategically identifies the parity bits of selected pixels to embed information in cover images. It uses a six-bit encryption for each symbol, allowing ample space to hide information while preserving similarity and secrecy. Additionally, encoding hidden data indices in a three-bit code enhances data concealment and ensures greater confidentiality.

A Generic Construction of CCA-Secure Identity-Based Encryption with Equality Test against Insider Attacks

Identity-based encryption with equality test (IBEET) is a generalization of the traditional identity-based encryption (IBE) and public key searchable encryption, where trapdoors enable users to check whether two ciphertexts of distinct identities are encryptions of the same plaintext. By definition, IBEET cannot achieve indistinguishability security against insiders, i.e., users who have trapdoors. To address this issue, IBEET against insider attacks (IBEETIA) was later introduced as a dual primitive. While all users of IBEETIA are able to check whether two ciphertexts are encryptions of the same plaintext, only users who have tokens are able to encrypt plaintexts. Hence, IBEETIA is able to achieve indistinguishability security. On the other hand, the definition of IBEETIA weakens the notion of IBE due to its encryption inability. Nevertheless, known schemes of IBEETIA made use of rich algebraic structures such as bilinear groups and lattices. In this paper, we propose a generic construction of IBEETIA without resorting to rich algebraic structures. In particular, the only building blocks of the proposed construction are symmetric key encryption and pseudo-random permutations in the standard model. If a symmetric key encryption scheme satisfies CCA security, our proposed IBEETIA scheme also satisfies CCA security.

ФОРМИРОВАНИЕ СТРУКТУРНОЙ СХЕМЫ РАДИООБМЕНА С ПРИМЕНЕНИЕМ ПСП

The structure of the radio exchange demonstrates the interconnection pattern of the drones with the control center. To protect against unauthorized access to control and navigation channels it is necessary to hide such data and increase their noise immunity. The aim of the work is to use signals with a pseudorandom sequence and duplicate control and navigation blocks in the information channel of a small-scale aerial vehicle. Thus, at the beginning of the paper, a general structural diagram of radio communication between the unmanned aerial vehicle and the control center is presented. The model of 2-element antenna array consisting of two non-directional antenna elements is considered. On the basis of which it is possible to conclude about the signal arrival with a phase shift, taking into account which it is possible to determine the output signal of the array. An important factor is the synchronization and encryption of the signal. Data synchronization can be used by synchronous signal transmission between the drone and the control center. To reduce the probability of interception of the synchronous signal, the data packets containing it are transmitted in a pseudo-random sequence. Synchronization is achieved by using a micronavigation system through continuous radio transmissions from a ground source and simultaneous reception and recording of the signal on the drone. A one-time encryption or scrambler with a reversible symmetric transformation of the encoded information can be used as an encryption or scrambler. A random number generator is used to generate a sequence of random data, from which an array of key information tied to a specific period of use is created. The phase method can be used to process the signal. By measuring the phase shift with a phase detector, you can determine the location of the radio source with respect to the base normal. Measurements can be made with a digital receiving antenna array. Signal processing with digital receiving antenna array is performed by the diagramming device and the adaptive processor unit. As a result, all data using this approach is entered into the information block with the use of a pseudo-random coding change scheme, pseudo-random permutation of the navigation and control blocks.

Designing tweakable enciphering schemes using public permutations

A tweakable enciphering scheme (TES) is a length preserving (tweakable) encryption scheme that provides (tweakable) strong pseudorandom permutation security on arbitrarily long messages. TES is traditionally built using block ciphers and the security of the mode depends on the strong pseudorandom permutation security of the underlying block cipher. In this paper, we construct TESs using public random permutations. Public random permutations are being considered as a replacement of block cipher in several cryptographic schemes including AEs, MACs, etc. However, to our knowledge, a systematic study of constructing TES using public random permutations is missing. In this paper, we give a generic construction of a TES which uses a public random permutation, a length expanding public permutation based PRF and a hash function which is both almost xor universal and almost regular. Further, we propose a concrete length expanding public permutation based PRF construction. We also propose a single keyed TES using a public random permutation and an AXU and almost regular hash function.

A New Construction Method for Keystream Generators

We introduce a new construction method of diffusion layers for Substitution Permutation Network (SPN) structures along with its security proofs. The new method can be used in block ciphers, stream ciphers, hash functions, and sponge constructions. Moreover, we define a new stream cipher mode of operation through a fixed pseudorandom permutation and provide its security proofs in the indistinguishability model. We refer to a stream cipher as a Small Internal State Stream (SISS) cipher if its internal state size is less than twice its key size. There are not many studies about how to design and analyze SISS ciphers due to the criterion on the internal state sizes, resulting from the classical tradeoff attacks. We utilize our new mode and diffusion layer construction to design an SISS cipher having two versions, which we call DIZY. We further provide security analyses and hardware implementations of DIZY. In terms of area cost, power, and energy consumption, the hardware performance is among the best when compared to some prominent stream ciphers, especially for frame-based encryptions that need frequent initialization. Unlike recent SISS ciphers such as Sprout, Plantlet, LILLE, and Fruit; DIZY does not have a keyed update function, enabling efficient key changing.

Short Non-Malleable Codes from Related-Key Secure Block Ciphers, Revisited

We construct non-malleable codes in the split-state model with codeword length m + 3λ or m + 5λ, where m is the message size and λ is the security parameter, depending on how conservative one is. Our scheme is very simple and involves a single call to a block cipher meeting a new security notion which we dub entropic fixed-related-key security, which essentially means that the block cipher behaves like a pseudorandom permutation when queried upon inputs sampled from a distribution with sufficient min-entropy, even under related-key attacks with respect to an arbitrary but fixed key relation. Importantly, indistinguishability only holds with respect to the original secret key (and not with respect to the tampered secret key).In a previous work, Fehr, Karpman, and Mennink (ToSC 2018) used a related assumption (where the block cipher inputs can be chosen by the adversary, and where indistinguishability holds even with respect to the tampered key) to construct a nonmalleable code in the split-state model with codeword length m + 2λ. Unfortunately, no block cipher (even an ideal one) satisfies their assumption when the tampering function is allowed to be cipher-dependent. In contrast, we are able to show that entropic fixed-related-key security holds in the ideal cipher model with respect to a large class of cipher-dependent tampering attacks (including those which break the assumption of Fehr, Karpman, and Mennink).

Quantum statistical mechanics of encryption: Reaching the speed limit of classical block ciphers

We cast encryption via classical block ciphers in terms of operator spreading in a dual space of Pauli strings, a formulation which allows us to characterize classical ciphers by using tools well known in the analysis of quantum many-body systems. We connect plaintext and ciphertext attacks to out-of-time order correlators (OTOCs) and quantify the quality of ciphers using measures of delocalization in string space such as participation ratios and corresponding entropies obtained from the wave function amplitudes in string space. In particular, we show that in Feistel ciphers the entropy saturates its bound to exponential precision for ciphers with 4 or more rounds, consistent with the classic Luby–Rackoff result that it takes these many rounds to generate strong pseudorandom permutations. The saturation of the string-space information entropy and the vanishing of the OTOCs to exponential precision are taken as necessary conditions for the security of the cipher — we conjecture these criteria are also sufficient, as physically they signal irreversibility and chaos. We argue that the conditions on both OTOCs and string entropies can be satisfied by n-bit block ciphers implemented via random reversible circuits with O(nlogn) gates. This paper focuses on a tree-structured cipher composed of layers of n/3 3-bit gates, for which a “key” specifies uniquely the sequence of gates that comprise the circuit. We show that in order to reach this “speed limit” one must employ a three-stage circuit consisting of a nonlinear stage implemented by layers of nonlinear gates that proliferate the number of strings, flanked by two linear stages, each deploying layers of a special set of linear “inflationary” gates that accelerate the growth of small individual strings. The close formal correspondence to quantum scramblers established in this work leads us to suggest that this three-stage construction is also required in order to scramble quantum states to similar precision and with circuits of similar size. A shallow, O(logn)-depth cipher of the type described here can be used in constructing a polynomial-overhead scheme for computation on encrypted data proposed in another publication as an alternative to Homomorphic Encryption.

Securing color images using DNA coding and cosine stockwell transformation in wavelet domain

In this paper, a color image encoding algorithm is developed using cosine stockwell transformation and DNA coding in wavelet domain. Firstly, a color image is decomposed into its primary color components and then each component is wavelet transformed, which results four subbands for each component. The approximation subband of wavelet transformation is normalized and DNA coding is used followed by the proposed double phase encoding while the detail wavelet subbands are cosine stockwell transformed to get intermediate sub-images. The modified approximation and detail subbands are arranged by their indexing and pseudo random permutation is used to generate an encrypted image. At the receiver end, on having the exact knowledge of all the keys in correct order the original image can be recovered from the encrypted image. The bands of DCST, Tent Sine map is used to generate the random phase mask and key for pseudo random permutation is used as encryption and decryption keys. Numerical analysis and robustness of proposed work is evaluated on encrypted image to show the superiority of proposed work.

On the Quantum Security of OCB

The OCB mode of operation for block ciphers has three variants, OCB1, OCB2 and OCB3. OCB1 and OCB3 can be used as secure authenticated encryption schemes whereas OCB2 has been shown to be classically insecure (Inoue et al., Crypto 2019). Even further, in the presence of quantum queries to the encryption functionality, a series of works by Kaplan et al. (Crypto 2016), Bhaumik et al. (Asiacrypt 2021) and Bonnetain et al. (Asiacrypt 2021) have shown how to break the unforgeability of the OCB modes. However, these works did not consider the confidentiality of OCB in the presence of quantum queries.We fill this gap by presenting the first formal analysis of the IND-qCPA security of OCB. In particular, we show the first attacks breaking the IND-qCPA security of the OCB modes. Surprisingly, we are able to prove that OCB2 is IND-qCPA secure when used without associated data, while relying on the assumption that the underlying block cipher is a quantum-secure pseudorandom permutation. Additionally, we present new quantum attacks breaking the universal unforgeability of OCB. Our analysis of OCB has implications for the post-quantum security of XTS, a well-known disk encryption standard, that was considered but mostly left open by Anand et al. (PQCrypto 2016).

Bandwidth-Optimal Random Shuffling for GPUs

Linear-time algorithms that are traditionally used to shuffle data on CPUs, such as the method of Fisher-Yates, are not well suited to implementation on GPUs due to inherent sequential dependencies, and existing parallel shuffling algorithms are unsuitable for GPU architectures because they incur a large number of read/write operations to high latency global memory. To address this, we provide a method of generating pseudo-random permutations in parallel by fusing suitable pseudo-random bijective functions with stream compaction operations. Our algorithm, termed “bijective shuffle” trades increased per-thread arithmetic operations for reduced global memory transactions. It is work-efficient, deterministic, and only requires a single global memory read and write per shuffle input, thus maximising use of global memory bandwidth. To empirically demonstrate the correctness of the algorithm, we develop a statistical test for the quality of pseudo-random permutations based on kernel space embeddings. Experimental results show that the bijective shuffle algorithm outperforms competing algorithms on GPUs, showing improvements of between one and two orders of magnitude and approaching peak device bandwidth.

Improve Neural Distinguishers of SIMON and SPECK

Deep learning has played an important role in many fields, which shows significant potential for cryptanalysis. Although these existing works opened a new direction of machine learning aided cryptanalysis, there is still a research gap that researchers are eager to fill. How to further improve neural distinguishers? In this paper, we propose a new algorithm and model to improve neural distinguishers in terms of accuracy and the number of rounds. First, we design an algorithm based on SAT to improve neural distinguishers. With the help of SAT/SMT solver, we obtain new effective neural distinguishers of SIMON using the input differences of high-probability differential characteristics. Second, we propose a new neural distinguisher model using multiple output differences. Inspired by the existing works and data augmentation in deep learning, we use the output differences to exploit more derived features and train neural distinguishers, by splicing output differences into a matrix as a sample. Based on the new model, we construct neural distinguishers of SIMON and SPECK with round and accuracy promotion. Utilizing our neural distinguishers, we can distinguish reduced-round SIMON or SPECK from pseudorandom permutation better.

An Efficient Image Encryption Using a Dynamic, Nonlinear and Secret Diffusion Scheme

The growing use of tele This paper presents a new secret diffusion scheme called Round Key Permutation (RKP) based on the nonlinear, dynamic and pseudorandom permutation for encrypting images by block, since images are considered particular data because of their size and their information, which are two-dimensional nature and characterized by high redundancy and strong correlation. Firstly, the permutation table is calculated according to the master key and sub-keys. Secondly, scrambling pixels for each block to be encrypted will be done according the permutation table. Thereafter the AES encryption algorithm is used in the proposed cryptosystem by replacing the linear permutation of ShiftRows step with the nonlinear and secret permutation of RKP scheme; this change makes the encryption system depend on the secret key and allows both to respect the second Shannon’s theory and the Kerckhoff principle. Security analysis of cryptosystem demonstrates that the proposed diffusion scheme of RKP enhances the fortress of encryption algorithm, as can be observed in the entropy and other obtained values. communications implementing electronic transfers of personal data, require reliable techniques and secure. In fact, the use of a communication network exposes exchanges to certain risks, which require the existence of adequate security measures. The data encryption is often the only effective way to meet these requirements. This paper present a cryptosystem by block for encrypting images, as images are considered particular data because of their size and their information, which are two dimensional nature and characterized by high redundancy and strong correlation. In this cryptosystem, we used a new dynamic diffusion technique called round key permutation, which consists to permute pixels of each bloc in a manner nonlinear, dynamic and random using permutation table calculated according to the master key and sub-keys. We use thereafter the AES encryption algorithm in our cryptosystem by replacing the linear permutation of ShiftRows with round key permutation technique; this changing makes the encryption scheme depend on encryption key. Security analysis of cryptosystem demonstrate that the modification made on using the proposed technique of Round Key Permutation enhances the fortress of encryption algorithm, as can be observed in the entropy and other obtained values.

New Automatic Search Method for Truncated-Differential Characteristics Application to Midori, SKINNY and CRAFT

Abstract In this paper, using Mixed-Integer Linear Programming, a new automatic search tool for truncated differential characteristic is presented. Our method models the problem of finding a maximal probability truncated differential characteristic, being able to distinguish the cipher from a pseudo-random permutation. Using this method, we analyze Midori64, SKINNY64/X and CRAFT block ciphers, for all of which the existing results are improved. In all cases, the truncated differential characteristic is much more efficient than the (upper bound of) bit-wise differential characteristic proven by the designers, for any number of rounds. More specifically, the highest possible rounds, for which an efficient differential characteristic can exist for Midori64, SKINNY64/X and CRAFT are 6, 7 and 10 rounds, respectively, for which differential characteristics with maximum probabilities of $2^{-60}$, $2^{-52}$ and $2^{-62.61}$ (may) exist. Using our new method, we introduce new truncated differential characteristics for these ciphers with respective probabilities $2^{-54}$, $2^{-4}$ and $2^{-24}$ at the same number of rounds. Moreover, the longest truncated differential characteristics found for SKINNY64/X and CRAFT have 10 and 12 rounds, respectively. This method can be used as a new tool for differential analysis of SPN block ciphers.

SEPAR: A New Lightweight Hybrid Encryption Algorithm with a Novel Design Approach for IoT

This paper presents a new hybrid encryption algorithm with 16-bit block size and a 128-bit initialization vector, referred to as SEPAR, and it is suitable for IoT devices. The design idea of this algorithm combines pseudorandom permutation and pseudorandom generator functions. This smart integration causes resistance improvement against common cryptographic attacks meanwhile leads to cipher speed increment. Investigation of security analysis on the algorithm and results of the NIST statistical test suit proves its resistance against common cryptographic attacks as linear and differential cryptanalysis. Furthermore, efficient software implementation of SEPAR is presented on 8, 16 and 32-bit platforms. Compared to BORON cipher, SEPAR provides 42.22% throughput improvement on 32-bit ARM CPU. Also, for 8-bit and 16-bit microcontroller, SEPAR provides 87.91% and 98.01% performance improvements compared to present, respectively.

DESSE: A Dynamic Efficient Forward Searchable Encryption Scheme

Under the cloud computing environment, Searchable Symmetric Encryption (SSE) is an effective method to solve the problem of encrypted data retrieval, and helps to protect the users' privacy. Recent researches show that some attacks may bring great security threats to SSE, and forward privacy can effectively prevent these attacks, so forward privacy is very necessary for SSE scheme. Most of the existing forward privacy SSE schemes fall into two types: ORAM-based and Bost-based. The former is simple, but it has large communication overhead and low dynamic update efficiency. The latter is better than the former, but it is based on asymmetric encryption primitives. Based on symmetric encryption primitives, we propose a dynamic efficient forward privacy scheme DESSE in this paper. DESSE uses pseudo-random permutation to realize forward privacy, and uses delete list to identify the final state of the same file added and deleted repeatedly, so as to realize the dynamic update of data. The method proposed in this paper is simple and flexible in structure, takes up less additional space, and can significantly improve the efficiency of updating. At the same time, it can achieve real-time updating of data. The correctness of our proposed scheme is tested using the Enron email data set in the end.

Block Cipher in the Ideal Cipher Model: A Dedicated Permutation Modeled as a Black-Box Public Random Permutation

Designing a secure construction has always been a fascinating area for the researchers in the field of symmetric key cryptography. This research aimed to make contributions to the design of secure block cipher in the ideal cipher model whose underlying primitive is a family of n − b i t to n − b i t random permutations indexed by secret key. Our target construction of a secure block ciphers denoted as E [ s ] is built on a simple XOR operation and two block cipher invocations, under the assumptions that the block cipher in use is a pseudorandom permutation. One out of these two block cipher invocations produce a subkey that is derived from the secret key. It has been accepted that at least two block cipher invocations with XOR operations are required to achieve beyond birthday bound security. In this paper, we investigated the E [ s ] instances with the advanced proof technique and efficient block cipher constructions that bypass the birthday-bound up to 2 n provable security was achieved. Our study provided new insights to the block cipher that is beyond birthday bound security.

Strong Stationary Times and its use in Cryptography

This paper presents applicability of Strong Stationary Times (SST) techniques in the area of cryptography. The applicability is in three areas: *) Propositions of a new class of cryptographic algorithms (pseudo-random permutation generators) which do not run for the predefined number of steps. Instead, these algorithms stop according to a stopping rule defined as SST, for which one can obtain provable properties: *** results are perfect samples from uniform distribution, *** immunity to timing attacks (no information about the resulting permutation leaks through the information about the number of steps SST algorithm *) We show how one can leverage properties of SST-based algorithms to construct an implementation (of a symmetric encryption scheme) which is immune to the timing-attack by reusing implementations which are not secure against timing-attacks. In symmetric key cryptography researchers mainly focus on constant time (re)implementations. Our approach goes in a different direction and explores ideas of input masking. *) Analysis of idealized (mathematical) models of existing cryptographic schemes -- i.e., we improve a result by Mironov ((Not So) Random Shuffles of RC4; Advances in Cryptology -- CRYPTO 2002)

Key regression from constrained pseudorandom functions

Key regression is a primitive that allows a content publisher to give a small amount of keying material, for time stamp i, to a party such that they can derive key ki and all keys kj for time stamps j<i, but not for time stamps j>i. Existing key-regression schemes based on random oracles, pseudorandom permutations, and pseudorandom generators require a publisher to maintain state of size linear in the number of potential keys. In previous work, constant sized publisher state has only been accessible through the use of trapdoor permutations (e.g., RSA). This paper presents a novel key-regression scheme where the publisher must store only a constant amount of state information without trapdoor permutations. This is achieved through the use of constrained pseudorandom functions, a primitive that allows for the delegation of partial evaluation without revealing the key.

Quantum cryptanalysis on some generalized Feistel schemes

Post-quantum cryptography has attracted much attention from worldwide cryptologists.In ISIT 2010, Kuwakado and Morii gave a quantum distinguisher with polynomial time against 3-round Feistel networks. However, generalized Feistel schemes (GFS) have not been systematically investigated against quantum attacks.In this paper, we study the quantum distinguishers about some generalized Feistel schemes. For $d$-branch Type-1 GFS (CAST256-like Feistel structure), we introduce ($2d-1$)-round quantum distinguishers with polynomial time. For $2d$-branch Type-2 GFS (RC6/CLEFIA-like Feistel structure), we give ($2d+1$)-round quantum distinguishers with polynomial time. Classically, Moriai and Vaudenay proved that a 7-round $4$-branch Type-1 GFS and 5-round $4$-branch Type-2 GFS are secure pseudo-random permutations. Obviously, they are no longer secure in quantum setting.Using the above quantum distinguishers, we introduce generic quantum key-recovery attacks by applying the combination of Simons and Grovers algorithms recently proposed by Leander and May. We denote $n$ as the bit length of a branch. For $(d^2-d+2)$-round Type-1 GFS with $d$ branches, the time complexity is $2^{(\frac{1}{2}d^2-\frac{3}{2}d+2)\cdot~\frac{n}{2}}$, which is better than the quantum brute force search (Grover search) by a factor $2^{(\frac{1}{4}d^2+\frac{1}{4}d)n}$. For $4d$-round Type-2 GFS with $2d$ branches, the time complexity is $2^{{\frac{d^2~n}{2}}}$, which is better than the quantum brute force search by a factor linebreak $2^{{\frac{3d^2~n}{2}}}$.

Generalized Tweakable Even-Mansour Cipher and Its Applications

This paper describes a generalized tweakable blockcipher HPH (Hash-Permutation-Hash), which is based on a public random permutation P and a family of almost-XOR-universal hash functions $$ \mathcal{H}={\left\{ HK\right\}}_{K\in \mathcal{K}} $$ as a tweak and key schedule, and defined as y = HPHK((t1, t2), x) = P(x ⊕ HK(t1)) ⊕ HK(t2), where K is a key randomly chosen from a key space $$ \mathcal{K} $$ , (t1, t2) is a tweak chosen from a valid tweak space $$ \mathcal{T} $$ , x is a plaintext, and y is a ciphertext. We prove that HPH is a secure strong tweakable pseudorandom permutation (STPRP) by using H-coefficients technique. Then we focus on the security of HPH against multi-key and related-key attacks. We prove that HPH achieves both multi-key STPRP security and related-key STPRP security. HPH can be extended to wide applications. It can be directly applied to authentication and authenticated encryption modes. We apply HPH to PMAC1 and OPP, provide an improved authentication mode HPMAC and a new authenticated encryption mode OPH, and prove that the two modes achieve single-key security, multi-key security, and related-key security.