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Random numbers are used in a variety of applications including simulation, sampling, and cryptography. Fortunately, there exist many well-established methods of random number generation. An example of a well-known pseudorandom number generator is the lagged-Fibonacci generator (LFG). Marsaglia showed that the lagged-Fibonacci generator using addition failed some of his DIEHARD statistical tests, while it passed all when longer lags were used. This paper presents a scrambler that takes bits from a pseudorandom number generator and outputs (hopefully) improved pseudorandom numbers. The scrambler is based on a modified Feistel function, a method used in the generation of cryptographic random numbers, and multiplication by a chosen multiplier. We show that this scrambler improves the quality of pseudorandom numbers by applying it to the additive LFG with small lags. The scrambler performs well based on its performance with the TestU01 suite of randomness tests. The TestU01 suite of randomness tests is more comprehensive than the DIEHARD tests. In fact, the specific suite of tests we used from TestU01 includes the DIEHARD tests The scrambling of the LFG is so successful that scrambled LFGs with small lags perform as well as unscrambled LFGs with long lags. This comes at the cost of a doubling of execution time, and provides users with generators with small memory footprints that can provide parallel generators like the LFGs in the SPRNG parallel random number generation package. [ABSTRACT FROM AUTHOR]

In 2017, we decided to start the annual series of MathCrypt Workshops in order to encourage more mathematicians and computational number theorists to propose and work on hard problems in cryptography. In fact, a Program Officer from NSF spoke at the first MathCrypt workshop in August and encouraged participants to apply to the NSF SaTC program for potential support for their research. The founders of MathCrypt, Jung Hee Cheon and Kristin Lauter, acted as Program Chairs, and were joined by Jintai Ding to form the Organizing Committee. [Extracted from the article]

The paper studies mappings F of binary vector spaces of large dimensions. The mappings are assumed to be represented by deep branching superpositions of local non-linear mappings of low-dimensional spaces. We propose and investigate the methods for construction of probabilistic linear and differential relations connecting the arguments and the values of a mapping F. Relation selection is based on optimization not the exact probability of satisfying these relations, but some approximation of it since it is easier to estimate. We prove theorems on exact values of the probability of satisfying the relations obtained, identify the shortcomings and features of the proposed approach to the relation construction and illustrate them by a number of examples. We discuss the role of the developed theory for cryptographic synthesis. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to provide an efficient image encryption for each and every single person in order to secure their own records while saving them in social networks. We have formulated the delayed fuzzy cellular neural networks (FCNNs) with suitable keys that are the values of the parameters of FCNNs and obtain the irregular dynamical signal (solution) which encrypts the images. We have utilized entirely 42 parameters as a key sensitivity in the order of 10−15 among them three elements of initial condition parameters are sensitive to the order of 10−14. Lastly, comparison results are provided with the existing literature. The measurements show that the proposed algorithm is a novel overall solution for image encryption. [ABSTRACT FROM AUTHOR]

In [2], Bellare, Pietrzak and Rogaway proved an O(ℓq2/2n) bound for the PRF (pseudorandom function) security of the CBC-MAC based on an n-bit random permutation II, provided ℓ< 2n/3. Here an adversary can make at most q prefix-free queries each having at most ℓ many "blocks" (elements of {0, 1}n). In the same paper an O(ℓo(1)q2/2n) bound for EMAC (or encrypted CBC-MAC) was proved, provided ℓ < 2n/4. Both proofs are based on structure graphs representing all collisions among "intermediate inputs" to II during the computation of CBC. The problem of bounding PRF-advantage is shown to be reduced to bounding the number of structure graphs satisfying certain collision patterns. In the present paper, we show that [2, Lemma 10], stating an important result on structure graphs, is incorrect. This is due to the fact that the authors overlooked certain structure graphs. This invalidates the proofs of the PRF bounds. In [31], Pietrzak improved the bound for EMAC by showing a tight bound O(q2/2n) under the restriction that ℓ < 2n/8. As he used the same flawed lemma, this proof also becomes invalid. In this paper, we have revised and sometimes simplified these proofs. We revisit structure graphs in a slightly different mathematical language and provide a complete characterization of certain types of structure graphs. Using this characterization, we show that PRF security of CBC-MAC is about σq/2n provided ℓ < 2n/3 where σ is the total number of blocks in all queries. We also recover tight bound for PRF security of EMAC with a much relaxed constraint (ℓ < 2n/4) than the original (ℓ < 2n/8). [ABSTRACT FROM AUTHOR]

Watermarking is the process of concealing the secret message into multimedia sources, such as audio, image, and video. Rather than other steganography, video watermarking is mainly focused on the robustness of the system. In this paper, we propose the multiobjective cost function for video watermarking. Initially, the cover image (video frame) is subjected into cost function computation. Then, the cost function is newly designed and developed by various objectives, such as intensity, energy, edge, coverage, and brightness. Subsequently, the wavelet transform is applied to the original frame that acquires a wavelet coefficient-based video frame. Simultaneously, the secret message is partitioned into binary images using the bit plane technique. According to the cost value, the message bit is embedded into the wavelet coefficients in the embedding phase. In the extraction phase, the secret message is retrieved. Finally, the experimental results are validated, and performance is analyzed using metrics, correlation coefficients, and peak-to-signal noise ratio (PSNR). From the results, it can be shown that the proposed method attains 98.19 dB PSNR and 1.00 correlation coefficient value to provide better robustness of the system. [ABSTRACT FROM AUTHOR]

Batch verification for digital signature scheme is a method to verify multiple signatures simultaneously. The complex exponent test (CE test for short) proposed by Cheon and Lee is one of the most efficient batch verification tests for several digital signature schemes on certain types of elliptic curves (including Koblitz curves). The security of the CE test relies essentially on the cardinality of a subset of a residue ring of the endomorphism ring of an elliptic curve over an ideal. They have evaluated the cardinality of the above subset, and have illustrated the effectiveness of the CE test by using the evaluation. The aim of this paper is to point out that their evaluation contains a flaw. The flaw is generally related to two roots of a quadratic equation which is used in their argument. We mend the flaw of their evaluation. Our correct evaluation shows that the CE test can achieve the same security as the underlying signature scheme on Koblitz curves. As a result, the CE test is a secure batch verification when the underlying signature scheme uses Koblitz curves. [ABSTRACT FROM AUTHOR]

A family of ring-based cryptosystems, including the multilinear maps of Garg, Gentry and Halevi [Candidate multilinear maps from ideal lattices, Advances in Cryptology—EUROCRYPT 2013, Lecture Notes in Comput. Sci. 7881, Springer, Heidelberg 2013, 1–17] and the fully homomorphic encryption scheme of Smart and Vercauteren [Fully homomorphic encryption with relatively small key and ciphertext sizes, Public Key Cryptography—PKC 2010, Lecture Notes in Comput. Sci. 6056, Springer, Berlin 2010, 420–443], are based on the hardness of finding a short generator of a principal ideal (short-PIP) in a number field typically in ℚ ⁢ (ζ 2 s) {\mathbb{Q}(\zeta_{2^{s}})}. In this paper, we present a polynomial-time quantum algorithm for recovering a generator of a principal ideal in ℚ ⁢ (ζ 2 s) {\mathbb{Q}(\zeta_{2^{s}})} , and we recall how this can be used to attack the schemes relying on the short-PIP in ℚ ⁢ (ζ 2 s) {\mathbb{Q}(\zeta_{2^{s}})} by using the work of Cramer et al. [R. Cramer, L. Ducas, C. Peikert and O. Regev, Recovering short generators of principal ideals in cyclotomic rings, IACR Cryptology ePrint Archive 2015, https://eprint.iacr.org/2015/313], which is derived from observations of Campbell, Groves and Shepherd [SOLILOQUY, a cautionary tale]. We put this attack into perspective by reviewing earlier attempts at providing an efficient quantum algorithm for solving the PIP in ℚ ⁢ (ζ 2 s) {\mathbb{Q}(\zeta_{2^{s}})}. The assumption that short-PIP is hard was challenged by Campbell, Groves and Shepherd. They proposed an approach for solving short-PIP that proceeds in two steps: first they sketched a quantum algorithm for finding an arbitrary generator (not necessarily short) of the input principal ideal. Then they suggested that it is feasible to compute a short generator efficiently from the generator in step 1. Cramer et al. validated step 2 of the approach by giving a detailed analysis. In this paper, we focus on step 1, and we show that step 1 can run in quantum polynomial time if we use an algorithm for the continuous hidden subgroup problem (HSP) due to Eisenträger et al. [K. Eisenträger, S. Hallgren, A. Kitaev and F. Song, A quantum algorithm for computing the unit group of an arbitrary degree number field, Proceedings of the 2014 ACM Symposium on Theory of Computing—STOC'14, ACM, New York 2014, 293–302]. [ABSTRACT FROM AUTHOR]

In this paper, a new chaotic image encryption scheme is proposed, which uses the combination of stream cipher and block cipher to spread and then uses the Logistic mapping matrix to perform the block sort transformation to complete the confusion. The specific method is as follows: First, perform the triple XOR operation, non-linear S-box transformation and linear cyclic shift transformation on the key. Second, the triple XOR operation of the transformed key and the plaintext and Logistic mapping sequence are used to obtain the semi-ciphertext. And set the obtained semi-ciphertext and plaintext as key components of the next round of encryption. Finally, the transformation of sorting and partition of the Logistic mapping matrix are used to confuse the semi-ciphertext. The experimental results show that the proposed algorithm improves the encryption efficiency, has good security and can resist common attacks. [ABSTRACT FROM AUTHOR]

The article offers information on the periodical including editorial board members like Marston Conder and Murray Elder; along with a table of content for the issue of the periodical on topics including algebraic cryptography and submonoids of virtually free groups.

The main objective of this paper is to propose a medical image watermarking technique in E-healthcare application based on the hybridization of compression and cryptography algorithm. Basically, the proposed system consists of two stages: (i) watermark embedding process and (ii) watermark extraction process. In the embedding process, at first, we segment the tumor part separately using a region growing algorithm. Then, we encrypt the region of interest part using Secure Hash Algorithm-256 and encrypt the electronic health record (EHR) using the elliptical curve cryptography algorithm. Thereafter, we concatenate and compress the information using an arithmetic coding algorithm. Finally, we embed the compressed bit into the original image. The same process is repeated for the extraction process. The experimental results are shown for different medical images with EHR and the effectiveness of the proposed algorithm is analyzed with the help of the peak signal-to-noise ratio and normalized correlation. [ABSTRACT FROM AUTHOR]

This paper presents an efficient algorithm for computing 11th-power residue symbols in the cyclo-tomic field ℚ (ζ 11 ) , $ \mathbb{Q}\left({{\zeta }_{11}} \right), $ where 11 is a primitive 11th root of unity. It extends an earlier algorithm due to Caranay and Scheidler (Int. J. Number Theory, 2010) for the 7th-power residue symbol. The new algorithm finds applications in the implementation of certain cryptographic schemes. [ABSTRACT FROM AUTHOR]

Recently, supersingular isogeny cryptosystems have received attention as a candidate of post-quantum cryptography (PQC). Their security relies on the hardness of solving isogeny problems over supersingular elliptic curves. The meet-in-the-middle approach seems the most practical to solve isogeny problems with classical computers. In this paper, we propose two algebraic approaches for isogeny problems of prime power degrees. Our strategy is to reduce isogeny problems to a system of algebraic equations, and to solve it by Gröbner basis computation. The first one uses modular polynomials, and the second one uses kernel polynomials of isogenies. We report running times for solving isogeny problems of 3-power degrees on supersingular elliptic curves over 𝔽p2 with 503-bit prime p, extracted from the NIST PQC candidate SIKE. Our experiments show that our first approach is faster than the meet-in-the-middle approach for isogeny degrees up to 310. [ABSTRACT FROM AUTHOR]

In the past when only "paper and pencil" ciphers were in use, a mnemonic Bellaso's method was applied to obtain a permutation from a meaningful phrase. It turns out that even nowadays this method and its variations are employed and provide a simple but at the same time efficient tool for some ciphers. To the best of our knowledge the security of such ciphers has not been evaluated yet in all respects. Therefore, in this paper we initiate a study of their security with respect to the probability distribution of permutations obtained by Bellaso's method. [ABSTRACT FROM AUTHOR]

Trustworthy applications in fully decentralized systems require a trust anchor. However, in p2p systems there does not exist a central trust anchor. This paper describes how a distributed anchor can be implemented efficiently in such and environment. Different alternatives have been proposed in the literature; most of them suggesting distributing the trust anchor by using a quorum decision, assuming that a random quorum would ensure trustworthiness. However, there are major issues, e.g., can it be assumed that a quorum was actually randomly chosen? how can it be verified, that a signature was created by a truly random quorum? In this paper a solution for this is presented through the token-based accounting scheme using specific mechanisms that ensure a distributed trust anchor in p2p systems and its evaluation. [ABSTRACT FROM AUTHOR]

The paper provides a cryptanalysis of the AAββ-cryptosystem recently proposed by Ariffin and Abu. The scheme is in essence a key agreement scheme whose security is based on a discrete logarithm problem in the infinite (additive) group ℝℝ/ℤℤ (the reals modulo 1). The paper breaks the AAββ-cryptosystem (in a passive adversary model) by showing that this discrete logarithm problem can be efficiently solved in practice. [ABSTRACT FROM AUTHOR]

Cryptographic primitives from coding theory are some of the most promising candidates for NIST's Post-Quantum Cryptography Standardization process. In this paper, we introduce a variety of techniques to improve operations on dyadic matrices, a particular type of symmetric matrices that appear in the automorphism group of certain linear codes. Besides the independent interest, these techniques find an immediate application in practice. In fact, one of the candidates for the Key Exchange functionality, called DAGS, makes use of quasi-dyadic matrices to provide compact keys for the scheme. [ABSTRACT FROM AUTHOR]

This paper aims to propose a method for data hiding in video by utilizing the least significant bit (LSB) method and improving it by utilizing the knight tour algorithm for concealing the data inside the AVI video file and using a key function encryption method for encrypting the secret message. First, the secret message is encrypted by utilizing a mathematical equation. The key used in the equation is a set of random numbers. These numbers differ in each implementation to warrant the safety of the hidden message and to increase the security of the secret message. Then, the cover video was converted from a set of frames into separated images to take the advantage of the large size of video file. Afterward, the knight tour algorithm is utilized for random selecting of the pixels inside the frame utilized for embedding the secret message inside it to overcome the shortcoming of the conventional LSB method that utilized the serial selection of pixel and to increase the robustness and security of the proposed method. Afterward, the encrypted secret message is embedded inside the selected pixels by utilizing the LSB method in bits (7 and 8). The observational results have drawn that the proposed method has a superior performance compared to the previous steganography method in terms of quality by a high PSNR of 67.3638 dB and the lowest MSE of 0.2578. Furthermore, this method preserves the security where the secret message cannot be drawn out without knowing the decoding rules. [ABSTRACT FROM AUTHOR]

Steganography is the foremost influential approach to hide data. Images serve as the most appropriate cover media for steganography. This paper intends to do a performance evaluation of color images and its comparison with the recently proposed approaches, using the modified technique already proposed for grayscale images, by the authors. This approach hides large data in color image using the blocking concept. The blocking process is applied on approximation coefficients of secret image and detail coefficients of red, green and blue components of cover image. The blocks of detail coefficients are replaced with approximation coefficients of secret image using root mean square error method. The key is used to store the position of best matching blocks. It is being predicated that the work will be able to hide large data in a single image. The stego image (ST) has better visual quality based on the peak signal to noise ratio values. [ABSTRACT FROM AUTHOR]

MDS diffusion layers are critical components in the design of symmetric ciphers. In this paper, after introducing some new algebraic structures, we provide new MDS matrices over special types of R-modules. With the help of the proposed methodology, we have more flexibility in designing software-oriented diffusion layers. Most notably, we construct randomized and/or nonlinear MDS diffusion layers, based upon the presented theoretical results, and discuss the resistance of the presented diffusion layers against various kinds of cryptanalysis, compared with classical linear diffusion layers. [ABSTRACT FROM AUTHOR]

Unconditionally secure signature (USS) schemes provide the ability to electronically sign documents without the reliance on computational assumptions needed in traditional digital signatures. Unlike digital signatures, USS schemes require that verification algorithms are not public - for any possible signer, a given user must have a different secret verification algorithm corresponding to that signer. Thus, any viable security definition for aUSS scheme must carefully treat the subject ofwhat constitutes a valid signature. That is, it is important to distinguish between signatures that are created using a user's signing algorithm and signatures that may satisfy one or more user verification algorithms. Moreover, given that each verifier has his own distinct verification algorithm, a USS scheme must necessarily handle the event of a disagreement. In this paper, we present a new security model for USS schemes that incorporates these notions, as well as give a formal treatment of dispute resolution and the trust assumptions required. We provide formal definitions of non-repudiation and transferability in the context of dispute resolution, and give sufficient conditions for a USS scheme to satisfy these properties. We then extend our basic framework to the setting of strong keyinsulated signatures, which increase robustness against key exposure. Finally, we give security analyses for two constructions: Hanaoka et al.'s construction, which we show is secure in our basic USS model, and a key-insulated extension of this construction, which is secure in our strong key-insulated model. This is an extended version of the conference paper [19], which appeared in ICITS 2011. [ABSTRACT FROM AUTHOR]

A family of ring-based cryptosystems, including the multilinear maps of Garg, Gentry and Halevi [Candidate multilinear maps from ideal lattices, Advances in Cryptology—EUROCRYPT 2013, Lecture Notes in Comput. Sci. 7881, Springer, Heidelberg 2013, 1–17] and the fully homomorphic encryption scheme of Smart and Vercauteren [Fully homomorphic encryption with relatively small key and ciphertext sizes, Public Key Cryptography—PKC 2010, Lecture Notes in Comput. Sci. 6056, Springer, Berlin 2010, 420–443], are based on the hardness of finding a short generator of a principal ideal (short-PIP) in a number field typically in ℚ ⁢ (ζ 2 s) {\mathbb{Q}(\zeta_{2^{s}})}. In this paper, we present a polynomial-time quantum algorithm for recovering a generator of a principal ideal in ℚ ⁢ (ζ 2 s) {\mathbb{Q}(\zeta_{2^{s}})} , and we recall how this can be used to attack the schemes relying on the short-PIP in ℚ ⁢ (ζ 2 s) {\mathbb{Q}(\zeta_{2^{s}})} by using the work of Cramer et al. [R. Cramer, L. Ducas, C. Peikert and O. Regev, Recovering short generators of principal ideals in cyclotomic rings, IACR Cryptology ePrint Archive 2015, https://eprint.iacr.org/2015/313], which is derived from observations of Campbell, Groves and Shepherd [SOLILOQUY, a cautionary tale]. We put this attack into perspective by reviewing earlier attempts at providing an efficient quantum algorithm for solving the PIP in ℚ ⁢ (ζ 2 s) {\mathbb{Q}(\zeta_{2^{s}})}. The assumption that short-PIP is hard was challenged by Campbell, Groves and Shepherd. They proposed an approach for solving short-PIP that proceeds in two steps: first they sketched a quantum algorithm for finding an arbitrary generator (not necessarily short) of the input principal ideal. Then they suggested that it is feasible to compute a short generator efficiently from the generator in step 1. Cramer et al. validated step 2 of the approach by giving a detailed analysis. In this paper, we focus on step 1, and we show that step 1 can run in quantum polynomial time if we use an algorithm for the continuous hidden subgroup problem (HSP) due to Eisenträger et al. [K. Eisenträger, S. Hallgren, A. Kitaev and F. Song, A quantum algorithm for computing the unit group of an arbitrary degree number field, Proceedings of the 2014 ACM Symposium on Theory of Computing—STOC'14, ACM, New York 2014, 293–302]. [ABSTRACT FROM AUTHOR]

In this paper, we will offer a new symmetric-key cryptographic scheme which is based on the existence of exponentially distorted subgroups in arithmetic groups. Aside from this, we will also provide new examples of distorted subgroups in SL n ⁢ (ℤ ⁢ [ x ]) {\mathrm{SL}_{n}(\mathbb{Z}[x])} which can be utilized for the same purpose. [ABSTRACT FROM AUTHOR]

Recently, Shpilrain and Sosnovski proposed a hash function based on composition of affine maps. In this paper, we show that this hash function with its proposed parameters is not weak collision resistant, for plaintexts of size at least 1.9MB (about 2 24 {2^{24}} bits). Our approach is to reduce the preimage problem to a (very) high density instance of the Random Modular Subset Sum Problem, for which we give an algorithm capable of solving instances of the resulting size. Specifically, given plaintexts of about 1.9MB, we were able to produce other plaintexts of the same size with the same hash value in about 13 hours each, on average. [ABSTRACT FROM AUTHOR]

Random number generators (RNGs) are basic cryptographic primitives. They are used to generate cryptographic keys, initialization vectors, challenges and nonces in cryptographic protocols, and random masks in countermeasures against side channel attacks. RNGs designed for cryptography must generate unpredictable random numbers. According to recent security standards, the unpredictability of generated random numbers must be thoroughly evaluated. In this paper, we provide a concrete example – a phase-locked loop based RNG protected by novel dedicated embedded tests, on which we show how stringent security requirements including unpredictability of generated numbers can be met, while respecting the standards. [ABSTRACT FROM AUTHOR]

Rotation symmetric Boolean functions have been extensively studied in the last 15 years or so because of their importance in cryptography and coding theory. Until recently, very littlewas known about such basic questions as when two such functions are affine equivalent. This question in important in applications, because almost all important properties of Boolean functions (such as Hamming weight, nonlinearity, etc.) are affine invariants, so when searching a set for functions with useful properties, it suffices to consider just one function in each equivalence class. This can greatly reduce computation time. Even for quadratic functions, the analysis of affine equivalence was only completed in 2009. The much more complicated case of cubic functions was completed in the special case of affine equivalence under permutations for monomial rotation symmetric functions in two papers from 2011 and 2014. There has also been recent progress for some special cases for functions of degree > 3. In 2007 it was found that functions satisfying a new notion of k-rotation symmetry for k > 1 (where the case k = 1 is ordinary rotation symmetry) were of substantial interest in cryptography and coding theory. Since then several researchers have used these functions for k = 2 and 3 to study such topics as construction of bent functions, nonlinearity and covering radii of various codes. In this paper we develop a detailed theory for the monomial 3-rotation symmetric cubic functions, extending earlier work for the case k = 2 of these functions. [ABSTRACT FROM AUTHOR]

Code-based cryptography is one of the main areas of interest for NIST's Post-Quantum Cryptography Standardization call. In this paper, we introduce DAGS, a Key Encapsulation Mechanism (KEM) based on quasi-dyadic generalized Srivastava codes. The scheme is proved to be IND-CCA secure in both random oracle model and quantum random oracle model. We believe that DAGS will offer competitive performance, especially when compared with other existing code-based schemes, and represent a valid candidate for post-quantum standardization. [ABSTRACT FROM AUTHOR]

A block is an n-bit string, and a (possibly keyed) block-function is a non-linear mapping that maps one block to another, e.g., a block-cipher. In this paper, we consider various symmetric key primitives with ℓ {\ell} block inputs and raise the following question: what is the minimum number of block-function invocations required for a mode to be secure? We begin with encryption modes that generate ℓ ′ {\ell^{\prime}} block outputs and show that at least (ℓ + ℓ ′ - 1) {(\ell+\ell^{\prime}-1)} block-function invocations are necessary to achieve the PRF security. In presence of a nonce, the requirement of block-functions reduces to ℓ ′ {\ell^{\prime}} blocks only. If ℓ = ℓ ′ {\ell=\ell^{\prime}} , in order to achieve SPRP security, the mode requires at least 2 ⁢ ℓ {2\ell} many block-function invocations. We next consider length preserving r-block (called chunk) online encryption modes and show that, to achieve online PRP security, each chunk should have at least 2 ⁢ r - 1 {2r-1} many and overall at least 2 ⁢ r ⁢ ℓ - 1 {2r\ell-1} many block-functions for ℓ {\ell} many chunks. Moreover, we show that it can achieve online SPRP security if each chunk contains at least 2 ⁢ r {2r} non-linear block-functions. We next analyze affine MAC modes and show that an integrity-secure affine MAC mode requires at least ℓ {\ell} many block-function invocations to process an ℓ {\ell} block message. Finally, we consider affine mode authenticated encryption and show that in order to achieve INT-RUP security or integrity security under a nonce-misuse scenario, either (i) the number of non-linear block-functions required to generate the ciphertext is more than ℓ {\ell} or (ii) the number of extra non-linear block-functions required to generate the tag depends on ℓ {\ell}. [ABSTRACT FROM AUTHOR]

Asymmetric password based key exchange is a key exchange protocol where a client and a server share a low entropic password while the server additionally owns a high entropic secret with respect to a public key. There are simple solutions for this, e.g., [ACM Trans. Inf. Syst. Secur. 2 (1999), 230-268] and its improvement in [Proceedings of CCS 1999, ACM (1999), 63-72]. In the present paper, we consider a new threat to this type of protocol: if a server's high entropic secret gets compromised (e.g., due to cryptanalysis or a poor management), the adversary might quickly break lots of passwords and cause uncountable damage. In this case, one should not expect the protocol to be secure against an off-line dictionary attack since, otherwise, the protocol is in fact a secure password-only key exchange by making the server high entropic secret public. Of course a password-only key exchange does not suffer from this threat as the server does not have a high entropic secret at all. However, known password-only key exchange protocols are not very efficient (note: we only consider protocols without random oracles). This motivates us to study an efficient and secure asymmetric password key exchange that avoids the new threat. In this paper, we first provide a formal model for the new threat, where essentially we require that the active adversary can break passwords in steps (for ) only with a probability negligibly close to for some , where is a password dictionary. Then, we construct a framework of asymmetric password based key exchange. We prove that our protocol is secure in the regular model where server high entropic key is never compromised and that it prevents the new threat. To do this, we introduce a new technique by abstracting a probabilistic experiment from the main proof and providing a neat analysis of it. [ABSTRACT FROM AUTHOR]

As the technology is growing day by day, information security plays a very important role in our lives. In order to protect the information, several cryptographic algorithms have been proposed. The aim of this paper is to present an effective Advanced Encryption Standard (AES) architecture to achieve high throughput for security applications. The Parallel Sub-Pipelined architecture (PSP) is proposed in order to obtain high throughput. The proposed architecture is also compared with loop unrolled, pipelined, sub-pipelined, parallel and parallel pipelined architecture in terms of throughput. The AES algorithm using Parallel Sub-Pipelined architecture was prototyped in FPGA (Field Programmable Gate Array) and ASIC (Application Specific Integrated Circuit).The proposed architecture yielded a throughput of 59.59 Gbps at a frequency of 450.045 MHz on FPGA Virtex XC6VLX75T which is higher than the throughput yielded in other architectures. In ASIC 0.13 µm technology, the proposed architecture yielded a throughput of 25.60 Gbps and in 0.18 µm, it yielded a throughput of 20.56 Gbps. [ABSTRACT FROM AUTHOR]

An introduction to the journal is presented in which various reports within the issues are discussed on topics including discrete logarithm based cryptography, norm equation solution, and application of numerical methods in the cryptanalysis of stream ciphers.

In this paper, we construct some cartesian authentication codes from geometries over finite commutative rings. We only assume the uniform probability distribution over the set of encoding rules in order to be able to compute the probabilities of successful impersonation attack and substitution attack. Our methods are comfortable and secure for users, i.e., our encoding rules reduce the probabilities of successful impersonation attack and substitution attack. [ABSTRACT FROM AUTHOR]

In this paper, we consider a two party key-exchange protocol proposed in [D. Grigoriev and V. Shpilrain, Tropical cryptography, Comm. Algebra 43 (2014), 2624–2632, Section 2], which uses tropical matrix algebra as the platform. Our analysis shows that the scheme is not secure. [ABSTRACT FROM AUTHOR]

With the ever-increasing need for concealing messages within cover media like image, video, and audio, numerous attempts have been developed for steganography. Most of the steganographic techniques perform their embedding operation on the cover image without selecting a better location. The right selection of location for embedding the information can lead to high imperceptibility and robustness. Accordingly, in this paper, we develop a new cost function for estimating the cost of every pixel to identify the good location to embed the message data. The proposed cost estimation procedure utilizes multiple parameters like wavelet coefficient, edge transformation, and pixel intensity. The proposed cost matrix is then utilized to embed the message data into the cover media using an embedding integer. The proposed steganographic technique is experimented with two magnetic resonance brain images, and the results are analyzed with the peak-to-peak signal-to-noise ratio (PSNR) and mean square error. The robustness analysis ensured that the proposed steganographic technique outperforms the existing methods by reaching the maximum PSNR of 72.74 dB. [ABSTRACT FROM AUTHOR]

Many illegal copies of original digital videos are being made, as they can be replicated perfectly through the Internet. Thus, it is extremely necessary to protect the copyrights of the owner and prevent illegal copying. This paper presents a novel approach to digital video watermarking for copyright protection using two different algorithms, whereby successive estimation of a statistical measure was used to detect scene boundaries and watermark was embedded in the detected scenes with discrete wavelet transform. Haar wavelet was used for decomposition. For embedding, the approaches used were (i) the detailed subband (LH subband) and (ii) the approximate subband (LL subband) of the cover video. Imperceptibility, robustness, and channel capacity were measured using both algorithms. The system was tested for robustness in the presence of 15 different attacks of five different categories, and, under multiple attacks, ensured that a wide spectrum of attack analysis has been done. The performance metrics measured included mean square error, peak signal-to-noise ratio, structural similarity index, normalized correlation, and bit error rate. The experimental results demonstrated the better visual imperceptibility and improved performance in terms of normalized correlation and bit error rate with embedding using the LL subband. Comparative analysis with existing schemes proved the improved robustness, better imperceptibility, and reduced computational time of both the proposed schemes. [ABSTRACT FROM AUTHOR]

There has been considerable recent interest in 'cloud storage' wherein a user asks a server to store a large file. One issue is whether the user can verify that the server is actually storing the file, and typically a challenge-response protocol is employed to convince the user that the file is indeed being stored correctly. The security of these schemes is phrased in terms of an extractor which will recover or retrieve the file given any 'proving algorithm' that has a sufficiently high success probability. This paper treats proof-of-retrievability schemes in the model of unconditional security, where an adversary has unlimited computational power. In this case retrievability of the file can be modelled as error-correction in a certain code. We provide a general analytical framework for such schemes that yields exact (non-asymptotic) reductions that precisely quantify conditions for extraction to succeed as a function of the success probability of a proving algorithm, and we apply this analysis to several archetypal schemes. In addition, we provide a new methodology for the analysis of keyed schemes in an unconditionally secure setting, and use it to prove the security of a modified version of a scheme due to Shacham and Waters [Lecture Notes in Comput. Sci. 5350, Springer (2008), 90-107] under a slightly restricted attack model, thus providing the first example of a keyed scheme with unconditional security. We also show how classical statistical techniques can be used to evaluate whether the responses of the prover are accurate enough to permit successful extraction. Finally, we prove a new lower bound on storage and communication complexity of schemes. [ABSTRACT FROM AUTHOR]

HMAC is the most widely-deployed cryptographic-hash-function-based message authentication code. First, we describe a security issue that arises because of inconsistencies in the standards and the published literature regarding keylength. We prove a separation result between two versions of HMAC, which we denote and , the former being the real-world version standardized by Bellare et al. in 1997 and the latter being the version described in Bellare's proof of security in his Crypto 2006 paper. Second, we describe how (the FIPS version standardized by NIST), while provably secure (in the single-user setting), succumbs to a practical attack in the multi-user setting. Third, we describe a fundamental defect from a practice-oriented standpoint in Bellare's 2006 security result for HMAC, and show that because of this defect his proof gives a security guarantee that is of little value in practice. We give a new proof of NMAC security that gives a stronger result for NMAC and HMAC and we discuss why even this stronger result by itself fails to give convincing assurance of HMAC security. [ABSTRACT FROM AUTHOR]

Since their introduction, the notions of indistinguishability and non-malleability have been changed and extended by different authors to support different goals. In this paper, we propose new flavors of these notions, investigate their relative strengths with respect to previous notions, and provide the full picture of relationships (i.e., implications and separations) among the security notions for public-key encryption schemes. We take into account the two general security goals of indistinguishability and non-malleability, each in the message space, key space, and hybrid message-key space to find six specific goals, a couple of them, namely complete indistinguishability and key non-malleability, are new. Then for each pair of goals, coming from the indistinguishability or non-malleability classes, we prove either an implication or a separation, completing the full picture of relationships among all these security notions. The implications and separations are respectively supported by formal proofs (i.e., reductions) in the concrete-security framework and by counterexamples. [ABSTRACT FROM AUTHOR]

Message authentication codes (MACs) based on universal hash-function families are becoming increasingly popular due to their fast implementation. In this paper, we investigate a family of universal hash functions that has been appeared repeatedly in the literature and provide a detailed algebraic analysis for the security of authentication codes based on this universal hash family. In particular, the universal hash family under analysis, as appeared in the literature, uses operation in the finite field ℤℤ p. No previous work has studied the extension of such universal hash family when computations are performed modulo a non-prime integer n. In this work, we provide the first such analysis. We investigate the security of authentication when computations are performed over arbitrary finite integer rings ℤℤ n and derive an explicit relation between the prime factorization of n and the bound on the probability of successful forgery. More specifically, we show that the probability of successful forgery against authentication codes based on such a universal hash-function family is bounded by the reciprocal of the smallest prime factor of the modulus n. [ABSTRACT FROM AUTHOR]

Biggs has recently proposed the critical group of a certain class of finite graphs as a platform group for cryptosystems relying on the difficulty of the discrete log problem. The paper uses techniques from the theory of Picard groups on finite graphs to show that the discrete log problem can be efficiently solved in Biggs's groups. Thus this class of groups is not suitable as a platform for discrete logarithm based cryptography. [ABSTRACT FROM AUTHOR]

In this paper, we present an approach to apply numerical methods in the cryptanalysis of modern cryptographic algorithms. We focus on the stream cipher Trivium. It is a stream cipher recommended by the eStream project in the hardware category. We use numerical methods to attack a reduced version of Trivium - called Bivium A. We first set up a system of equations describing the internal state of the cipher and convert it into a system over the reals. Four different techniques for the conversion are discussed. At this point we are able to apply numerical methods. We choose the DIRECT algorithm by D. R. Jones et al. and the Interior Reflective Newton Method by Coleman and Li. Results, occurring problems in this approach and possible future research directions are discussed. [ABSTRACT FROM AUTHOR]

This paper shows that the advantage of any q-query adversary (which makes at most q queries) for distinguishing OMAC from a uniform random function is roughly Lq2/2 n. Here L is the number of blocks of the longest query and n is the output size of the uniform random function. The so far best bound is roughly σσ2/2 n == O( L2 q2/2 n) and hence our new bound is an improved bound. Our improved security analysis also works for OMAC1 and CMAC which has been recommended by NIST as a candidate of blockcipher based MAC. [ABSTRACT FROM AUTHOR]

Statistical analysis of symmetric key attacks aims to obtain an expression for the data complexity which is the number of plaintext-ciphertext pairs needed to achieve the parameters of the attack. Existing statistical analyses invariably use some kind of approximation, the most common being the approximation of the distribution of a sum of random variables by a normal distribution. Such an approach leads to expressions for data complexities which are inherently approximate. Prior works do not provide any analysis of the error involved in such approximations. In contrast, this paper takes a rigorous approach to analyzing attacks on block ciphers. In particular, no approximations are used. Expressions for upper bounds on the data complexities of several basic and advanced attacks are obtained. The analysis is based on the hypothesis testing framework. Probabilities of type-I and type-II errors are upper bounded by using standard tail inequalities. In the cases of single linear and differential cryptanalysis, we use the Chernoff bound. For the cases of multiple linear and multiple differential cryptanalysis, Hoeffding bounds are used. This allows bounding the error probabilities and obtaining expressions for data complexities. We believe that our method provides important results for the attacks considered here and more generally, the techniques that we develop should have much wider applicability. [ABSTRACT FROM AUTHOR]

In this paper, we observe simple yet subtle interconnections among design theory, coding theory and cryptography. Maximum distance separable (MDS) matrices have applications not only in coding theory but are also of great importance in the design of block ciphers and hash functions. It is nontrivial to find MDS matrices which could be used in lightweight cryptography. In the SAC 2004 paper [12], Junod and Vaudenay considered bi-regular matrices which are useful objects to build MDS matrices. Bi-regular matrices are those matrices all of whose entries are nonzero and all of whose 2 x 2 submatrices are nonsingular. Therefore MDS matrices are bi-regular matrices, but the converse is not true. They proposed the constructions of efficient MDS matrices by studying the two major aspects of a d x d bi-regular matrix M, namely v1(M), i.e. the number of occurrences of 1 in M, and c1(M), i.e. the number of distinct elements in M other than 1. They calculated the maximum number of ones that can occur in a d x d bi-regular matrices, i.e. v1d,d for d up to 8, but with their approach, finding v1d,d for d ≥9 seems difficult. In this paper, we explore the connection between the maximum number of ones in bi-regular matrices and the incidence matrices of Balanced Incomplete Block Design (BIBD). In this paper, tools are developed to compute v1d,d for arbitrary d. Using these results, we construct a restrictive version of d x d bi-regular matrices, introducing by calling almost-bi-regular matrices, having v1d,d ones for d ≤21. Since, the number of ones in any d x d MDS matrix cannot exceed the maximum number of ones in a d x d bi-regular matrix, our results provide an upper bound on the number of ones in any d x d MDS matrix. We observe an interesting connection between Latin squares and bi-regular matrices and study the conditions under which a Latin square becomes a bi-regular matrix and finally construct MDS matrices from Latin squares. Also a lower bound of c1(M)is computed for d x d bi-regular matrices M such that v1(M)=v1d,d, where d =q² +q +1 and q is any prime power. Finally, d x d efficient MDS matrices are constructed for d up to 8 from bi-regular matrices having maximum number of ones and minimum number of other distinct elements for lightweight applications. [ABSTRACT FROM AUTHOR]

The paper is concerned with relations between the correlation-immunity (stability) and the perfectly balancedness of Boolean functions. It is shown that an arbitrary perfectly balanced Boolean function fails to satisfy a certain property that is weaker than the 1-stability. This result refutes some assertions by Markus Dichtl. On the other hand, we present new results on barriers of perfectly balanced Boolean functions which show that any perfectly balanced function such that the sum of the lengths of barriers is smaller than the length of variables, is 1-stable. [ABSTRACT FROM AUTHOR]

Vulnerability of communication of digital images is an extremely important issue nowadays, particularlywhen the images are communicated through insecure channels. To improve communication security, many cryptosystems have been presented in the image encryption literature. This paper proposes a novel image encryption technique based on an algorithm that is faster than current methods. The proposed algorithm eliminates the step in which the secrete key is shared during the encryption process. It is formulated based on the symmetric encryption, asymmetric encryption and steganography theories. The image is encrypted using a symmetric algorithm, then, the secret key is encrypted by means of an asymmetrical algorithm and it is hidden in the ciphered image using a least significant bits steganographic scheme. The analysis results show that while enjoying the faster computation, our method performs close to optimal in terms of accuracy. [ABSTRACT FROM AUTHOR]

In this paper we first investigate the use of Markov Chain Monte Carlo (MCMC) methods to attack classical ciphers. MCMC has previously been used to break simple substitution, transposition and substitution-transposition ciphers. Here, we improve the accuracy of obtained results by these algorithms and we show the performance of the algorithms using quasi random numbers such as Faure, Sobol and Niederreiter sequences. [ABSTRACT FROM AUTHOR]

Two Boolean functions are affine equivalent if one can be obtained from the other by applying an affine transformation to the input variables. For a long time, there have been efforts to investigate the affine equivalence of Boolean functions. Due to the complexity of the general problem, only affine equivalence under certain groups of permutations is usually considered. Boolean functions which are invariant under the action of cyclic rotation of the input variables are known as rotation symmetric (RS) Boolean functions. Due to their speed of computation and the prospect of being good cryptographic Boolean functions, this class of Boolean functions has received a lot of attention from cryptographic researchers. In this paper, we study affine equivalence for the simplest rotation symmetric Boolean functions, called MRS functions, which are generated by the cyclic permutations of a single monomial. Using Pólya's enumeration theorem, we compute the number of equivalence classes, under certain large groups of permutations, for these MRS functions in any number n of variables. If n is prime, we obtain the number of equivalence classes under the group of all permutations of the variables. [ABSTRACT FROM AUTHOR]

The paper is concerned with n-place Boolean functions not admitting implicents of k variables, 1 ¢ k < n. Estimates for the minimal possible weight w(n, k) of such functions are obtained. It is shown that w(n, 1) = 2, n = 2, 3,…, and w(n, 2) È log2n as n Ù ∞, and moreover, for k > 2 there exists n0 such that w(n, k) > 2k-2 - log2n for all n > n0. [ABSTRACT FROM AUTHOR]

The paper is concerned with problems in steganography on the detection of embeddings and statistical estimation of positions at which message bits are embedded. Binary stationary Markov chains with known or unknown matrices of transition probabilities are used as mathematical models of cover sequences (container files). Based on the runs statistics and the likelihood ratio statistic, statistical tests are constructed for detecting the presence of embeddings. For a family of contiguous alternatives, the asymptotic power of statistical tests based on the runs statistics is found. An algorithm of polynomial complexity is developed for the statistical estimation of positions with embedded bits. Results of computer experiments are presented. [ABSTRACT FROM AUTHOR]