Private-key Encryption Scheme Research Articles

SeIMC: A GSW-Based Secure and Efficient Integer Matrix Computation Scheme With Implementation

As atomic operations, secure matrix-based computations using homomorphic encryption (HE) have attracted much attention in cloud-based machine learning. However, most existing secure matrix computation solutions that focus on HE schemes suffer efficiency loss as the size of the matrix, which greatly limits their applications in the big data environment. To address these issues, this paper proposes seIMC, an integer matrix computation scheme based on the Gentry-Sahai-Waters (GSW) scheme, to cope with privacy protection and secure computation of large-scale data. In detail, we translate the GSW scheme to encrypt an integer matrix modulo $q$ (i.e., a large positive integer), and homomorphically compute matrix addition and multiplication, which is a natural extension of HAO scheme. Besides, the correctness and security analysis of seIMC are shown, and complexity analysis is also given in this study. Furthermore, the proposed schemes are implemented, including public-key encryption and private-key encryption schemes. Compared with existing secure matrix computation schemes, the proposed scheme performs better in execution time. Finally, seIMC is applied to solve the problem of the number of ways in which any two participants make friends through $k$ steps in an encrypted social network. Experiments show that when the cloud server processes an integer matrix of 1000 people with a security level of 90, namely, 1 million data volumes, it only takes approximately 1.9 minutes for each homomorphic matrix multiplication. Hence, the practicality of the proposed seIMC in privacy protection under a big data environment is highly proven.

A Private Key Encryption Scheme based on Amicable Number with User defined Cipher Block Sequencing Techniques

A Private Key Encryption Scheme based on Amicable Number with User defined Cipher Block Sequencing Techniques

Physical‐layer security in Internet of Things based on compressed sensing and frequency selection

Information security is a vital concern in Internet of Things (IoT). Traditional security method based on public or private key encryption scheme is limited by the trade-off between low cost and high level of security. Among different security solutions, utilising compressed sensing (CS) in combination with the physical-layer security to achieve the security is a remarkable method. However, in the current literatures, little attention has been given to the area of static environment, which will lead the risk of information leakage in the CS security model. In this study, the authors propose a new CS security model, in which circulant matrix is exploited to improve the generation efficiency of the measurement matrix, and binary resilient functions are utilised to enhance the security. Furthermore, considering the practical application, they present a feasible framework, named CS security scheme based on frequency-selective, where the frequency-selective feature of the wireless channel is applied to support the static environment. To verify the effectiveness of the proposed scheme, they conducted experiments and numerical simulations to evaluate the performance, and the results are satisfactory.

Incremental Deterministic Public-Key Encryption

Motivated by applications in large storage systems, we initiate the study of incremental deterministic public-key encryption. Deterministic public-key encryption, introduced by Bellare, Boldyreva, and O'Neill (CRYPTO '07), provides an alternative to randomized public-key encryption in various scenarios where the latter exhibits inherent drawbacks. A deterministic encryption algorithm, however, cannot satisfy any meaningful notion of security for low-entropy plaintexts distributions, but Bellare et al. demonstrated that a strong notion of security can in fact be realized for relatively high-entropy plaintext distributions. In order to achieve a meaningful level of security, a deterministic encryption algorithm should be typically used for encrypting rather long plaintexts for ensuring a sufficient amount of entropy. This requirement may be at odds with efficiency constraints, such as communication complexity and computation complexity in the presence of small updates. Thus, a highly desirable property of deterministic encryption algorithms is incrementality: Small changes in the plaintext translate into small changes in the corresponding ciphertext. We present a framework for modeling the incrementality of deterministic public-key encryption. Our framework extends the study of the incrementality of cryptography primitives initiated by Bellare, Goldreich and Goldwasser (CRYPTO '94). Within our framework, we propose two schemes, which we prove to enjoy an optimal tradeoff between their security and incrementality up to lower-order factors. Our first scheme is a generic method which can be based on any deterministic public-key encryption scheme, and, in particular, can be instantiated with any semantically secure (randomized) public-key encryption scheme in the random-oracle model. Our second scheme is based on the Decisional Diffie---Hellman assumption in the standard model. The approach underpinning our schemes is inspired by the fundamental "sample-then-extract" technique due to Nisan and Zuckerman (JCSS '96) and refined by Vadhan (J. Cryptology '04), and by the closely related notion of "locally computable extractors" due to Vadhan. Most notably, whereas Vadhan used such extractors to construct private-key encryption schemes in the bounded-storage model, we show that techniques along these lines can also be used to construct incremental public-key encryption schemes.

Low-Complexity Multiclass Encryption by Compressed Sensing

The idea that compressed sensing may be used to encrypt information from unauthorised receivers has already been envisioned, but never explored in depth since its security may seem compromised by the linearity of its encoding process. In this paper we apply this simple encoding to define a general private-key encryption scheme in which a transmitter distributes the same encoded measurements to receivers of different classes, which are provided partially corrupted encoding matrices and are thus allowed to decode the acquired signal at provably different levels of recovery quality. The security properties of this scheme are thoroughly analysed: firstly, the properties of our multiclass encryption are theoretically investigated by deriving performance bounds on the recovery quality attained by lower-class receivers with respect to high-class ones. Then we perform a statistical analysis of the measurements to show that, although not perfectly secure, compressed sensing grants some level of security that comes at almost-zero cost and thus may benefit resource-limited applications. In addition to this we report some exemplary applications of multiclass encryption by compressed sensing of speech signals, electrocardiographic tracks and images, in which quality degradation is quantified as the impossibility of some feature extraction algorithms to obtain sensitive information from suitably degraded signal recoveries.

Quantum probabilistic encryption scheme based on conjugate coding

We present a quantum probabilistic encryption algorithm for a private-key encryption scheme based on conjugate coding of the qubit string. A probabilistic encryption algorithm is generally adopted in public-key encryption protocols. Here we consider the way it increases the unicity distance of both classical and quantum private-key encryption schemes. The security of quantum probabilistic private-key encryption schemes against two kinds of attacks is analyzed. By using the no-signalling postulate, we show that the scheme can resist attack to the key. The scheme's security against plaintext attack is also investigated by considering the information-theoretic indistinguishability of the encryption scheme. Finally, we make a conjecture regarding Breidbart's attack.

Obfuscation for Cryptographic Purposes

Loosely speaking, an obfuscation O of a function f should satisfy two requirements: firstly, using O, it should be possible to evaluate f; secondly, O should not reveal anything about f that cannot be learnt from oracle access to f alone. Several definitions for obfuscation exist. However, most of them are very hard to satisfy, even when focusing on specific applications such as obfuscating a point function (e.g., for authentication purposes). In this work, we propose and investigate two new variants of obfuscation definitions. Our definitions are simulation-based (i.e., require the existence of a simulator that can efficiently generate fake obfuscations) and demand only security on average (over the choice of the obfuscated function). We stress that our notions are not free from generic impossibilities: there exist natural classes of function families that cannot be securely obfuscated. Hence we cannot hope for a general-purpose obfuscator with respect to our definition. However, we prove that there also exist several natural classes of functions for which our definitions yield interesting results. Specifically, we show that our definitions have the following properties: Usefulness: -- Securely obfuscating (the encryption function of) a secure private-key encryption scheme yields a secure public-key encryption scheme. Achievability: -- There exist obfuscatable private-key encryption schemes. Also, a point function chosen uniformly at random can easily be obfuscated with respect to the weaker one (but not the stronger one) of our definitions. (Previous work focused on obfuscating point functions from arbitrary distributions.) Generic impossibilities: -- There exist unobfuscatable private-key encryption schemes. Furthermore, pseudorandom functions cannot be obfuscated with respect to our definitions. Our results show that, while it is hard to avoid generic impossibilities, useful and reasonable obfuscation definitions are possible when considering specific tasks (i.e., function families).

Bounds on the Efficiency of Generic Cryptographic Constructions

A central focus of modern cryptography is the construction of efficient, high-level cryptographic tools (e.g., encryption schemes) from weaker, low-level cryptographic primitives (e.g., one-way functions). Of interest are both the existence of such constructions and their efficiency. Here, we show essentially tight lower bounds on the best possible efficiency of any black-box construction of some fundamental cryptographic tools from the most basic and widely used cryptographic primitives. Our results hold in an extension of the model introduced by Impagliazzo and Rudich and improve and extend earlier results of Kim, Simon, and Tetali. We focus on constructions of pseudorandom generators, universal one-way hash functions, and digital signatures based on one-way permutations, as well as constructions of public- and private-key encryption schemes based on trapdoor permutations. In each case, we show that any black-box construction beating our efficiency bound would yield the unconditional existence of a one-way function and thus, in particular, prove $P \neq NP$.

Improving the information rate of a private-key cryptosystem based on product codes

Recently, Sun proposed a private-key encryption scheme based on the product codes with the capability of correcting a special type of structured errors. In this paper, we present a novel method to improve the information rate of Sun's scheme. This method uses the added error vector to carry additional information. Some information bits are mapped into an error vector with the special structure to be added to a codeword. Once the error vector can be identified, the additional information can be recovered.

On private-key encryption using product codes

In this paper, we analyze the security of J. and R.M. Campello de Souza's private-key encryption scheme, which is based on the product codes with the capability of correcting a special type of structured errors. According to our cryptanalysis, we show that J. and R.M. Campello de Souza's scheme is insecure against chosen-plaintext attacks. A secure modified scheme is consequently proposed to enhance the security. In addition, we propose a modification of the proposed scheme which provides joint error correction and encryption.

Secret sharing over infinite domains

Let ? n be a monotone, nontrivial family of sets over {1, 2, ?,n}. An ? n perfect secret-sharing scheme is a probabilistic mapping of a secret ton shares, such that: Various secret-sharing schemes have been proposed, and applications in diverse contexts were found. In all these cases the set of secrets and the set of shares are finite. In this paper we study the possibility of secret-sharing schemes overinfinite domains. The major case of interest is when the secrets and the shares are taken from acountable set, for example all binary strings. We show that no ? n secret-sharing scheme over any countable domain exists (for anyn ? 2). One consequence of this impossibility result is that noperfect private-key encryption schemes, over the set of all strings, exist. Stated informally, this means that there is no way to encrypt all strings perfectly without revealing information about their length. These impossibility results are stated and proved not only for perfect secret-sharing and private-key encryption schemes, but also for wider classes--weak secret-sharing and private-key encryption schemes. We constrast these results with the case where both the secrets and the shares are real numbers. Simple perfect secret-sharing schemes (and perfect private-key encryption schemes) are presented. Thus, infinity alone does not rule out the possibility of secret sharing.