An Integer Erasure Correction Coding and Its Application for Security Enhancement of Encryption

We develop a systematic approach, based on convex programming and real analysis for obtaining upper bounds on the capacity of the binary deletion channel and, more generally, channels with i.i.d. insertions and deletions. Other than the classical deletion channel, we give special attention to the Poisson-repeat channel introduced by Mitzenmacher and Drinea (IEEE Transactions on Information Theory, 2006). Our framework can be applied to obtain capacity upper bounds for any repetition distribution (the deletion and Poisson-repeat channels corresponding to the special cases of Bernoulli and Poisson distributions). Our techniques essentially reduce the task of proving capacity upper bounds to maximizing a univariate, real-valued, and often concave function over a bounded interval. The corresponding univariate function is carefully designed according to the underlying distribution of repetitions, and the choices vary depending on the desired strength of the upper bounds as well as the desired simplicity of the function (e.g., being only efficiently computable versus having an explicit closed-form expression in terms of elementary, or common special, functions). Among our results, we show the following: (1) The capacity of the binary deletion channel with deletion probability d is at most (1 − d ) φ for d ≥ 1/2 and, assuming that the capacity function is convex, is at most 1 − d log(4/φ) for d < 1/2, where φ = (1 + √5)/2 is the golden ratio. This is the first nontrivial capacity upper bound for any value of d outside the limiting case d → 0 that is fully explicit and proved without computer assistance. (2) We derive the first set of capacity upper bounds for the Poisson-repeat channel. Our results uncover further striking connections between this channel and the deletion channel and suggest, somewhat counter-intuitively, that the Poisson-repeat channel is actually analytically simpler than the deletion channel and may be of key importance to a complete understanding of the deletion channel. (3) We derive several novel upper bounds on the capacity of the deletion channel. All upper bounds are maximums of efficiently computable, and concave, univariate real functions over a bounded domain. In turn, we upper bound these functions in terms of explicit elementary and standard special functions, whose maximums can be found even more efficiently (and sometimes analytically, for example, for d = 1/2).

We derive upper and lower bounds on the encoding and decoding complexity of two capacity-achieving ensembles of irregular repeat-accumulate (IRA1 and IRA2) codes on the binary erasure channel (BEC). These bounds are expressed in terms of the gap between the channel capacity and the rate of a typical code from this ensemble for which reliable communications is achievable under message-passing iterative (MPI) decoding. The complexity of the ensemble of IRA1 codes grows like the negative logarithm of the gap to capacity. On the other hand, the complexity of the ensemble of IRA2 codes with any choice of the degree distribution grows at least like the inverse square root of the gap to capacity, and at most like the inverse of the gap to capacity.

We present a simple proof that the capacity of the binary independent and identically distributed (i.i.d.) deletion channel, where each bit is deleted independently with probability d, is at least (1-d)/9, by developing a correspondence between the deletion channel and an insertion/deletion channel that we call a Poisson-repeat channel

This paper considers the problem of bit-wise channel coding over a Binary Symmetric Channel (BSC) with feedback. While it is known that feedback does not increase the capacity of a memoryless channel, it is believed to simplify the coding schemes for some channels. The most significant one is the Binary Erasure Channel (BEC) where capacity is achieved by a simple sequential bit-wise repetition code under which each bit is (re-)transmitted until it is received. This sequential bit-wise feedback code has the added advantage that it can be used for streaming applications over BECs. In contrast, there is no known sequential bit-wise code with feedback that can achieve nonzero transmission rate for a BSC. For example, under Posterior Matching for a binary input channel with feedback, also known as Horstein scheme, each message is considered in its entirety in a block coding manner. This paper proposes a sequential feedback coding scheme with a nested bit-wise structure that generalizes repetition codes. This scheme is shown to achieve strictly positive rate for a large class of binary input channels including a BSC with arbitrary cross-over probability $p \in(0, \frac{1}{2})$ . The analysis relies on characterizing a lower bound on the step-wise Extrinsic Jensen Shannon divergence.

4 - Serial interfaces

Liskov proposed several weakened versions of the random oracle model, called weakened random oracle models (WROMs), to capture the vulnerability of ideal compression functions, which are expected to have the standard security of hash functions, i.e., collision resistance, second-preimage resistance, and one-wayness properties. The WROMs offer additional oracles to break such properties of the random oracle. In this paper, we investigate whether public-key encryption schemes in the random oracle model essentially require the standard security of hash functions by the WROMs. In particular, we deal with four WROMs associated with the standard security of hash functions; the standard, collision tractable, second-preimage tractable, first-preimage tractable ones (ROM, CT-ROM, SPT-ROM, and FPT-ROM, respectively), done by Numayama et al. for digital signature schemes in the WROMs. We obtain the following results: (1) The OAEP is secure in all the four models. (2) The encryption schemes obtained by the Fujisaki-Okamoto conversion (FO) are secure in the SPT-ROM. However, some encryption schemes with FO are insecure in the FPT-ROM. (3) We consider two artificial variants wFO and dFO of FO for separation of the WROMs in the context of encryption schemes. The encryption schemes with wFO (dFO, respectively) are secure in the CT-ROM (ROM, respectively). However, some encryption schemes obtained by wFO (dFO, respectively) are insecure in the SPT-ROM (CT-ROM, respectively). These results imply that standard encryption schemes such as the OAEP and FO-based one do not always require the standard security of hash functions. Moreover, in order to make our security proofs complete, we construct an efficient sampling algorithm for the binomial distribution with exponentially large parameters, which was left open in Numayama et al.’s paper.

We consider binary deletion channels, where bits are deleted independently with probability d. We extend the framework used to analyze the capacity of binary deletion channels established by Diggavi and Grossglauser [2001], improving on their lower bounds. In Diggavi and Grossglauser, the codewords are generated by a first order Markov chain. Our improvements arise from two considerations. First, Diggavi and Grossglauser consider typical outputs, where an output is typical if an N bit input produces an output of at least N(1-d)(1-/spl epsi/) bits. We provide a stronger notion of a typical output that yields better bounds even for the cases studied in Diggavi and Grossglauser. Second, we consider codewords generated by more general processes than first order Markov chains.

We propose a network information flow strategy of optimal multicast with erasure correction coding (OMEC), in which erasure correction is a means of utilizing diversities rather than combating packet losses. An information source is first encoded by an erasure correction code and then optimally multicast by a server to sinks. The OMEC scheme has the following characteristics: (1) It is at least as good as optimal routing and, for some cases, can realize a network throughput arbitrarily larger than that achievable by pure routing. (2) For most scenarios, the approach yields a throughput comparable with the optimal throughput achievable with network coding. In fact, for most examples in the literature for which network coding makes high throughput gains compared to pure routing, OMEC performs close to the optimal. (3) Unlike general network coding, intermediate nodes are only required to route information. This makes OMEC compatible with currently deployed network structures. (4) Surprisingly, unlike pure optimal routing, OMEC can be efficiently computed in polynomial time. While OMEC is, in general, suboptimal compared to full fledged network coding, it enjoys most of the computational and throughput benefits associated with network coding over pure routing, without requiring any changes to existing hardware infrastructures or protocol stacks

Recently, it has been verified that the Reed-Muller (RM) code, which has been predicted for a long time in the field of code theory, achieves capacity in a binary erasure channel (BEC) with a MAP (maximum a posteriori) decoder. Through weight distribution interpretation, it was also discovered that the RM code achieves a binary memoryless symmetric (BMS) channel capacity. A successive cancellation list (SCL) technique has been studied as a practical decoder instead of a MAP decoder. In this paper, the performance improvement potential that can be improved when a generalized concatenated code (GCC) with an outer code is designed to improve the practical SCL decoder performance is analyzed. When information bits are used as frozen bits in these code-word designs, we analyze an inter-code-word distance and the decoding outage probability of the designed code. We expect that our results can be used as a conceptual base for improving communication methods in the future development of channel encoding technology.

We consider here a single sender-destination multi-relay channel. The links connecting the nodes are supposed to be erasure where symbols are received correctly without any error, or lost. We consider that the nodes are not able to use any interference cancellation mechanism. The interference might be suppressed through using separated physical channel or thought a time-sharing mechanism. This model is realistic for many practical scenarios in the context of wireless networks. In previous works, the capacity region of broadcast erasure channels as well as the capacity of the single-sender relay channel (under degraded and non-degraded hypothesis) has been derived. This paper extends the previous results to the more general case of multi-relay channels. We derive the cut-set bound for a general (stationary ergodic) multi-relay erasure channel, and we show that it can be reached through a practical linear coding scheme based on MDS codes.

In this paper, we have proposed a novel encryption scheme with chaotic process based on Enigma. The encryption scheme takes the advantage of the approximate non-linear mechanism of original Enigma, with the chaos controlling the encryption process. It has strengthened the randomness of plaintext replacement and improved the security of the encryption scheme. The results of encrypting images and letters proved that the novel encryption scheme shows good performances in the analysis of key sensitivity related coefficient between adjacent pixels and differential cryptanalysis.

An image encryption scheme based on chaotic systems is proposed in this paper. By combining the spatial-domain encryption of digital images and the traditional stream ciphers technology, the security of the encryption scheme is enhanced effectively. Instead of encrypting an image in a chaotic signal directly, the proposed scheme uses two chaotic systems based on the thought of higher secrecy of multi-system. One of the chaotic systems is used to generate a chaotic sequence. Then this chaotic sequence is transformed into a binary stream by a threshold function. The other chaotic system is used to construct a permutation matrix. Firstly, the pixel values of a plain image are modified randomly using the binary stream as a key stream. Secondly, the modified image is encrypted again by permutation matrix. The security of encryption scheme is analyzed in detail. And the simulation results show that the proposed scheme has a better efficiency than others' and a high security performance

Specific attack and security enhancement to optical image cryptosystem based on two random masks and interference

The concept of policy-based cryptography is a promising paradigm for trust establishment and authorization in largescale open environments like the Internet and Mobile Networks. It aims at providing a framework for performing cryptographic operations with respect to policies formalized as monotone Boolean expressions written in standard normal forms. A policy involves conjunctions and disjunctions of conditions where each condition is fulfilled by a digital credential representing the signature of a specific credential issuer on a set of statements about a certain entity. Therefore, an entity fulfills a policy if any only if it has been issued a set of credentials fulfilling the combination of conditions specified by the policy.In this work, we focus on policy-based encryption schemes which allow to encrypt a message according to a policy so that only entities fulfilling the policy are able to decrypt the message. More generally, policy-based encryption belongs to an emerging family of encryption schemes sharing the ability to integrate encryption with access control structures. This ability is mainly enabled by bilinear pairings over elliptic curves and allows for several interesting applications in different contexts.A policy-based encryption scheme has to fulfill two primary requirements: on one hand, provable security under well defined attack models. On the other hand, efficiency, especially when dealing with the conjunctions and disjunctions of credential-based conditions.The contributions of our research work are twofold:1. The standard acceptable notion of security for public-key encryption schemes is indistinguishability against chosen ciphertext attacks. Hence, it is natural to require that a policy-based encryption scheme also satisfies this strong notion of security. However, the definition of this security notion must be adapted to the policy-based setting. Our first contribution is the definition of policy-oriented security model for policy-based encryption schemes as well as the development of an efficient policy-based encryption scheme that is provably secure under our security model in the random oracle model.2. Policy-based encryption schemes may suffer from the key-escrow property i.e. in addition to the legitimate holder of the credentials fulfilling the encryption policy, any collusion of credential issuers who are able to issue a set of credentials fulfilling the policy can decrypt the message. Our second contribution is to address this issue through the notion of policy-based public-key encryption. The latter allows encrypting a message not only with respect to a policy but also according to a public-key so that only an entity fulfilling the policy and having access to the corresponding private-key is able to decrypt the message. We developed a policy-based public-key encryption scheme from bilinear pairings and proved its security under the corresponding security model. Our proposal improves related work in terms of both security and efficiency.

The Fujisaki-Okamoto (FO) conversion is a generic conversion to enhance a public key encryption scheme with security of one-way against chosen plaintext attacks (OW-CPA) to security of indistinguishable against adaptive chosen ciphertext attacks (IND-CCA) in the random oracle model. Existing works have shown that the FO conversion also can generically upgrade the security of the identity-based encryption (IBE) schemes or certificateless public key encryption (CL-PKE) schemes. However, it is still unknown if the same holds for certificate-based encryption (CBE) schemes. In this paper, we investigate the generic security of the CBE scheme obtained by applying the FO conversion to an arbitrary underlying OW-CBE-CPA secure CBE scheme and confirm that the FO conversion can generically convert any OW-CBE-CPA secure CBE into an IND-CBE-CCA secure CBE. We also note that the straightforward application of the FO conversion only leads to a CBE scheme with a loose reduction. To solve this problem, we propose an enhanced FO conversion which just introduces minor extra computation overhead, but results in considerably more efficient security reduction.