Quantum Noise Randomized Ciphers

We review the notion of a classical random cipher and its advantages. We sharpen the usual description of random ciphers to a particular mathematical characterization suggested by the salient feature responsible for their increased security. We describe a concrete system known as AlphaEta and show that it is equivalent to a random cipher in which the required randomization is effected by coherent-state quantum noise. We describe the currently known security features of AlphaEta and similar systems, including lower bounds on the unicity distances against ciphertext-only and known-plaintext attacks. We show how AlphaEta used in conjunction with any standard stream cipher such as AES (Advanced Encryption Standard) provides an additional, qualitatively different layer of security from physical encryption against known-plaintext attacks on the key. We refute some claims in the literature that AlphaEta is equivalent to a non-random stream cipher.Comment: Accepted for publication in Phys. Rev. A; Discussion augmented and re-organized; Section 5 contains a detailed response to 'T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, H. Imai: Phys. Lett. A 327 (2004) 28-32 /quant-ph/0310168' & 'T. Nishioka, T. Hasegawa, H. Ishizuka, K. Imafuku, H. Imai: Phys. Lett. A 346 (2005) 7

Variable-to-Fixed Length Homophonic Coding Suitable for Asymmetric Channel Coding

In communication through asymmetric channels the capacity-achieving input distribution is not uniform in general. Homophonic coding is a framework to invertibly convert a (usually uniform) message into a sequence with some target distribution, and is a promising candidate to generate codewords with the nonuniform target distribution for asymmetric channels. In particular, a Variable-to-Fixed length (VF) homophonic code can be used as a suitable component for channel codes to avoid decoding error propagation. However, the existing VF homophonic code requires the knowledge of the maximum relative gap of probabilities between two adjacent sequences beforehand, which is an unrealistic assumption for long block codes. In this paper we propose a new VF homophonic code without such a requirement by allowing one-symbol decoding delay. We evaluate this code theoretically and experimentally to verify its asymptotic optimality.Comment: Full version of the paper to appear in 2017 IEEE International Symposium on Information Theory (ISIT2017

Universal homophonic coding

Redundancy in plaintext is a fertile source of attack in any encryption system. Compression before encryption reduces the redundancy in the plaintext, but this does not make a cipher more secure. The cipher text is still susceptible to known-plaintext and chosen-plaintext attacks. The aim of homophonic coding is to convert a plaintext source into a random sequence by randomly mapping each source symbol into one of a set of homophones. Each homophone is then encoded by a source coder after which it can be encrypted with a cryptographic system. The security of homophonic coding falls into the class of unconditionally secure ciphers. The main advantage of homophonic coding over pure source coding is that it provides security both against known-plaintext and chosen-plaintext attacks, whereas source coding merely protects against a ciphertext-only attack. The aim of this dissertation is to investigate the implementation of an adaptive homophonic coder based on an arithmetic coder. This type of homophonic coding is termed universal, as it is not dependent on the source statistics.Computer ScienceM.Sc. (Computer Science

Digital rights management (DRM) - watermark encoding scheme for JPEG images

The aim of this dissertation is to develop a new algorithm to embed a watermark in JPEG compressed images, using encoding methods. This encompasses the embedding of proprietary information, such as identity and authentication bitstrings, into the compressed material. This watermark encoding scheme involves combining entropy coding with homophonic coding, in order to embed a watermark in a JPEG image. Arithmetic coding was used as the entropy encoder for this scheme. It is often desired to obtain a robust digital watermarking method that does not distort the digital image, even if this implies that the image is slightly expanded in size before final compression. In this dissertation an algorithm that combines homophonic and arithmetic coding for JPEG images was developed and implemented in software. A detailed analysis of this algorithm is given and the compression (in number of bits) obtained when using the newly developed algorithm (homophonic and arithmetic coding). This research shows that homophonic coding can be used to embed a watermark in a JPEG image by using the watermark information for the selection of the homophones. The proposed algorithm can thus be viewed as a ‘key-less’ encryption technique, where an external bitstring is used as a ‘key’ and is embedded intrinsically into the message stream. The algorithm has achieved to create JPEG images with minimal distortion, with Peak Signal to Noise Ratios (PSNR) of above 35dB. The resulting increase in the entropy of the file is within the expected 2 bits per symbol. This research endeavor consequently provides a unique watermarking technique for images compressed using the JPEG standard.Dissertation (MEng)--University of Pretoria, 2008.Electrical, Electronic and Computer Engineeringunrestricte

Adaptive homophonic coding techniques for enhanced e-commerce security

This dissertation considers a method to convert an ordinary cipher system, as used to secure e-commerce transactions, into an unconditionally secure cipher system, i.e. one that generates ciphertext that does not contain enough statistical information to break the cipher, irrespective of how much ciphertext is available. Shannon showed that this can be achieved by maximizing the entropy of the message sequence to be encrypted. This, in turn, achieved by means of homophonic coding. Homophonic coding substitutes characters in the message source with randomly chosen codewords. It offers the advantage that it enables protection against known- and chosen plaintext attacks on cipher algorithms since source statistics are randomly changed before encryption. The disadvantage of homophonic substitution is that it will in general increase the length of the message sequence. To compensate for this, homophonic coding is combined with the data compression algorithm known as arithmetic coding. It is shown that the arithmetic coding algorithm can be adapted to perform homophonic coding by dyadically decomposing the character probabilities in its probability estimation phase. By doing this, a faster version of arithmetic coding, known as shift-and-add arithmetic coding can be implemented. A new method of statistical modelling, based on an Infinite Impulse Response filtering method is presented. A method to adapt the well-known Lempel-Ziv- Welch compression algorithm to perform homophonic coding is also presented. The procedure involves a bit-wise exclusive-or randomization operation during encoding. The results show that the adapted algorithms do indeed increase the entropy of the source sequences by no more than 2 bits/symbol, and even offers compression in some cases.Dissertation (MEng (Data Security))--University of Pretoria, 2006.Electrical, Electronic and Computer Engineeringunrestricte

How to Achieve the Capacity of Asymmetric Channels

We survey coding techniques that enable reliable transmission at rates that approach the capacity of an arbitrary discrete memoryless channel. In particular, we take the point of view of modern coding theory and discuss how recent advances in coding for symmetric channels help provide more efficient solutions for the asymmetric case. We consider, in more detail, three basic coding paradigms. The first one is Gallager's scheme that consists of concatenating a linear code with a non-linear mapping so that the input distribution can be appropriately shaped. We explicitly show that both polar codes and spatially coupled codes can be employed in this scenario. Furthermore, we derive a scaling law between the gap to capacity, the cardinality of the input and output alphabets, and the required size of the mapper. The second one is an integrated scheme in which the code is used both for source coding, in order to create codewords distributed according to the capacity-achieving input distribution, and for channel coding, in order to provide error protection. Such a technique has been recently introduced by Honda and Yamamoto in the context of polar codes, and we show how to apply it also to the design of sparse graph codes. The third paradigm is based on an idea of B\"ocherer and Mathar, and separates the two tasks of source coding and channel coding by a chaining construction that binds together several codewords. We present conditions for the source code and the channel code, and we describe how to combine any source code with any channel code that fulfill those conditions, in order to provide capacity-achieving schemes for asymmetric channels. In particular, we show that polar codes, spatially coupled codes, and homophonic codes are suitable as basic building blocks of the proposed coding strategy.Comment: 32 pages, 4 figures, presented in part at Allerton'14 and published in IEEE Trans. Inform. Theor

From plurals to superplurals: in defence of higher-level plural logic

Plural Logic is an extension of First-Order Logic with plural terms and quantifiers. When its plural terms are interpreted as denoting more than one object at once, Plural Logic is usually taken to be ontologically innocent: plural quantifiers do not require a domain of their own, but range plurally over the first-order domain of quantification. Given that Plural Logic is equi-interpretable with Monadic Second-Order Logic, it gives us its expressive power at the low ontological cost of a first-order language. This makes it a valuable tool in various areas of philosophy. Some authors believe that Plural Logic can be extended into an even more expressive logic, Higher-Level Plural Logic, by adding higher-level plural terms and quantifiers to it. The basic idea is that second-level plurals stand to plurals like plurals stand to singulars (analogously for higher levels). Allegedly, Higher-Level Plural Logic enjoys the expressive power of type theory while, again, committing us only to the austere ontology of a first-order language. Were this really the case, Higher-Level Plural Logic would be a very useful tool, extending and strengthening some of the applications of Plural Logic. However, while the notions of plural reference and quantification enjoy widespread acceptance today, their higher-level counterparts have been received with scepticism. The main objection raised against them is that higher-level plural reference is unintelligible. This has been argued, among others, on the grounds that there are no higher-level plurals in natural language and that, if there were any, they could be eliminated. In this thesis, after introducing the debate on plurals in Chapters 1 and 2, I turn to defending the legitimacy of the notion of higher-level plural reference. To this end, in Chapter 3, I present and elucidate the notion. Next, in Chapter 4, I show that some natural languages clearly contain these expressions and that they do so in an ineliminable manner. Finally, in Chapters 5 and 6, I develop a semantics for higher-level plurals that employs only devices previously well-understood by English speakers. To finish, in Chapter 7, I describe an application of Higher-level Plural Logic: a strengthening of the neo-Fregean programme. After describing my proposal, I turn to the issue of the logical status of this formalism and defend an optimistic take on the matter

Supervenience, Dependence, Disjunction

This paper explores variations on and connections between the topics mentioned in its title, using as something of an anchor the discussion in Valentin Goranko and Antti Kuusisto’s “Logics for propositional determinacy and independence”, a venture into what the authors call the logic of determinacy, which they contrast with (a demodalized version of) Jouko Väänänen’s modal dependence logic. As they make clear in their discussion, these logics are closely connected with the topics of noncontingency and supervenience. Two opening sections of the present paper address some of these connections, including related earlier logical work by the present author as well as very recent work by Jie Fan. The Väänänen-inspired treatment is presented in a third section, and then, in Sections 4 and 5, as a kind of centerpiece for the discussion, we follow Goranko and Kuusisto in elaborating one principal reason offered for preferring their own approach over that treatment, which concerns some anomalies over the behaviour of disjunction in the latter treatment. Sections 6 and 7 look at dependence and (several different versions of) disjunction in inquisitive logic, especially as presented by Ivano Ciardelli. Section 8 revisits the less formal property-supervenience literature with issues from the first two sections of the paper in mind, and we conclude with a Postscript addressing a further conceptual issue pertaining to the relation between modal and quantificational dependence logics