Hiding Symbols and Functions: New Metrics and Constructions for Information-Theoretic Security

We present information-theoretic definitions and results for analyzing symmetric-key encryption schemes beyond the perfect secrecy regime, i.e. when perfect secrecy is not attained. We adopt two lines of analysis, one based on lossless source coding, and another akin to rate-distortion theory. We start by presenting a new information-theoretic metric for security, called symbol secrecy, and derive associated fundamental bounds. We then introduce list-source codes (LSCs), which are a general framework for mapping a key length (entropy) to a list size that an eavesdropper has to resolve in order to recover a secret message. We provide explicit constructions of LSCs, and demonstrate that, when the source is uniformly distributed, the highest level of symbol secrecy for a fixed key length can be achieved through a construction based on minimum-distance separable (MDS) codes. Using an analysis related to rate-distortion theory, we then show how symbol secrecy can be used to determine the probability that an eavesdropper correctly reconstructs functions of the original plaintext. We illustrate how these bounds can be applied to characterize security properties of symmetric-key encryption schemes, and, in particular, extend security claims based on symbol secrecy to a functional setting.Comment: Submitted to IEEE Transactions on Information Theor

Plaintext Recovery in DES-like Cryptosystems Based on S-boxes with Embedded Parity Check

We describe an approach for recovering the plaintext in block ciphers having a design structure similar to the Data Encryption Standard but with improperly constructed S-boxes. The experiments with a backtracking search algorithm performing this kind of attack against modified DES/Triple-DES in ECB mode show that the unknown plaintext can be recovered with a small amount of uncertainty and this algorithm is highly efficient both in time and memory costs for plaintext sources with relatively low entropy. Our investigations demonstrate once again that modifications resulting to S-boxes which still satisfy some design criteria may lead to very weak ciphers. ACM Computing Classification System (1998): E.3, I.2.7, I.2.8.This work was presented in part at the 1-st International Conference Bulgarian Cryptography Days 2012, Sofia, Bulgaria, 20–21 September 2012

On applications of simulated annealing to cryptology

Boolean functions are critical building blocks of symmetric-key ciphers. In most cases, the security of a cipher against a particular kind of attacks can be explained by the existence of certain properties of its underpinning Boolean functions. Therefore, the design of appropriate functions has received significant attention from researchers for several decades. Heuristic methods have become very powerful tools for designing such functions. In this thesis, we apply simulated annealing methods to construct Boolean functions with particular properties. Our results meet or exceed the best results of available theoretical constructions and/or heuristic searches in the literature, including a 10-variable balanced Boolean function with resiliency degree 2, algebraic degree 7, and nonlinearity 488 for the first time. This construction affirmatively answers the open problem about the existence of such functions. This thesis also includes results of cryptanalysis for symmetric ciphers, such as Geffe cipher and TREYFER cipher

On a secondary construction of quadratic APN functions

Almost perfect nonlinear functions possess the optimal resistance to the differential cryptanalysis and are widely studied. Most known constructions of APN functions are obtained as functions over finite fields F27 and very little is known about combinatorial constructions in F2n. We consider how to obtain a quadratic APN function in n + 1 variables from a given quadratic APN function in n variables using special restrictions on new terms

Where's Crypto?: Automated Identification and Classification of Proprietary Cryptographic Primitives in Binary Code

The continuing use of proprietary cryptography in embedded systems across many industry verticals, from physical access control systems and telecommunications to machine-to-machine authentication, presents a significant obstacle to black-box security-evaluation efforts. In-depth security analysis requires locating and classifying the algorithm in often very large binary images, thus rendering manual inspection, even when aided by heuristics, time consuming. In this paper, we present a novel approach to automate the identification and classification of (proprietary) cryptographic primitives within binary code. Our approach is based on Data Flow Graph (DFG) isomorphism, previously proposed by Lestringant et al. Unfortunately, their DFG isomorphism approach is limited to known primitives only, and relies on heuristics for selecting code fragments for analysis. By combining the said approach with symbolic execution, we overcome all limitations of their work, and are able to extend the analysis into the domain of unknown, proprietary cryptographic primitives. To demonstrate that our proposal is practical, we develop various signatures, each targeted at a distinct class of cryptographic primitives, and present experimental evaluations for each of them on a set of binaries, both publicly available (and thus providing reproducible results), and proprietary ones. Lastly, we provide a free and open-source implementation of our approach, called Where's Crypto?, in the form of a plug-in for the popular IDA disassembler.Comment: A proof-of-concept implementation can be found at https://github.com/wheres-crypto/wheres-crypt

An analysis and a comparative study of cryptographic algorithms used on the internet of things (IoT) based on avalanche effect

Ubiquitous computing is already weaving itself around us and it is connecting everything to the network of networks. This interconnection of objects to the internet is new computing paradigm called the Internet of Things (IoT) networks. Many capacity and non-capacity constrained devices, such as sensors are connecting to the Internet. These devices interact with each other through the network and provide a new experience to its users. In order to make full use of this ubiquitous paradigm, security on IoT is important. There are problems with privacy concerns regarding certain algorithms that are on IoT, particularly in the area that relates to their avalanche effect means that a small change in the plaintext or key should create a significant change in the ciphertext. The higher the significant change, the higher the security if that algorithm. If the avalanche effect of an algorithm is less than 50% then that algorithm is weak and can create security undesirability in any network. In this, case IoT. In this study, we propose to do the following: (1) Search and select existing block cryptographic algorithms (maximum of ten) used for authentication and encryption from different devices used on IoT. (2) Analyse the avalanche effect of select cryptographic algorithms and determine if they give efficient authentication on IoT. (3) Improve their avalanche effect by designing a mathematical model that improves their robustness against attacks. This is done through the usage of the initial vector XORed with plaintext and final vector XORed with cipher tect. (4) Test the new mathematical model for any enhancement on the avalanche effect of each algorithm as stated in the preceding sentences. (5) Propose future work on how to enhance security on IoT. Results show that when using the proposed method with variation of key, the avalanche effect significantly improved for seven out of ten algorithms. This means that we have managed to improve 70% of algorithms tested. Therefore indicating a substantial success rate for the proposed method as far as the avalanche effect is concerned. We propose that the seven algorithms be replaced by our improved versions in each of their implementation on IoT whenever the plaintext is varied.Electrical and Mining EngineeringM. Tech. (Electrical Engineering

Type checking cryptography implementations

Proceedings da conferência Fundamentals of Software Engineering 2011Cryptographic software development is a challenging field: high performance must be achieved, while ensuring correctness and compliance with low-level security policies. CAO is a domain specific language designed to assist development of cryptographic software. An important feature of this language is the design of a novel type system introducing native types such as predefined sized vectors, matrices and bit strings, residue classes modulo an integer, finite fields and finite field extensions, allowing for extensive static validation of source code. We present the formalisation, validation and implementation of this type system.(undefined

Links among Impossible Differential, Integral and Zero Correlation Linear Cryptanalysis

As two important cryptanalytic methods, impossible differential cryptanalysis and integral cryptanalysis have attracted much attention in recent years. Although relations among other important cryptanalytic approaches have been investigated, the link between these two methods has been missing. The motivation in this paper is to fix this gap and establish links between impossible differential cryptanalysis and integral cryptanalysis. Firstly, by introducing the concept of structure and dual structure, we prove that $a\rightarrow b$ is an impossible differential of a structure $\mathcal E$ if and only if it is a zero correlation linear hull of the dual structure $\mathcal E^\bot$. More specifically, constructing a zero correlation linear hull of a Feistel structure with $SP$-type round function where $P$ is invertible, is equivalent to constructing an impossible differential of the same structure with $P^T$ instead of $P$. Constructing a zero correlation linear hull of an SPN structure is equivalent to constructing an impossible differential of the same structure with $(P^{-1})^T$ instead of $P$. Meanwhile, our proof shows that the automatic search tool presented by Wu and Wang could find all impossible differentials of both Feistel structures with $SP$-type round functions and SPN structures, which is useful in provable security of block ciphers against impossible differential cryptanalysis. Secondly, by establishing some boolean equations, we show that a zero correlation linear hull always indicates the existence of an integral distinguisher while a special integral implies the existence of a zero correlation linear hull. With this observation we improve the integral distinguishers of Feistel structures by $1$ round, build a $24$-round integral distinguisher of CAST-$256$ based on which we propose the best known key recovery attack on reduced round CAST-$256$ in the non-weak key model, present a $12$-round integral distinguisher of SMS4 and an $8$-round integral distinguisher of Camellia without $FL/FL^{-1}$. Moreover, this result provides a novel way for establishing integral distinguishers and converting known plaintext attacks to chosen plaintext attacks. Finally, we conclude that an $r$-round impossible differential of $\mathcal E$ always leads to an $r$-round integral distinguisher of the dual structure $\mathcal E^\bot$. In the case that $\mathcal E$ and $\mathcal E^\bot$ are linearly equivalent, we derive a direct link between impossible differentials and integral distinguishers of $\mathcal E$. Specifically, we obtain that an $r$-round impossible differential of an SPN structure, which adopts a bit permutation as its linear layer, always indicates the existence of an $r$-round integral distinguisher. Based on this newly established link, we deduce that impossible differentials of SNAKE(2), PRESENT, PRINCE and ARIA, which are independent of the choices of the $S$-boxes, always imply the existence of integral distinguishers. Our results could help to classify different cryptanalytic tools. Furthermore, when designing a block cipher, the designers need to demonstrate that the cipher has sufficient security margins against important cryptanalytic approaches, which is a very tough task since there have been so many cryptanalytic tools up to now. Our results certainly facilitate this security evaluation process