A New Algorithm for Solving Ring-LPN with a Reducible Polynomial

The LPN (Learning Parity with Noise) problem has recently proved to be of great importance in cryptology. A special and very useful case is the RING-LPN problem, which typically provides improved efficiency in the constructed cryptographic primitive. We present a new algorithm for solving the RING-LPN problem in the case when the polynomial used is reducible. It greatly outperforms previous algorithms for solving this problem. Using the algorithm, we can break the Lapin authentication protocol for the proposed instance using a reducible polynomial, in about 2^70 bit operations

Adaptive learning and cryptography

Significant links exist between cryptography and computational learning theory. Cryptographic functions are the usual method of demonstrating significant intractability results in computational learning theory as they can demonstrate that certain problems are hard in a representation independent sense. On the other hand, hard learning problems have been used to create efficient cryptographic protocols such as authentication schemes, pseudo-random permutations and functions, and even public key encryption schemes.;Learning theory / coding theory also impacts cryptography in that it enables cryptographic primitives to deal with the issues of noise or bias in their inputs. Several different constructions of fuzzy primitives exist, a fuzzy primitive being a primitive which functions correctly even in the presence of noisy , or non-uniform inputs. Some examples of these primitives include error-correcting blockciphers, fuzzy identity based cryptosystems, fuzzy extractors and fuzzy sketches. Error correcting blockciphers combine both encryption and error correction in a single function which results in increased efficiency. Fuzzy identity based encryption allows the decryption of any ciphertext that was encrypted under a close enough identity. Fuzzy extractors and sketches are methods of reliably (re)-producing a uniformly random secret key given an imperfectly reproducible string from a biased source, through a public string that is called the sketch .;While hard learning problems have many qualities which make them useful in constructing cryptographic protocols, such as their inherent error tolerance and simple algebraic structure, it is often difficult to utilize them to construct very secure protocols due to assumptions they make on the learning algorithm. Due to these assumptions, the resulting protocols often do not have security against various types of adaptive adversaries. to help deal with this issue, we further examine the inter-relationships between cryptography and learning theory by introducing the concept of adaptive learning . Adaptive learning is a rather weak form of learning in which the learner is not expected to closely approximate the concept function in its entirety, rather it is only expected to answer a query of the learner\u27s choice about the target. Adaptive learning allows for a much weaker learner than in the standard model, while maintaining the the positive properties of many learning problems in the standard model, a fact which we feel makes problems that are hard to adaptively learn more useful than standard model learning problems in the design of cryptographic protocols. We argue that learning parity with noise is hard to do adaptively and use that assumption to construct a related key secure, efficient MAC as well as an efficient authentication scheme. In addition we examine the security properties of fuzzy sketches and extractors and demonstrate how these properties can be combined by using our related key secure MAC. We go on to demonstrate that our extractor can allow a form of related-key hardening for protocols in that, by affecting how the key for a primitive is stored it renders that protocol immune to related key attacks

New foundations for efficient authentication, commutative cryptography, and private disjointness testing

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 105-115).This dissertation presents new constructions and security definitions related to three areas: authentication, cascadable and commutative crytpography, and private set operations. Existing works relevant to each of these areas fall into one of two categories: efficient solutions lacking formal proofs of security or provably-secure, but highly inefficient solutions. This work will bridge this gap by presenting new constructions and definitions that are both practical and provably-secure. The first contribution in the area of efficient authentication is a provably-secure authentication protocol named HB+. The HB+ protocol is efficient enough to be implemented on extremely low-cost devices, or even by a patient human with a coin to flip. The security of HB+ is based on the hardness of a long-standing learning problem that is closely related to coding theory. HB+ is the first authentication protocol that is both practical for low-cost devices, like radio frequency identification (RFID) tags, and provably secure against active adversaries. The second contribution of this work is a new framework for defining and proving the security of cascadable cryptosystems, specifically commutative cryptosystems.(cont.) This new framework addresses a gap in existing security definitions that fail to handle cryptosystems where ciphertexts produced by cascadable encryption and decryption perations may contain some message-independent history. Several cryptosystems, including a new, practical commutative cryptosystem, are proven secure under this new framework. Finally, a new and efficient private disjointness testing construction named HW is offered. Unlike previous constructions, HW is secure in the face of malicious parties, but without the need for random oracles or expensive zero-knowledge protocols. HW is as efficient as previous constructions and may be implemented using standard software libraries. The security of HW is based on a novel use of subgroup assumptions. These assumptions may prove useful in solving many other private set operation problems.by Stephen A. Weis.Ph.D

Lightweight symmetric cryptography

The Internet of Things is one of the principal trends in information technology nowadays. The main idea behind this concept is that devices communicate autonomously with each other over the Internet. Some of these devices have extremely limited resources, such as power and energy, available time for computations, amount of silicon to produce the chip, computational power, etc. Classical cryptographic primitives are often infeasible for such constrained devices. The goal of lightweight cryptography is to introduce cryptographic solutions with reduced resource consumption, but with a sufficient security level. Although this research area was of great interest to academia during the last years and a large number of proposals for lightweight cryptographic primitives have been introduced, almost none of them are used in real-word. Probably one of the reasons is that, for academia, lightweight usually meant to design cryptographic primitives such that they require minimal resources among all existing solutions. This exciting research problem became an important driver which allowed the academic community to better understand many cryptographic design concepts and to develop new attacks. However, this criterion does not seem to be the most important one for industry, where lightweight may be considered as "rightweight". In other words, a given cryptographic solution just has to fit the constraints of the specific use cases rather than to be the smallest. Unfortunately, academic researchers tended to neglect vital properties of the particular types of devices, into which they intended to apply their primitives. That is, often solutions were proposed where the usage of some resources was reduced to a minimum. However, this was achieved by introducing new costs which were not appropriately taken into account or in such a way that the reduction of costs also led to a decrease in the security level. Hence, there is a clear gap between academia and industry in understanding what lightweight cryptography is. In this work, we are trying to fill some of these gaps. We carefully investigate a broad number of existing lightweight cryptographic primitives proposed by academia including authentication protocols, stream ciphers, and block ciphers and evaluate their applicability for real-world scenarios. We then look at how individual components of design of the primitives influence their cost and summarize the steps to be taken into account when designing primitives for concrete cost optimization, more precisely - for low energy consumption. Next, we propose new implementation techniques for existing designs making them more efficient or smaller in hardware without the necessity to pay any additional costs. After that, we introduce a new stream cipher design philosophy which enables secure stream ciphers with smaller area size than ever before and, at the same time, considerably higher throughput compared to any other encryption schemes of similar hardware cost. To demonstrate the feasibility of our findings we propose two ciphers with the smallest area size so far, namely Sprout and Plantlet, and the most energy efficient encryption scheme called Trivium-2. Finally, this thesis solves a concrete industrial problem. Based on standardized cryptographic solutions, we design an end-to-end data-protection scheme for low power networks. This scheme was deployed on the water distribution network in the City of Antibes, France

Lightweight cryptography on ultra-constrained RFID devices

Devices of extremely small computational power like RFID tags are used in practice to a rapidly growing extent, a trend commonly referred to as ubiquitous computing. Despite their severely constrained resources, the security burden which these devices have to carry is often enormous, as their fields of application range from everyday access control to human-implantable chips providing sensitive medical information about a person. Unfortunately, established cryptographic primitives such as AES are way to 'heavy' (e.g., in terms of circuit size or power consumption) to be used in corresponding RFID systems, calling for new solutions and thus initiating the research area of lightweight cryptography. In this thesis, we focus on the currently most restricted form of such devices and will refer to them as ultra-constrained RFIDs. To fill this notion with life and in order to create a profound basis for our subsequent cryptographic development, we start this work by providing a comprehensive summary of conditions that should be met by lightweight cryptographic schemes targeting ultra-constrained RFID devices. Building on these insights, we then turn towards the two main topics of this thesis: lightweight authentication and lightweight stream ciphers. To this end, we first provide a general introduction to the broad field of authentication and study existing (allegedly) lightweight approaches. Drawing on this, with the (n,k,L)^-protocol, we suggest our own lightweight authentication scheme and, on the basis of corresponding hardware implementations for FPGAs and ASICs, demonstrate its suitability for ultra-constrained RFIDs. Subsequently, we leave the path of searching for dedicated authentication protocols and turn towards stream cipher design, where we first revisit some prominent classical examples and, in particular, analyze their state initialization algorithms. Following this, we investigate the rather young area of small-state stream ciphers, which try to overcome the limit imposed by time-memory-data tradeoff (TMD-TO) attacks on the security of classical stream ciphers. Here, we present some new attacks, but also corresponding design ideas how to counter these. Paving the way for our own small-state stream cipher, we then propose and analyze the LIZARD-construction, which combines the explicit use of packet mode with a new type of state initialization algorithm. For corresponding keystream generator-based designs of inner state length n, we prove a tight (2n/3)-bound on the security against TMD-TO key recovery attacks. Building on these theoretical results, we finally present LIZARD, our new lightweight stream cipher for ultra-constrained RFIDs. Its hardware efficiency and security result from combining a Grain-like design with the LIZARD-construction. Most notably, besides lower area requirements, the estimated power consumption of LIZARD is also about 16 percent below that of Grain v1, making it particularly suitable for passive RFID tags, which obtain their energy exclusively through an electromagnetic field radiated by the reading device. The thesis is concluded by an extensive 'Future Research Directions' chapter, introducing various new ideas and thus showing that the search for lightweight cryptographic solutions is far from being completed

Solving the LPN problem in cube-root time

In this paper it is shown that given a sufficient number of (noisy) random binary linear equations, the Learning from Parity with Noise (LPN) problem can be solved in essentially cube root time in the number of unknowns. The techniques used to recover the solution are known from fast correlation attacks on stream ciphers. As in fast correlation attacks, the performance of the algorithm depends on the number of equations given. It is shown that if this number exceeds a certain bound, and the bias of the noisy equations is polynomial in number of unknowns, the running time of the algorithm is reduced to almost cube root time compared to the brute force checking of all possible solutions. The mentioned bound is explicitly given and it is further shown that when this bound is exceeded, the complexity of the approach can even be further reduced

Security and privacy in RFID systems

Vu que les tags RFID sont actuellement en phase de large déploiement dans le cadre de plusieurs applications (comme les paiements automatiques, le contrôle d'accès à distance, et la gestion des chaînes d approvisionnement), il est important de concevoir des protocoles de sécurité garantissant la protection de la vie privée des détenteurs de tags RFID. Or, la conception de ces protocoles est régie par les limitations en termes de puissance et de calcul de la technologie RFID, et par les modèles de sécurité qui sont à notre avis trop forts pour des systèmes aussi contraints que les tags RFID. De ce fait, on limite dans cette thèse le modèle de sécurité; en particulier, un adversaire ne peut pas observer toutes les interactions entre tags et lecteurs. Cette restriction est réaliste notamment dans le contexte de la gestion des chaînes d approvisionnement qui est l application cible de ce travail. Sous cette hypothèse, on présente quatre protocoles cryptographiques assurant une meilleure collaboration entre les différents partenaires de la chaîne d approvisionnement. D abord, on propose un protocole de transfert de propriété des tags RFID, qui garantit l authentification des tags en temps constant alors que les tags implémentent uniquement des algorithmes symétriques, et qui permet de vérifier l'authenticité de l origine des tags. Ensuite, on aborde le problème d'authenticité des produits en introduisant deux protocoles de sécurité qui permettent à un ensemble de vérificateurs de vérifier que des tags sans capacité de calcul ont emprunté des chemins valides dans la chaîne d approvisionnement. Le dernier résultat présenté dans cette thèse est un protocole d appariement d objets utilisant des tags sans capacité de calcul , qui vise l automatisation des inspections de sécurité dans la chaîne d approvisionnement lors du transport des produits dangereux. Les protocoles introduits dans cette thèse utilisent les courbes elliptiques et les couplages bilinéaires qui permettent la construction des algorithmes de signature et de chiffrement efficaces, et qui minimisent donc le stockage et le calcul dans les systèmes RFID. De plus, la sécurité de ces protocoles est démontrée sous des modèles formels bien définis qui prennent en compte les limitations et les contraintes des tags RFID, et les exigences strictes en termes de sécurité et de la protection de la vie privée des chaines d approvisionnement.While RFID systems are one of the key enablers helping the prototype of pervasive computer applications, the deployment of RFID technologies also comes with new privacy and security concerns ranging from people tracking and industrial espionage to produ ct cloning and denial of service. Cryptographic solutions to tackle these issues were in general challenged by the limited resources of RFID tags, and by the formalizations of RFID privacy that are believed to be too strong for such constrained devices. It follows that most of the existing RFID-based cryptographic schemes failed at ensuring tag privacy without sacrificing RFID scalability or RFID cost effectiveness. In this thesis, we therefore relax the existing definitions of tag privacy to bridge the gap between RFID privacy in theory and RFID privacy in practice, by assuming that an adversary cannot continuously monitor tags. Under this assumption, we are able to design sec ure and privacy preserving multi-party protocols for RFID-enabled supply chains. Namely, we propose a protocol for tag ownership transfer that features constant-time authentication while tags are only required to compute hash functions. Then, we tackle the problem of product genuineness verification by introducing two protocols for product tracking in the supply chain that rely on storage only tags. Finally, we present a solution for item matching that uses storage only tags and aims at the automation of safety inspections in the supply chain.The protocols presented in this manuscript rely on operations performed in subgroups of elliptic curves that allow for the construction of short encryptions and signatures, resulting in minimal storage requirements for RFID tags. Moreover, the privacy and the security of these protocols are proven under well defined formal models that take into account the computational limitations of RFID technology and the stringent privacy and security requirements of each targeted supply chain application.PARIS-Télécom ParisTech (751132302) / SudocSudocFranceF

On solving LPN using BKW and variants Implementation and Analysis

The Learning Parity with Noise problem (LPN) is appealing in cryptography as it is considered to remain hard in the post-quantum world. It is also a good candidate for lightweight devices due to its simplicity. In this paper we provide a comprehensive analysis of the existing LPN solving algorithms, both for the general case and for the sparse secret scenario. In practice, the LPN-based cryptographic constructions use as a reference the security parameters proposed by Levieil and Fouque. But, for these parameters, there remains a gap between the theoretical analysis and the practical complexities of the algorithms we consider. The new theoretical analysis in this paper provides tighter bounds on the complexity of LPN solving algorithms and narrows this gap between theory and practice. We show that for a sparse secret there is another algorithm that outperforms BKW and its variants. Following from our results, we further propose practical parameters for different security levels

Ensuring Application Specific Security, Privacy and Performance Goals in RFID Systems

Radio Frequency IDentification (RFID) is an automatic identification technology that uses radio frequency to identify objects. Securing RFID systems and providing privacy in RFID applications has been the focus of much academic work lately. To ensure universal acceptance of RFID technology, security and privacy issued must be addressed into the design of any RFID application. Due to the constraints on memory, power, storage capacity, and amount of logic on RFID devices, traditional public key based strong security mechanisms are unsuitable for them. Usually, low cost general authentication protocols are used to secure RFID systems. However, the generic authentication protocols provide relatively low performance for different types of RFID applications. We identified that each RFID application has unique research challenges and different performance bottlenecks based on the characteristics of the system. One strategy is to devise security protocols such that application specific goals are met and system specific performance requirements are maximized. This dissertation aims to address the problem of devising application specific security protocols for current and next generation RFID systems so that in each application area maximum performance can be achieved and system specific goals are met. In this dissertation, we propose four different authentication techniques for RFID technologies, providing solutions to the following research issues: 1) detecting counterfeit as well as ensuring low response time in large scale RFID systems, 2) preserving privacy and maintaining scalability in RFID based healthcare systems, 3) ensuring security and survivability of Computational RFID (CRFID) networks, and 4) detecting missing WISP tags efficiently to ensure reliability of CRFID based system\u27s decision. The techniques presented in this dissertation achieve good levels of privacy, provide security, scale to large systems, and can be implemented on resource-constrained RFID devices