The Interpolating Random Spline Cryptosystem and the Chaotic-Map Public-Key Cryptosystem

The feasibility of implementing the interpolating cubic spline function as encryption and decryption transformations is presented. The encryption method can be viewed as computing a transposed polynomial. The main characteristic of the spline cryptosystem is that the domain and range of encryption are defined over real numbers, instead of the traditional integer numbers. Moreover, the spline cryptosystem can be implemented in terms of inexpensive multiplications and additions. Using spline functions, a series of discontiguous spline segments can execute the modular arithmetic of the RSA system. The similarity of the RSA and spline functions within the integer domain is demonstrated. Furthermore, we observe that such a reformulation of RSA cryptosystem can be characterized as polynomials with random offsets between ciphertext values and plaintext values. This contrasts with the spline cryptosystems, so that a random spline system has been developed. The random spline cryptosystem is an advanced structure of spline cryptosystem. Its mathematical indeterminacy on computing keys with interpolants no more than 4 and numerical sensitivity to the random offset t( increases its utility. This article also presents a chaotic public-key cryptosystem employing a one-dimensional difference equation as well as a quadratic difference equation. This system makes use of the El Gamal’s scheme to accomplish the encryption process. We note that breaking this system requires the identical work factor that is needed in solving discrete logarithm with the same size of moduli

Digital Signatures from Symmetric-Key Primitives

We propose practically efficient signature schemes which feature several attractive properties: (a) they only rely on the security of symmetric-key primitives (block ciphers, hash functions), and are therefore a viable candidate for post-quantum security, (b) they have extremely small signing keys, essentially the smallest possible, and, (c) they are highly parametrizable. For this result we take advantage of advances in two very distinct areas of cryptography. The first is the area of primitives in symmetric cryptography, where recent developments led to designs which exhibit an especially low number of multiplications. The second is the area of zero-knowledge proof systems, where significant progress for efficiently proving statements over general circuits was recently made. We follow two different directions, one of them yielding the first practical instantiation of a design paradigm due to Bellare and Goldwasser without relying on structured hardness assumptions. For both our schemes we explore the whole design spectrum to obtain optimal parameter choices for different settings. Within limits, in all cases our schemes allow to trade-off computational effort with signature sizes. We also demonstrate that our schemes are parallelizable to the extent that they can practically take advantage of several cores on a CPU

Anonymous Point Collection - Improved Models and Security Definitions

This work is a comprehensive, formal treatment of anonymous point collection. The proposed definition does not only provide a strong notion of security and privacy, but also covers features which are important for practical use. An efficient realization is presented and proven to fulfill the proposed definition. The resulting building block is the first one that allows for anonymous two-way transactions, has semi-offline capabilities, yields constant storage size, and is provably secure

Design and Analysis of Opaque Signatures

Digital signatures were introduced to guarantee the authenticity and integrity of the underlying messages. A digital signature scheme comprises the key generation, the signature, and the verification algorithms. The key generation algorithm creates the signing and the verifying keys, called also the signer’s private and public keys respectively. The signature algorithm, which is run by the signer, produces a signature on the input message. Finally, the verification algorithm, run by anyone who knows the signer’s public key, checks whether a purported signature on some message is valid or not. The last property, namely the universal verification of digital signatures is undesirable in situations where the signed data is commercially or personally sensitive. Therefore, mechanisms which share most properties with digital signatures except for the universal verification were invented to respond to the aforementioned need; we call such mechanisms “opaque signatures”. In this thesis, we study the signatures where the verification cannot be achieved without the cooperation of a specific entity, namely the signer in case of undeniable signatures, or the confirmer in case of confirmer signatures; we make three main contributions. We first study the relationship between two security properties important for public key encryption, namely data privacy and key privacy. Our study is motivated by the fact that opaque signatures involve always an encryption layer that ensures their opacity. The properties required for this encryption vary according to whether we want to protect the identity (i.e. the key) of the signer or hide the validity of the signature. Therefore, it would be convenient to use existing work about the encryption scheme in order to derive one notion from the other. Next, we delve into the generic constructions of confirmer signatures from basic cryptographic primitives, e.g. digital signatures, encryption, or commitment schemes. In fact, generic constructions give easy-to-understand and easy-to-prove schemes, however, this convenience is often achieved at the expense of efficiency. In this contribution, which constitutes the core of this thesis, we first analyze the already existing constructions; our study concludes that the popular generic constructions of confirmer signatures necessitate strong security assumptions on the building blocks, which impacts negatively the efficiency of the resulting signatures. Next, we show that a small change in these constructionsmakes these assumptions drop drastically, allowing as a result constructions with instantiations that compete with the dedicated realizations of these signatures. Finally, we revisit two early undeniable signatures which were proposed with a conjectural security. We disprove the claimed security of the first scheme, and we provide a fix to it in order to achieve strong security properties. Next, we upgrade the second scheme so that it supports a iii desirable feature, and we provide a formal security treatment of the new scheme: we prove that it is secure assuming new reasonable assumptions on the underlying constituents

Security and Privacy in RFID Systems

This PhD thesis is concerned with authentication protocols using portable lightweight devices such as RFID tags. these devices have lately gained a significant attention for the diversity of the applications that could benefit form their features, ranging from inventory systems and building access control, to medical devices. However, the emergence of this technology has raised concerns about the possible loss of privacy carrying such tags induce in allowing tracing persons or unveiling the contents of a hidden package. this fear led to the appearance of several organizations which goal is to stop the spread of RFID tags. We take a cryptographic viewpoint on the issue and study the extent of security and privacy that RFID-based solutions can offer. In the first part of this thesis, we concentrate on analyzing two original primitives that were proposed to ensure security for RFID tags. the first one, HB#, is a dedicated authentication protocol that exclusively uses very simple arithmetic operations: bitwise AND and XOR. HB# was proven to be secure against a certain class of man-in-the-middle attacks and conjectured secure against more general ones. We show that the latter conjecture does not hold by describing a practical attack that allows an attacker to recover the tag's secret key. Moreover, we show that to be immune against our attack, HB#'s secret key size has to be increased to be more than 15 000 bits. this is an unpractical value for the considered applications. We then turn to SQUASH, a message authentication code built around a public-key encryption scheme, namely Rabin's scheme. By mounting a practical key recovery attack on the earlier version of SQUASH, we show that the security of all versions of SQUASH is unrelated to the security of Rabin encryption function. The second part of the thesis is dedicated to the privacy aspects related to the RFID technology. We first emphasize the importance of establishing a framework that correctly captures the intuition that a privacy-preserving protocol does not leak any information about its participants. For that, we show how several protocols that were supported by simple arguments, in contrast to a formal analysis, fail to ensure privacy. Namely, we target ProbIP, MARP, Auth2, YA-TRAP, YA-TRAP+, O-TRAP, RIPP-FS, and the Lim-Kwon protocol. We also illustrate the shortcomings of other privacy models such as the LBdM model. The rest of the dissertation is then dedicated to our privacy model. Contrarily to most RFID privacy models that limit privacy protection to the inability of linking the identity of two participants in two different protocol instances, we introduce a privacy model for RFID tags that proves to be the exact formalization of the intuition that a private protocol should not leak any information to the adversary. the model we introduce is a refinement of Vaudenay's one that invalidates a number of its limitations. Within these settings, we are able to show that the strongest notion of privacy, namely privacy against adversaries that have a prior knowledge of all the tags' secrets, is realizable. To instantiate an authentication protocol that achieves this level of privacy, we use plaintext-aware encryption schemes. We then extend our model to the case of mutual authentication where, in addition to a tag authenticating to the reader, the reverse operation is also required

Physical layer security for IoT applications

The increasing demands for Internet of things (IoT) applications and the tremendous increase in the volume of IoT generated data bring novel challenges for the fifth generation (5G) network. Verticals such as e-Health, vehicle to everything (V2X) and unmanned aerial vehicles (UAVs) require solutions that can guarantee low latency, energy efficiency,massive connectivity, and high reliability. In particular, finding strong security mechanisms that satisfy the above is of central importance for bringing the IoT to life. In this regards, employing physical layer security (PLS) methods could be greatly beneficial for IoT networks. While current security solutions rely on computational complexity, PLS is based on information theoretic proofs. By removing the need for computational power, PLS is ideally suited for resource constrained devices. In detail, PLS can ensure security using the inherit randomness already present in the physical channel. Promising schemes from the physical layer include physical unclonable functions (PUFs), which are seen as the hardware fingerprint of a device, and secret key generation (SKG) from wireless fading coefficients, which provide the wireless fingerprint of the communication channel between devices. The present thesis develops several PLS-based techniques that pave the way for a new breed of latency-aware, lightweight, security protocols. In particular, the work proposes: i) a fast multi-factor authentication solution with verified security properties based on PUFs, proximity detection and SKG; ii) an authenticated encryption SKG approach that interweaves data transmission and key generation; and, iii) a set of countermeasures to man-in-the-middle and jamming attacks. Overall, PLS solutions show promising performance, especially in the context of IoT applications, therefore, the advances in this thesis should be considered for beyond-5G networks

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

Efficient Anonymous Biometric Matching in Privacy-Aware Environments

Video surveillance is an important tool used in security and environmental monitoring, however, the widespread deployment of surveillance cameras has raised serious privacy concerns. Many privacy-enhancing schemes have been recently proposed to automatically redact images of selected individuals in the surveillance video for protection. To identify these individuals for protection, the most reliable approach is to use biometric signals as they are immutable and highly discriminative. If misused, these characteristics of biometrics can seriously defeat the goal of privacy protection. In this dissertation, an Anonymous Biometric Access Control (ABAC) procedure is proposed based on biometric signals for privacy-aware video surveillance. The ABAC procedure uses Secure Multi-party Computational (SMC) based protocols to verify membership of an incoming individual without knowing his/her true identity. To make SMC-based protocols scalable to large biometric databases, I introduce the k-Anonymous Quantization (kAQ) framework to provide an effective and secure tradeoff of privacy and complexity. kAQ limits systems knowledge of the incoming individual to k maximally dissimilar candidates in the database, where k is a design parameter that controls the amount of complexity-privacy tradeoff. The relationship between biometric similarity and privacy is experimentally validated using a twin iris database. The effectiveness of the entire system is demonstrated based on a public iris biometric database. To provide the protected subjects with full access to their privacy information in video surveillance system, I develop a novel privacy information management system that allows subjects to access their information via the same biometric signals used for ABAC. The system is composed of two encrypted-domain protocols: the privacy information encryption protocol encrypts the original video records using the iris pattern acquired during ABAC procedure; the privacy information retrieval protocol allows the video records to be anonymously retrieved through a GC-based iris pattern matching process. Experimental results on a public iris biometric database demonstrate the validity of my framework

Data Structures & Algorithm Analysis in C++

This is the textbook for CSIS 215 at Liberty University.https://digitalcommons.liberty.edu/textbooks/1005/thumbnail.jp