NTRU is a fast public-key cryptosystem that is constructed using polynomial rings with integer coefficients. We present ETRU, an NTRU-like cryptosystem based on the Eisenstein integers. We discuss parameter selection and develop a model for the probabilty of decryption failure. We also provide an implementation of ETRU. We use theoretical and experimental data to compare the security and efficiency of ETRU to NTRU with comparable parameter sets and show that ETRU is an improvement over NTRU in terms of security.

NTRU is a fast public-key cryptosystem that is constructed using polynomial rings with integer coefficients. We present ETRU, an NTRU-like cryptosystem based on the Eisenstein integers. We discuss parameter selection and develop a model for the probabilty of decryption failure. We also provide an implementation of ETRU. We use theoretical and experimental data to compare the security and efficiency of ETRU to NTRU with comparable parameter sets and show that ETRU is an improvement over NTRU in terms of security.

NTRU is a fast public-key cryptosystem that is constructed using polynomial rings with integer coefficients. We present ETRU, an NTRU-like cryptosystem based on the Eisenstein integers. We discuss parameter selection and develop a model for the probabilty of decryption failure. We also provide an implementation of ETRU. We use theoretical and experimental data to compare the security and efficiency of ETRU to NTRU with comparable parameter sets and show that ETRU is an improvement over NTRU in terms of security.

NTRU is a fast public-key cryptosystem that is constructed using polynomial rings with integer coefficients. We present ETRU, an NTRU-like cryptosystem based on the Eisenstein integers. We discuss parameter selection and develop a model for the probabilty of decryption failure. We also provide an implementation of ETRU. We use theoretical and experimental data to compare the security and efficiency of ETRU to NTRU with comparable parameter sets and show that ETRU is an improvement over NTRU in terms of security.

The theses firstly introduces the basics of lattice problems. Then it focuses on various aspects of the cryptosystem NTRU which is based on the mentioned problems. The system is then compared with the most common encryption methods used nowadays. Its supposed quantum resistence is mentioned briefly. Subsequently the author tries to minimize the system's disadvantages by various cryptosystem modifications. Powered by TCPDF (www.tcpdf.org)

NTRU is a public key cryptosystem, which was first introduced in 1996. It is a ring-based cryptosystem and its security relies on the complexity of a well-known lattice problem, i.e. shortest vector problem (SVP). There is no efficient algorithm known to solve SVP exactly in arbitrary high dimensional lattices. However, approximate solutions to SVP can be found by lattice reduction algorithms. LLL is the first polynomial time algorithm that finds reasonable short vectors of a lattice. The best known attacks on the NTRU cryptosystem are lattice attacks. In these attacks, the lattice constructed by the public key of the system is used to find the private key. The target vector, which includes private key of the system is one of the short vectors of the NTRU lattice. In this thesis, we study NTRU cryptosystem and lattice attacks on NTRU. Also, we applied an attack to a small dimensional NTRU lattice.

abstract: Lattice-based Cryptography is an up and coming field of cryptography that utilizes the difficulty of lattice problems to design lattice-based cryptosystems that are resistant to quantum attacks and applicable to Fully Homomorphic Encryption schemes (FHE). In this thesis, the parallelization of the Residue Number System (RNS) and algorithmic efficiency of the Number Theoretic Transform (NTT) are combined to tackle the most significant bottleneck of polynomial ring multiplication with the hardware design of an optimized RNS-based NTT polynomial multiplier. The design utilizes Negative Wrapped Convolution, the NTT, RNS Montgomery reduction with Bajard and Shenoy extensions, and optimized modular 32-bit channel arithmetic for nine RNS channels to accomplish an RNS polynomial multiplication. In addition to a full software implementation of the whole system, a pipelined and optimized RNS-based NTT unit with 4 RNS butterflies is implemented on the Xilinx Artix-7 FPGA(xc7a200tlffg1156-2L) for size and delay estimates. The hardware implementation achieves an operating frequency of 47.043 MHz and utilizes 13239 LUT's, 4010 FF's, and 330 DSP blocks, allowing for multiple simultaneously operating NTT units depending on FGPA size constraints. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2020

In program analysis, unknown properties for terms are typically represented symbolically as variables. Bound constraints on these variables can then specify multiple optimisation goals for computer programs and nd application in areas such as type theory, security, alias analysis and resource reasoning. Resolution of bound constraints is a problem steeped in graph theory; interdependencies between the variables is represented as a constraint graph. Additionally, constants are introduced into the system as concrete bounds over these variables and constants themselves are ordered over a lattice which is, once again, represented as a graph. Despite graph algorithms being central to bound constraint solving, most approaches to program optimisation that use bound constraint solving have treated their graph theoretic foundations as a black box. Little has been done to investigate the computational costs or design e cient graph algorithms for constraint resolution. Emerging examples of these lattices and bound constraint graphs, particularly from the domain of language-based security, are showing that these graphs and lattices are structurally diverse and could be arbitrarily large. Therefore, there is a pressing need to investigate the graph theoretic foundations of bound constraint solving. In this thesis, we investigate the computational costs of bound constraint solving from a graph theoretic perspective for Information Flow Analysis (IFA); IFA is a sub- eld of language-based security which veri es whether con dentiality and integrity of classified information is preserved as it is manipulated by a program. We present a novel framework based on graph decomposition for solving the (atomic) bound constraint problem for IFA. Our approach enables us to abstract away from connections between individual vertices to those between sets of vertices in both the constraint graph and an accompanying security lattice which defines ordering over constants. Thereby, we are able to achieve significant speedups compared to state-of-the-art graph algorithms applied to bound constraint solving. More importantly, our algorithms are highly adaptive in nature and seamlessly adapt to the structure of the constraint graph and the lattice. The computational costs of our approach is a function of the latent scope of decomposition in the constraint graph and the lattice; therefore, we enjoy the fastest runtime for every point in the structure-spectrum of these graphs and lattices. While the techniques in this dissertation are developed with IFA in mind, they can be extended to other application of the bound constraints problem, such as type inference and program analysis frameworks which use annotated type systems, where constants are ordered over a lattice.

Efficient quantum computers will break most of today’s public-key cryptosystems. Therefore, the National Institute of Standards and Technology (NIST) calls for proposals to standardise one or more quantum-secure cryptographic schemes. Eventually, banks must adopt the standardised schemes, but little is known about how efficient such an implementation would be in Java, one of the standard programming languages for banks. In this thesis, we test and evaluate a post-quantum secure encryption scheme known as FrodoKEM, which is based on a hard lattice problem known as Learning With Errors (LWE). We found that a post-quantum secure encryption version of FrodoKEM provides strong theoretical security regarding the criteria given by NIST, and is also sufficiently fast for key generation, encryption and decryption. These results imply that it could be possible to implement these types of post-quantum secure algorithms in high-level programming languages such as Java, demonstrating that we no longer are limited to use low-level languages such as C. Consequently, we can easier and cheaper implement post-quantum secure cryptography.

This dissertation addresses the confidentiality aspect of the information security problem from the viewpoint of the software architecture. It presents a new approach to secure system design in which the desired security properties, in particular, confidentiality, of the system are proven to hold at the architectural level. The architecture description language Wright is extended so that confidentiality authorizations can be specified. An architectural description in Wright/c, the extended language, assigns clearance to the ports of the components and treats security labels as a part of data type information. The security labels are declared along with clearance assignments in an access control lattice model, also expressed in Wright/c. This enables the static analysis of data flow over the architecture subject to confidentiality requirements as per Bell-LaPadula principles. An algorithm takes the Wright/c description and the lattice model as inputs, and checks if there is a potential violation of the Bell-LaPadula principles. The algorithm also detects excess privileges. A software tool, which features an XML-based front-end to the algorithm is constructed. Finally, the algorithm is analyzed for its soundness, completeness and computational complexity.