Efficient Deformable Shape Correspondence via Kernel Matching

We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior on the mapping, and propose a projected descent optimization procedure inspired by difference of convex functions (DC) programming. Surprisingly, in spite of the highly non-convex nature of the resulting quadratic assignment problem, our method converges to a semantically meaningful and continuous mapping in most of our experiments, and scales well. We provide preliminary theoretical analysis and several interpretations of the method.Comment: Accepted for oral presentation at 3DV 2017, including supplementary materia

Contributions to Lattice–based Cryptography

Post–quantum cryptography (PQC) is a new and fast–growing part of Cryptography. It focuses on developing cryptographic algorithms and protocols that resist quantum adversaries (i.e., the adversaries who have access to quantum computers). To construct a new PQC primitive, a designer must use a mathematical problem intractable for the quantum adversary. Many intractability assumptions are being used in PQC. There seems to be a consensus in the research community that the most promising are intractable/hard problems in lattices. However, lattice–based cryptography still needs more research to make it more efficient and practical. The thesis contributes toward achieving either the novelty or the practicality of lattice– based cryptographic systems

Construction of Communication Protocol Using Ring-LWE-Based Homomorphic Encryption in Iot-Cloud Environment

The rapid development of wireless communication and sensor networks is the basis for forming an Internet of things(IoT) infrastructure. In IoT-based applications, the cryptographic encryption and access control at cloud must be robust to withstand current attacks. The majority of security protocols are based on integer factorization and discrete logarithm problems, which are proved vulnerable to quantum attacks. In this paper, we proposed a scheme for the security and privacy of the user data in a cloud environment. Various types of homomorphic encryption schemes are studied for data privacy in the cloud. The Ring-LWE-based encryption scheme is presented for privacy protection in the cloud which meets the homomorphic properties. The scheme is analysed for security, privacy, reduced messaging overhead and computation overhead. The objective of this paper is to Design and Construct a Ring-LWE-based homomorphic encryption(HE) communication protocol for authenticated user message encryption in a IoT cloud computing environment. The evaluation function in holomorphic encryption defined based on Ring-LWE encryption for a practical sharing-enabled cloud storage. Then, formally proving the security of the proposed protocol for classical and quantum attacks in cloud environment like Manin-the-middle (MITM) attack, Denial of Service (DoS) and Replay Attack

Reinforcing Security and Usability of Crypto-Wallet with Post-Quantum Cryptography and Zero-Knowledge Proof

Crypto-wallets or digital asset wallets are a crucial aspect of managing cryptocurrencies and other digital assets such as NFTs. However, these wallets are not immune to security threats, particularly from the growing risk of quantum computing. The use of traditional public-key cryptography systems in digital asset wallets makes them vulnerable to attacks from quantum computers, which may increase in the future. Moreover, current digital wallets require users to keep track of seed-phrases, which can be challenging and lead to additional security risks. To overcome these challenges, a new algorithm is proposed that uses post-quantum cryptography (PQC) and zero-knowledge proof (ZKP) to enhance the security of digital asset wallets. The research focuses on the use of the Lattice-based Threshold Secret Sharing Scheme (LTSSS), Kyber Algorithm for key generation and ZKP for wallet unlocking, providing a more secure and user-friendly alternative to seed-phrase, brain and multi-sig protocol wallets. This algorithm also includes several innovative security features such as recovery of wallets in case of downtime of the server, and the ability to rekey the private key associated with a specific username-password combination, offering improved security and usability. The incorporation of PQC and ZKP provides a robust and comprehensive framework for securing digital assets in the present and future. This research aims to address the security challenges faced by digital asset wallets and proposes practical solutions to ensure their safety in the era of quantum computing

Provably secure NTRU instances over prime cyclotomic rings

Due to its remarkable performance and potential resistance to quantum attacks, NTRUEncrypt has drawn much attention recently; it also has been standardized by IEEE. However, classical NTRUEncrypt lacks a strong security guarantee and its security still relies on heuristic arguments. At Eurocrypt 2011, Stehlé and Steinfeld first proposed a variant of NTRUEncrypt with a security reduction from standard problems on ideal lattices. This variant is restricted to the family of rings ℤ[X]/(Xn + 1) with n a power of 2 and its private keys are sampled by rejection from certain discrete Gaussian so that the public key is shown to be almost uniform. Despite the fact that partial operations, especially for RLWE, over ℤ[X]/(Xn + 1) are simple and efficient, these rings are quite scarce and different from the classical NTRU setting. In this work, we consider a variant of NTRUEncrypt over prime cyclotomic rings, i.e. ℤ[X]/(Xn-1 +…+ X + 1) with n an odd prime, and obtain IND-CPA secure results in the standard model assuming the hardness of worst-case problems on ideal lattices. In our setting, the choice of the rings is much more flexible and the scheme is closer to the original NTRU, as ℤ[X]/(Xn-1+…+X+1) is a large subring of the NTRU ring ℤ[X]/(Xn-1). Some tools for prime cyclotomic rings are also developed