Isogeny-based post-quantum key exchange protocols

The goal of this project is to understand and analyze the supersingular isogeny Diffie Hellman (SIDH), a post-quantum key exchange protocol which security lies on the isogeny-finding problem between supersingular elliptic curves. In order to do so, we first introduce the reader to cryptography focusing on key agreement protocols and motivate the rise of post-quantum cryptography as a necessity with the existence of the model of quantum computation. We review some of the known attacks on the SIDH and finally study some algorithmic aspects to understand how the protocol can be implemented

Guessing based on length functions

A guessing wiretapper's performance on a Shannon cipher system is analyzed for a source with memory. Close relationships between guessing functions and length functions are first established. Subsequently, asymptotically optimal encryption and attack strategies are identified and their performances analyzed for sources with memory. The performance metrics are exponents of guessing moments and probability of large deviations. The metrics are then characterized for unifilar sources. Universal asymptotically optimal encryption and attack strategies are also identified for unifilar sources. Guessing in the increasing order of Lempel-Ziv coding lengths is proposed for finite-state sources, and shown to be asymptotically optimal. Finally, competitive optimality properties of guessing in the increasing order of description lengths and Lempel-Ziv coding lengths are demonstrated.Comment: 16 pages, Submitted to IEEE Transactions on Information Theory, Special issue on Information Theoretic Security, Simplified proof of Proposition

Improving the Efficiency of Homomorphic Encryption Schemes

In this dissertation, we explore different approaches to practical homomorphic encryption schemes. For partial homomorphic encryption schemes, we observe that the versatility is the main bottleneck. To solve this problem, we propose general approaches to improve versatility of them by either extending the range of supported circuits or extending the message space. These general approaches can be applied to a wide range of partial HE schemes and greatly increase the number of applications that they support. For fully homomorphic encryption schemes, the slow running speed and the large ciphertext are the main challenges. Therefore, we propose efficient implementations as well as methods to compress the ciphertext. In detail, the Gentry Halevi FHE scheme and the LTV FHE scheme are implemented and the resulting performance shows significant improvement over previous works. For ciphertext compression, the concept of scheme conversion is proposed. Given a scheme converter, we can convert between schemes with compact ciphertext for communication and homomorphic schemes for computation

Cryptographic Interweaving of Messages

During the past several decades, the information and communication technology sector has advanced significantly, enabling extensive information interchange over the internet, including message sharing and electronic transactions. These days, the main issue is how to transmit information securely. From ancient times, there has been interest in the field of cryptography research. A masterwork of cryptography is Muni Kumudendu's original work, Siribhoovalaya. His study served as the basis for the method suggested in this publication. Several messages can be sent using different keys utilising a single matrix. Encryption uses a variety of matrix traversal techniques, making it challenging for cryptanalysis to map the plaintext and ciphertext

The Meeting of Acquaintances: A Cost-efficient Authentication Scheme for Light-weight Objects with Transient Trust Level and Plurality Approach

Wireless sensor networks consist of a large number of distributed sensor nodes so that potential risks are becoming more and more unpredictable. The new entrants pose the potential risks when they move into the secure zone. To build a door wall that provides safe and secured for the system, many recent research works applied the initial authentication process. However, the majority of the previous articles only focused on the Central Authority (CA) since this leads to an increase in the computation cost and energy consumption for the specific cases on the Internet of Things (IoT). Hence, in this article, we will lessen the importance of these third parties through proposing an enhanced authentication mechanism that includes key management and evaluation based on the past interactions to assist the objects joining a secured area without any nearby CA. We refer to a mobility dataset from CRAWDAD collected at the University Politehnica of Bucharest and rebuild into a new random dataset larger than the old one. The new one is an input for a simulated authenticating algorithm to observe the communication cost and resource usage of devices. Our proposal helps the authenticating flexible, being strict with unknown devices into the secured zone. The threshold of maximum friends can modify based on the optimization of the symmetric-key algorithm to diminish communication costs (our experimental results compare to previous schemes less than 2000 bits) and raise flexibility in resource-constrained environments.Comment: 27 page