Vidal Attias

Primality generation is the cornerstone of several essential cryptographic systems. The problem has been a subject of deep investigations, but there is still a substantial room for improvements. Typically, the algorithms used have two parts – trial divisions aimed at eliminating numbers with small prime factors and primality tests based on an easy-to-compute statement that is valid for primes and invalid for composites. In this paper, we will showcase a technique that will eliminate the first phase of the primality testing algorithms. The computational simulations show a reduction of the primality generation time by about 30 percent in the case of 1024-bit RSA key pairs. This can be particularly beneficial in the case of decentralized environments for shared RSA keys as the initial trial division part of the key generation algorithms can be avoided at no cost. This also significantly reduces the communication complexity. Another essential contribution of the paper is the introduction of a new one-way function that is computationally simpler than the existing ones used in public-key cryptography. This function can be used to create new random number generators, and it also could be potentially used for designing entirely new public-key encryption systems.

Permissionless distributed ledgers provide a promising approach to deal with the Internet of Things (IoT) paradigm. Since IoT devices mostly generate data transactions and micropayments, distributed ledgers that use fees to regulate the network access are not an optimal choice. In this paper, we study a feeless architecture developed by IOTA and designed specifically for the IoT. Due to the lack of fees, malicious nodes can exploit this feature to generate an unbounded number of transactions and perform a denial of service attacks. We propose to mitigate these attacks through verifiable delay functions. These functions, which are non-parallelizable, hard to compute, and easy to verify, have been formulated only recently. In our work, we design a denial of service prevention mechanism which addresses network heterogeneity, limited node computational capabilities, and hardware-specific implementation optimizations. Verifiable delay functions have mostly been studied from a theoretical point of view, but little has been done in tangible applications. Hence, this paper can be considered as a pioneer work in the field, since it builds a bridge between this theoretical mathematical framework and a real-world problem.

RSA cryptography is still widely used. Some of its applications (e.g., distributed signature schemes, cryptosystems) do not allow the RSA modulus to be generated by a centralized trusted entity. Instead, the factorization must remain unknown to all the network participants. To this date, the existing algorithms are either computationally expensive, or limited to two-party settings. In this work, we design a decentralized multi-party computation algorithm able to generate efficiently the RSA modulus.