1. Adaptor Multi-Signatures

   Adaptor Signature is the new and upcoming cryptographic scheme with important applications in layer-2 and peer-to-peer blockchain applications such as cross-currency swaps and payment channel networks. In this work, we introduce Adaptor Multi-Signatures allowing a group of users to use adaptor signatures. This may be essential for organizations with using multi-signatures for scriptless scripts. We define Adaptor Multi-Signatures to incorporate the amalgam of adaptor signatures and multi-signatures, through the basic Schnorr signature scheme. Schnorr signatures have a shorter signature size which can increase the capacity of a blockchain network, according to the BIP32 Proposal. They also enable more advanced functionality, such as multisignature transactions and threshold signatures, which advance functionality for the Bitcoin network. For Adaptor Multi- Signatures, we make an attempt to prove security properties of this scheme in the Random Oracle Model. We make use of MuSig-2 as a base for multi-signatures, which is a simple and highly practical tworound multi-signature scheme. Finally, we explore the applications of this adaptor multi-signature for multi-signature wallets and multi-hop locks.

2. Parallelization of LTE Networks for 5G Optimization

   The purpose of this project is to parallelize the LTE network simulated through Network Simulator (NS-3) using Message Passing Interface (MPI). Developing an efficient parallel simulation for LTE in a multi- processor environment is necessary. A primary concern for this process is the limitation of the parallelization capacity of NS-3. This, combined with overheads imposed by event handling routines of the simulator and the problem of shared memory, defines the problem statement. An LTE network consists of three parts – the first being the EnB’s (which are similar to cell towers or radio based station) ; the second is the UE’s (which are any devices used directly by an end-user to communicate with EnB’s) ; and the third being the Internet (consisting of remote host and P-Gateways connected through a point to point link). The project objective was attempted through two ways – the first one involved splitting the network into different processes through a p2p connection of one Remote Host to multiple P-Gateways ; the second approach used the concept of network-twins, where the network arrangement was replicated in each process with optimizations for an efficient output. Upon careful consideration, the second approach produced higher success, although the first approach may be more efficient for future work.