<div><div>The blockchain offers a decentralized way to provide security guarantees for financial transactions. However, this ability comes with the cost of storing a large (distributed) blockchain state and introducing additional computation and communication overhead to all participants. All these drawbacks raise a challenging scalability problem, especially for resource-constrained blockchain clients. On the other hand, some scaling solutions typically require resource-constrained clients to rely on other nodes with higher computational and storage capabilities. However, such scaling solutions often expose the data of the clients to risks of compromise of the more powerful nodes they rely on (e.g., accidental, malicious through a break-in, insider misbehavior, or malware infestation). This potential for leakage raises a privacy concern for these constrained clients, in addition to other scaling-related concerns. This dissertation proposes several cryptographic constructions and system designs enabling resource-constrained devices to participate in the blockchain network securely and efficiently. </div><div><br></div><div>Our first proposal concerns the storage facet for which we propose two add-on privacy designs to address the scaling issue of storing a large blockchain state. </div><div>The first solution is an oblivious database framework, called T³, that allows resource-constrained clients to obliviously fetch blockchain data from potential malicious full clients. The second solution focuses on the problem of using and storing additional private-by-design blockchains (e.g., Monero or ZCash) to achieve privacy. We propose an add-on tumbler design, called AMR, that offers privacy directly to clients of non-private blockchains such as Ethereum without the cost of storing and using different blockchain states.</div><div><br></div><div>Our second proposal addresses the communication facet with focus on payment channels as a solution to address the communication overhead between the constrained clients and the blockchain network. A payment channel enables transactions between arbitrary pairs of constrained clients with a minimal communication overhead with the blockchain network. However, in popular blockchains like Ethereum and Bitcoin, the payment data of such channels are exposed to the public, which is undesirable for financial applications. Thus, to hide transaction data, one can use blockchains that are private by design like Monero. However, existing cryptographic primitives in Monero prevent the system from supporting any form of payment channels. Therefore, we present <i>Dual Linkable Spontaneous Anonymous Group Signature for Ad Hoc Groups (DLSAG),</i> a linkable ring signature scheme that enables, for the first time, off-chain scalability solutions in Monero. </div><div><br></div><div>To address the computation facet, we address the computation overhead of the gossip protocol used in all popular blockchain protocols. For this purpose, we propose a signature primitive called <i>Flexible Signature</i>. In a flexible signature scheme, the verification algorithm quantifies the validity of a signature based on the computational effort performed by the verifier. Thus, the resource-constrained devices can partially verify the signatures in the blockchain transactions before relaying transactions to other peers. This primitive allows the resource-constrained devices to prevent spam transactions from flooding the blockchain network with overhead that is consistent with their resource constraints. </div></div>