In this work, we study the blockchain leader election problem. The purpose of such protocols is to elect a leader who decides on the next block to be appended to the blockchain, for each block proposal round. Solutions to this problem are vital for the security of blockchain systems. We introduce an efficient blockchain leader election method with security based solely on standard assumptions for cryptographic hash functions (rather than public-key cryptographic assumptions) and that does not involve a racing condition as in Proof-of-Work based approaches. Thanks to the former feature, our solution provides the highest confidence in security, even in the post-quantum era. A particularly scalable application of our solution is in the Proof-of-Stake setting, and we investigate our solution in the Algorand blockchain system. We believe our leader election approach can be easily adapted to a range of other blockchain settings. At the core of Algorand's leader election is a verifiable random function (VRF). Our approach is based on introducing a simpler primitive which still suffices for the blockchain leader election problem. In particular, we analyze the concrete requirements in an Algorand-like blockchain setting to accomplish leader election, which leads to the introduction of indexed VRF (iVRF). An iVRF satisfies modified uniqueness and pseudorandomness properties (versus a full-fledged VRF) that enable an efficient instantiation based on a hash function without requiring any complicated zero-knowledge proofs of correct PRF evaluation. We further extend iVRF to an authenticated iVRF with forward-security, which meets all the requirements to establish an Algorand-like consensus. Our solution is simple, flexible and incurs only a 32-byte additional overhead when combined with the current best solution to constructing a forward-secure signature (in the post-quantum setting). We implemented our (authenticated) iVRF proposal in C language on a standard computer and show that it significantly outperforms other quantum-safe VRF proposals in almost all metrics. Particularly, iVRF evaluation and verification can be executed in 0.02 ms, which is even faster than ECVRF used in Algorand.

Adaptor signatures, also known as scriptless scripts, have recently become an important tool in addressing the scalability and interoperability issues of blockchain applications such as cryptocurrencies. An adaptor signature extends a digital signature in a way that a complete signature reveals a secret based on a cryptographic condition. It brings about various advantages such as (i) low on-chain cost, (ii) improved fungibility of transactions, and (iii) advanced functionality beyond the limitation of the blockchain’s scripting language. In this work, we introduce the first post-quantum adaptor signature, named $${\mathsf {LAS}}$$. Our construction relies on the standard lattice assumptions, namely Module-SIS and Module-LWE. There are certain challenges specific to the lattice setting, arising mainly from the so-called knowledge gap in lattice-based proof systems, that makes the realization of an adaptor signature and its applications difficult. We show how to overcome these technical difficulties without introducing additional on-chain costs. Our evaluation demonstrates that $${\mathsf {LAS}}$$ is essentially as efficient as an ordinary lattice-based signature in terms of both communication and computation. We further show how to achieve post-quantum atomic swaps and payment channel networks using $${\mathsf {LAS}}$$.