This chapter aims to summarize and provide an overview of the content of the entire document. The majority of this book focuses on the scenario where two entities are involved. More precisely, we are going to consider three classes of cryptographic functionality and show how to design efficient protocols to securely implement those functionality classes. In more detail, in Part I we consider Secure Two-Party Computation (2PC), and provide the first secure 2PC protocol with black-box simulation, secure under standard and generic assumptions, with optimal round complexity in the simultaneous message exchange model (In a secure simultaneous message exchange channel all parties can simultaneously send messages over the channel at the same communication round but the adversary is allowed to be rushing.) as stated in [49]. We also show, following [47] that the same round-complexity can be achieved for the coin-tossing functionality in the multi-party setting. We finally show an approach (proposed originally in [44]), to securely implement the Set Membership functionality in the semi-honest setting. The proposed construction can be combined with the right 2PC techniques to achieve more efficient protocols for computations of the form \(z=f(X\cap Y)\) for arbitrary functions f. In Part II we show a construct 4-round concurrent non-malleable commitment scheme assuming one-way functions (OWFs), as stated in [48]. We also show how to get down to 3 rounds assuming sub-exponentially secure one-way permutations (OWPs) as stated in [46]. In the last part of the document, we study the proof systems (When discussing informally we will use the word proof to mean both an unconditionally sound proof and a computationally sound proof (i.e., an argument). Only in the formal part of the document we will make a distinction between arguments and proofs.). More precisely, we first focus on the question of achieving adaptive-input proofs of partial knowledge, showing an efficient construction, as stated in [52, 53], of a 3-round public-coin witness-indistinguishable (k, n)-proof of partial knowledge where all or part of the instances can be decided in the third round. In the latest part of Part III we consider the notion of non-interactive Zero-Knowledge proof and show the construction provided in [54], that improves the state of the art both in terms of efficiency and generality. In the next sections of this chapter, we propose an overview of all the contributions we just mentioned.

Introduction

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发表日期：

2026年

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Michele Ciampi,
Luisa Siniscalchi

摘要

This chapter aims to summarize and provide an overview of the content of the entire document. The majority of this book focuses on the scenario where two entities are involved. More precisely, we are going to consider three classes of cryptographic functionality and show how to design efficient protocols to securely implement those functionality classes. In more detail, in Part I we consider Secure Two-Party Computation (2PC), and provide the first secure 2PC protocol with black-box simulation, secure under standard and generic assumptions, with optimal round complexity in the simultaneous message exchange model (In a secure simultaneous message exchange channel all parties can simultaneously send messages over the channel at the same communication round but the adversary is allowed to be rushing.) as stated in [49]. We also show, following [47] that the same round-complexity can be achieved for the coin-tossing functionality in the multi-party setting. We finally show an approach (proposed originally in [44]), to securely implement the Set Membership functionality in the semi-honest setting. The proposed construction can be combined with the right 2PC techniques to achieve more efficient protocols for computations of the form \(z=f(X\cap Y)\) for arbitrary functions f. In Part II we show a construct 4-round concurrent non-malleable commitment scheme assuming one-way functions (OWFs), as stated in [48]. We also show how to get down to 3 rounds assuming sub-exponentially secure one-way permutations (OWPs) as stated in [46]. In the last part of the document, we study the proof systems (When discussing informally we will use the word proof to mean both an unconditionally sound proof and a computationally sound proof (i.e., an argument). Only in the formal part of the document we will make a distinction between arguments and proofs.). More precisely, we first focus on the question of achieving adaptive-input proofs of partial knowledge, showing an efficient construction, as stated in [52, 53], of a 3-round public-coin witness-indistinguishable (k, n)-proof of partial knowledge where all or part of the instances can be decided in the third round. In the latest part of Part III we consider the notion of non-interactive Zero-Knowledge proof and show the construction provided in [54], that improves the state of the art both in terms of efficiency and generality. In the next sections of this chapter, we propose an overview of all the contributions we just mentioned.