SaTC: CORE: Small: Meta Coding and Applications in Cryptography

编码理论和密码学的领域相互交织，每个领域都会影响另一个领域：编码理论中的某些纠错码相当于密码学中用于实现安全多方计算的一种秘密共享方案。其他类型的编码/秘密共享方案（如不可延展码和泄漏弹性秘密共享）首先被提出来解决密码设置中出现的安全问题。目前存在许多编码/秘密共享方案的变体，并且大多数构造是复杂的或特设的。该项目的新颖之处是：提出了一个统一的框架，捕获的编码/秘密共享方案，已在文献中研究的频谱，开发新的方法，用于构建编码/秘密共享方案，是简单的，模块化的，可以在许多方面的实例化，并介绍了新的应用程序的编码/秘密共享方案，以解决各种问题中出现的安全多方计算和篡改弹性密码。该项目的影响是帮助统一/分类以前的工作，确定在这些领域的未来工作的兴趣和影响方向的新组合。为了确保这项工作在研究之外产生更广泛的影响，该项目纳入了各种教育和外联活动，建立了统一文献中各种类型的共享/编码方案的框架。研究人员将考虑该框架各方面的组合及其在密码学中以下领域的应用：（1）具有一般对抗结构的多方计算的公平性;（2）通过玩家模拟技术的非延展性/泄漏弹性秘密共享方案的模块化构造;以及（3）具有广泛篡改类别的操纵检测的非延展性代码。该研究计划的概念贡献包括提出编码/秘密共享方案的新应用，为这些方案的简单和模块化结构开发通用范式，并引入基于复杂性理论的新密码硬度假设。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

The fields of coding theory and cryptography are intertwined, with each field influencing the other: Certain error correcting codes from coding theory are equivalent to a type of secret sharing scheme used in cryptography to achieve secure multiparty computation. Other types of coding/secret sharing schemes (such as non-malleable codes and leakage-resilient secret sharing) were first proposed to solve security problems arising in cryptographic settings. There are currently many variants of coding/secret sharing schemes, and most of the constructions are complex or ad-hoc. This project's novelties are: proposing a unifying framework that captures a spectrum of coding/secret sharing schemes that have been studied in the literature, developing new approaches for constructing coding/secret sharing schemes that are simple, modular and can be instantiated in a number of ways, and introducing new applications of coding/secret sharing schemes to solve a variety of problems arising in secure multiparty computation and tamper-resilient cryptography. This project's impacts are to help unify/classify prior work, identify new combinations of interest and impact directions of future work in these areas. To ensure broader impact of this work beyond the research being conducted, this project incorporates various educational and outreach activities.This project establishes a framework for the unification of various types of sharing/coding schemes in the literature. The investigators will consider combinations of aspects of the framework and their applications to the following areas in cryptography: (1) fairness in multiparty computation with general adversarial structures; (2) modular constructions of non-malleable/leakage-resilient secret sharing schemes via player-simulation techniques; and (3) non-malleable codes with manipulation detection for broad classes of tampering. The conceptual contributions of the research program consist of suggesting novel applications of coding/secret sharing schemes, developing generic paradigms for simple and modular constructions of these schemes, and introducing new cryptographic hardness assumptions grounded in complexity theory.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.