Unconditionally Secure Cryptography

无条件安全的密码协议是指可以在数学上证明安全的协议，而不需要对底层计算问题的棘手性进行任何假设。无条件安全密码系统的第一个例子是一次性密码本，香农证明了它的安全性。迄今为止，此类方案的例子有很多。示例包括某些类型的认证码、秘密共享方案、密钥预分配方案、承诺方案、跟踪方案、广播加密，甚至是在公钥设置中最常研究的一些方案，例如签名方案。 在过去 10-15 年里，人们对后量子密码学的兴趣与日俱增，将其作为构建实用量子计算机的保险政策。事实上，美国国家安全局 (NSA) 于 2015 年 8 月宣布，打算在其标准化密码系统“Suite B”中过渡到抗量子密码技术。 后量子密码学的大多数工作都涉及基于计算问题构建系统，这些问题显然很难解决，即使是量子计算机（例如基于格的密码学）也是如此。无条件安全密码学可以被视为后量子密码学的最强形式，因为这些协议本质上不受（假设的）量子计算机的攻击。 无条件安全密码学中的安全证明最终依赖于信息论和概率的考虑。粗略地说，安全证明证明对手没有足够的信息来计算某些指定的秘密信息或成功执行指定的攻击。无条件安全密码方案的构建通常涉及数学各个分支的方法和技术，包括组合数学、编码理论、有限域、群论、数论等。 我的目标是继续研究无条件安全密码学中的各种长期研究问题，并启动新问题的研究。我计划进行的一些具体研究问题包括： 1. 构建新型指纹代码来追踪盗版内容。 2. 为无条件安全的可检索性证明方案提供新的构造，特别是在使用多个服务器的（分布式）设置中。 3. 给出代数操纵检测代码的新构造和必要条件，并研究与相关数学结构和密码原语的联系。 4. 为广义的全有或全无变换提供新的构造和必要条件。 这些特定领域（和其他领域）的研究将带来新的无条件安全的加密技术，这对于保护后量子环境中的互联网非常有价值。

Unconditionally secure cryptographic protocols refer to protocols that can be proven secure mathematically without the need for any assumptions regarding the intractability of underlying computational problems. The first example of an unconditionally secure cryptosystem was the one-time pad, which was proven secure by Shannon. There are by now many examples of many such schemes. Examples include certain types of authentication codes, secret sharing schemes, key predistribution schemes, commitment schemes, tracing schemes, broadcast encryption, and even some schemes that are most often studied in the public-key setting, such as signature schemes. There has been increasing interest in post-quantum cryptography over the last 10-15 years, as an insurance policy in case a practical quantum computer is built. Indeed, the NSA announced in August 2015 that it intends to transition to quantum-resistant cryptography in its "Suite B'' of standardized cryptosystems. Most work in post-quantum cryptography involves constructing systems based on computational problems that are apparently hard to solve, even by quantum computers (e.g., lattice-based cryptography). Unconditionally secure cryptography can be regarded as the strongest form of post-quantum cryptography, since these protocols are by their very nature immune to attacks by (hypothetical) quantum computers. Security proofs in unconditionally secure cryptography ultimately rely on considerations from information theory and probability. Roughly speaking, a security proof establishes that an adversary does not have sufficient information to be able to compute some specified secret information or to successfully carry out a specified attack. The construction of unconditionally secure cryptographic schemes typically involve methods and techniques from various branches of mathematics, including combinatorics, coding theory, finite fields, group theory, number theory, etc. My objective is to continue to study various long-term research problems in unconditionally secure cryptography, as well as to initiate the study of new problems. Some specific research problems I plan to undertake include the following: 1. Construct new types of fingerprinting codes for tracing pirated content. 2. Give new constructions for unconditionally secure proof-of-retrievability schemes, especially in the (distributed) setting which employs multiple servers. 3. Give new constructions and necessary conditions for algebraic manipulation detection codes and investigate connections with related mathematical structures and cryptographic primitives. 4. Give new constructions and necessary conditions for generalized all-or-nothing transforms. Research in these specific areas (and others) will lead to new unconditionally secure cryptographic techniques that will be valuable in securing the internet in a post-quantum setting.