This book is a concise, self-contained, up-to-date introduction to extremal combinatorics for
nonspecialists. There is a strong emphasis on theorems with particularly elegant and …

Interactive proofs (IPs) and arguments are cryptographic protocols that enable an untrusted
prover to provide a guarantee that it performed a requested computation correctly …

In this paper we give the first deterministic polynomial time algorithm for testing whether a
diagonal depth-3 circuit C (x 1,..., xn)(ie C is a sum of powers of linear functions) is zero. We …

The past decade has seen numerous major mathematical breakthroughs for topics such as
the finite field Kakeya conjecture, the cap set conjecture, Erdős's distinct distances problem …

We present novel homomorphic encryption schemes for integer arithmetic, intended
primarily for use in secure single-party computation in the cloud. These schemes are …

We develop a new notion called tester of a class M of functions f: A→ C that maps the
elements α∈ A in the domain A of the function to a finite number (the size of the tester) of …

The Ideal Proof System (IPS) of Grochow & Pitassi (FOCS 2014, J. ACM, 2018) is an
algebraic proof system that uses algebraic circuits to refute the solvability of unsatisfiable …

This book seeks to generalize techniques and experiences in designing and analyzing
cryptographic schemes for blockchain. It devotes three chapters to review the background …

We present novel homomorphic encryption schemes for integer arithmetic, intended for use
in secure single-party computation in the cloud. These schemes are capable of securely …

针对云存储系统由于静态的存储架构和存储模式而带来的安全威胁, 提出一种基于再生码的拟态
化存储方案. 该方案利用网络编码方案将数据存储在云端数据节点上, 采用一种基于再生码的 …