2023 EWHA-KMS International Workshop 

on Cryptography



Ewha Institute of Mathematical Sciences (EIMS)

Korean Mathematical Society (KMS)


Ewha Womans University, Seoul, July 10-12, 2023

Abstracts


We show the quantum complexity lower bounds and (almost) matching algorithms of the discrete logarithm and related problems in this model. Precisely, we prove that any generic quantum discrete logarithm algorithm for the underlying group G must make Omega(log |G|) depth of group operation queries. This shows that Shor's algorithm that makes O(|G|) group operations is asymptotically optimal among the generic quantum algorithms, even considering parallel algorithms. Furthermore, we extend this result to the generic hybrid quantum-classical algorithms and the bounded-size quantum memory setting, showing that variants of Shor's discrete logarithm algorithm are essentially optimal in each setting.

This talk is based on a joint work with Takashi Yamakawa and Aaram Yun.

Fully homomorphic encryption (FHE) is one of the most appropriate tools for privacy-preserving machine learning (PPML) to ensure strong security in the cryptographic sense. FHE is an encryption scheme that enables a server to process the encrypted data of clients without decrypting them. It allows the clients to outsource the processing of sensitive data to an untrusted server without leaking any information about the data. However, most current practical FHE schemes support only limited arithmetic operations and 1D data structures. In addition, due to the computational complexity of homomorphic encryption, it has been questioned whether performing the large number of operations required by machine learning over the FHE domain is practical.

In this talk, I will address these issues and introduce the method and latest achievements of deep convolutional neural networks based on homomorphic encryption. In particular, I will briefly introduce the following three points in this context: i) RNS-CKKS fully homomorphic encryption scheme, including high-precision bootstrapping schemes. ii) Polynomial approximation of the activation function and multiplexed parallel convolution for efficient CNN operations over FHE. iii) Privacy-preserving deep convolutional neural networks for ResNet and VGGNet with CIFAR and ImageNet datasets.

We develop this idea to improve the state-of-the-art proof of knowledge protocols for RLWE-based public-key encryption and BDLOP commitment schemes. In a nutshell, we present new proof of knowledge protocols without using noise flooding or rejection sampling which are provably secure under a computational hardness assumption, called Hint-MLWE. Our approach enjoys the best of two worlds because it has no computational overhead from repetition (abort) and achieves a polynomial overhead between the honest and proven languages.