Homomorphic Encryption
Homomorphic Encryption (HE) is a special type of encryption that enables computations on encrypted data without decrypting it first. A non-trusted party can therefore receive encrypted data and still perform computations on it. When the result of these computations is decrypted, the outcome is the same as if the computation had been performed on the unencrypted data. This makes HE very useful for privacy-compliant data processing in cloud applications, such as, for example, medical data analytics.
The homomorphic encryption schemes that allow arbitrary computations, known as Fully Homomorphic Encryption (FHE), are currently all based on lattices. But relying solely on lattice-based constructions is risky, because this means that the security of all FHE schemes builds on the same mathematical assumption, and can therefore be attacked all at once.
Therefore, it is important to explore constructions on alternative mathematical foundations, although all existing approaches based on alternative structures —such as code-based cryptography— currently only support limited operations on the ciphertext, i.e., they result in Somewhat Homomorphic Encryption (SHE) schemes rather than fully homomorphic ones.
At the Institute for Coding and Cryptography headed by Prof. Antonia Wachter-Zeh, we are working on Post-Quantum Cryptography, specifically lattice-based and code-based cryptography. Among other topics our research includes the construction of code-based homomorphic encryption schemes.
What we will do in this project:
Recently a code-based somewhat homomorphic encryption schemes was proposed in "Somewhat Homomorphic Encryption from Linear Homomorphism and Sparse LPN". This scheme has conceptual similarities to the well-established and lattice-based fully homomorphic encryption scheme from "Homomorphic Encryption from Learning with Errors: Conceptually-Simpler, Asymptotically-Faster, Attribute-Based". Nevertheless, despite their similar structure, the code-based scheme allows only limited operations on the ciphertext, while the lattice-based schemes allows arbitrary many operations.
Together with you, we would like to compare these two so closely related schemes, focusing on:
- the similarities of both schmes
- understanding the core differences of both schemes
- improving the efficiency of the code-based scheme
The exact tasks can also be changed depending on your interest and previous knowledge.
We are looking forward to welcoming you in Munich!
