Key-Homomorphic Pseudorandom Functions from LWE with Small Modulus

Explore a presentation on key-homomorphic pseudorandom functions derived from the Learning With Errors (LWE) problem using small modulus. Delve into the foundations of PRFs, including the GGM84 construction and lattice-based variants. Examine the impact of lattice modulus on security and efficiency. Investigate pseudorandom synthesizers, with a focus on the NR95 and BPR12 constructions. Analyze the security of Learning With Rounding (LWR) and its relationship to LWE. Study techniques for chaining LWE samples and the implications of introducing rounding and errors. Conclude by considering open problems and future directions in this area of cryptography.

Pseudorandom Functions (PRFS) GGM84
Lattice-based PRFS
Lattice Modulus
Results
Limitations on Reduction Loss
Pseudorandom Synthesizers NR95
Modular Rounding BPR12
LWE-based Synthesizers [BPR12]
Security of LWR BPR12
Chaining LWE Samples
Learning with Rounding and Errors
Conclusion and Open Problems