Project Seminar

Shubham Mishra (18CS10066)

Topic

Multiparty Post-Quantum Fully Homomorphic Encryption

Motivation

  • Today we want to perform heavy computations in the cloud without assuming confidentiality guarantee on the remote server. For that we need to use Fully Homomorphic Encryption techniques.

  • In addition to that, we also want multiple parties to jointly perform such computations keeping the inputs secret. This is the classic setup of Secure Multiparty Computation.

  • But current systems are slow and have huge ciphertext expansion issues. It is challenging to create efficient implementations of the same.

Problem Definition

  • To create an efficient and scalable implementation of Fully Homomorphic Multiparty Computation System using existing established papers.
  • To accelerate parts of the system using FPGAs and GPUs.
  • If possible, propose improvements upon the existing schemes to reduce noise and ciphertext sizes.

Reading list

  1. Regev’s paper on LWE
  2. GSW paper
  3. Mathematics of Lattices by Vindod Vaikuntanathan
  4. Craig Gentry’s PhD Thesis
  5. FHEW paper
  6. TFHE paper
  7. Multiparty Computation in FHE

Works done

  1. Examined the inner workings of the TFHE library.
  2. Using Library’s internal APIs, demonstrated 2-out-of-2 Threshold Decryption of LWE and TLWE encryption schemes with various bounds of smudging noise.
  3. Attempted to propose a MPC Scheme based on Mukherjee-Wilchs’ paper with less ciphertext expansion. But ended up with a partially homomorphic scheme based on GSW which works extra assumption of Public Key Infrastructure.

Next plans

  • Complete t-out-of-n Threshold Decryption using TFHE.
  • Complete noise vs modulus profiling and find out ways to reduce noise and modulus.
  • Port Mukherjee-Wilchs’ scheme to TFHE and create an efficient and scalable implementation out of it.
  • Help in porting FFT computations to FPGA.
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