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Modification to Fully Homomorphic Modified Rivest Scheme

Sona Alex, Bian Yang

Abstract

This document details the Fully Homomorphic Modified Rivest Scheme (FHMRS), a security issue in FHMRS, and a modification to FHMRS (mFHMRS) to mitigate the security issue.

Modification to Fully Homomorphic Modified Rivest Scheme

Abstract

This document details the Fully Homomorphic Modified Rivest Scheme (FHMRS), a security issue in FHMRS, and a modification to FHMRS (mFHMRS) to mitigate the security issue.
Paper Structure (16 sections, 10 equations)

This paper contains 16 sections, 10 equations.

Table of Contents

  1. Fully Homomorphic Modified Rivest Scheme (FHMRS)
  2. Known plaintext attack on FHMRS when it supports multiplicative homomorphism
  3. Modified FHMRS (mFHMRS)
  4. Homomorphic Properties
  5. Security analysis of modified FHMRS (mFHMRS)
  6. Ciphertext-only Attacks
  7. Brute-force Attack
  8. Lattice-based Attack
  9. Known-plaintext Attacks
  10. Brute-force Attack
  11. Lattice-based Attack
  12. Attack based on solving linear equations in u and $p_i$s
  13. Attack based on solving linear equations in $p_i$s
  14. Resistance to guessing $p_i$ values from $c_{i}$
  15. Lattice -based recovery of integer from noisy Chinese remaindering with known $p_i$s
  16. ...and 1 more sections