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Unidirectional Key Update in Updatable Encryption, Revisited

M. Jurkiewicz, K. Prabucka

TL;DR

The paper addresses long-term encrypted storage by designing a post-quantum updatable encryption scheme with backward-leak uni-directionality, based on the lattice-hardness of $LWE$ and implemented atop FrodoPKE. The construction uses homomorphic-like key updates via update tokens and bit-ordering with Tensor-$D$ to achieve constant-size ciphertexts and keys across epochs. A security reduction to $LWE$ under standard lattice assumptions is provided, along with a firewall-based proof that the scheme maintains security in the backward-leak model. Empirical performance is evaluated for FrodoKEM-640/976/1344 at AES and SHAKE variants, showing token generation is the primary cost while decryption remains fast, indicating practical viability for scalable, post-quantum UE. Overall, the work combines strong directional security, post-quantum resilience, and practical efficiency for secure outsourced storage under long-term threat models.

Abstract

In this paper we construct a new efficient updatable encryption (UE) scheme based on FrodoPKE learning with errors key encapsulation. We analyse the security of the proposed scheme in the backward-leak uni-directional setting within the rand-ind-eu-cpa model. Since the underlying computationally hard problem here is LWE, the scheme is secure against both classical and quantum attacks.

Unidirectional Key Update in Updatable Encryption, Revisited

TL;DR

The paper addresses long-term encrypted storage by designing a post-quantum updatable encryption scheme with backward-leak uni-directionality, based on the lattice-hardness of and implemented atop FrodoPKE. The construction uses homomorphic-like key updates via update tokens and bit-ordering with Tensor- to achieve constant-size ciphertexts and keys across epochs. A security reduction to under standard lattice assumptions is provided, along with a firewall-based proof that the scheme maintains security in the backward-leak model. Empirical performance is evaluated for FrodoKEM-640/976/1344 at AES and SHAKE variants, showing token generation is the primary cost while decryption remains fast, indicating practical viability for scalable, post-quantum UE. Overall, the work combines strong directional security, post-quantum resilience, and practical efficiency for secure outsourced storage under long-term threat models.

Abstract

In this paper we construct a new efficient updatable encryption (UE) scheme based on FrodoPKE learning with errors key encapsulation. We analyse the security of the proposed scheme in the backward-leak uni-directional setting within the rand-ind-eu-cpa model. Since the underlying computationally hard problem here is LWE, the scheme is secure against both classical and quantum attacks.
Paper Structure (11 sections, 8 theorems, 21 equations, 2 tables)

This paper contains 11 sections, 8 theorems, 21 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work and Discussion
  3. Preliminaries
  4. Lattices
  5. Gaussians
  6. Security Model for Updatable Encryption
  7. Frodo based UE scheme
  8. Frodo KEM
  9. Construction of EU scheme based on Frodo
  10. Security proof
  11. Implementation and Performance Analysis

Key Result

Lemma 3.1

Let $B_{1}=B_{1}(n)$, and $B_{2}=B_{2}(n)$ be positive integers and let $e_{1}\in [-B_{1}, B_{1}]$ be a fixed integer. Let $e_{2}\overset{\$}{\gets} [-B_{2}, B_{2}]$ be chosen uniformly at random. If $B_{1}/B_{2}=\negl$, the distribution of $e_{2}$ is statistically indistinguishable from that of $e_

Theorems & Definitions (10)

  • Lemma 3.1: smudging lemma (asharov2012multiparty)
  • Lemma 3.2
  • Lemma 5.1
  • Remark 6.1
  • Remark 6.2
  • Theorem 6.3
  • Theorem 6.4
  • Lemma 6.6
  • Lemma 6.8
  • Theorem 6.9