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Hybrid Encryption with Certified Deletion in Preprocessing Model

Kunal Dey, Reihaneh Safavi-Naini

TL;DR

The paper addresses the challenge of certifying data deletion when outsourcing to a remote party, leveraging quantum no-cloning to enable verifiable deletion. It introduces pHE-CD, a hybrid encryption in the preprocessing model that combines an information-theoretic iKEM with a DEM-CD to provide encryption plus certified deletion, yielding either information-theoretic or everlasting deletion security. It presents two constructions: Construction 1 achieves information-theoretic deletion using BI-based SKE-CD, while Construction 2 achieves everlasting deletion with a quantum-safe, computationally secure DEM-CD that uses a constant-length key; a composition theorem links the security of the components to overall pHE-CD security. The framework supports encryption of arbitrarily long messages and suggests future work on integrating quantum-enabled KEMs (qKEM) to further enhance security against evolving quantum attacks.

Abstract

Certified deletion allows Alice to outsource data to Bob and, at a later time, obtain a verifiable guarantee that the file has been irreversibly deleted at her request. The functionality, while impossible using classical information alone, can be achieved using quantum information. Existing approaches, rely on one-time pad (OTP) encryption, or use computational hardness assumptions that may be vulnerable to future advances in classical or quantum computing. In this work, we introduce and formalize hybrid encryption with certified deletion in the preprocessing model (pHE-CD) and propose two constructions. The constructions combine an information-theoretic key encapsulation mechanism (iKEM) with a data encapsulation mechanism that provides certified deletion (DEM-CD) and, respectively, provide {\em information-theoretic certified deletion}, where both confidentiality and deletion properties are provided against a computationally unbounded adversary; and {\em everlasting certified deletion}, where confidentiality is computational before deletion, and upon successful verification of the deletion certificate, the message becomes information-theoretically hidden from an adversary that is computationally unbounded. Our pHE-CD schemes provide IND-$q_e$-CPA notion of security and support encryption of arbitrarily long messages. In the second construction, using a computationally secure DEM-CD that is quantum-safe (i.e. constructed using quantum coding and AES), we obtain quantum-safe security with keys that are significantly shorter than the message. Instantiating the proposed framework using quantum enabled kem (qKEM) as the iKEM, is a future work.

Hybrid Encryption with Certified Deletion in Preprocessing Model

TL;DR

The paper addresses the challenge of certifying data deletion when outsourcing to a remote party, leveraging quantum no-cloning to enable verifiable deletion. It introduces pHE-CD, a hybrid encryption in the preprocessing model that combines an information-theoretic iKEM with a DEM-CD to provide encryption plus certified deletion, yielding either information-theoretic or everlasting deletion security. It presents two constructions: Construction 1 achieves information-theoretic deletion using BI-based SKE-CD, while Construction 2 achieves everlasting deletion with a quantum-safe, computationally secure DEM-CD that uses a constant-length key; a composition theorem links the security of the components to overall pHE-CD security. The framework supports encryption of arbitrarily long messages and suggests future work on integrating quantum-enabled KEMs (qKEM) to further enhance security against evolving quantum attacks.

Abstract

Certified deletion allows Alice to outsource data to Bob and, at a later time, obtain a verifiable guarantee that the file has been irreversibly deleted at her request. The functionality, while impossible using classical information alone, can be achieved using quantum information. Existing approaches, rely on one-time pad (OTP) encryption, or use computational hardness assumptions that may be vulnerable to future advances in classical or quantum computing. In this work, we introduce and formalize hybrid encryption with certified deletion in the preprocessing model (pHE-CD) and propose two constructions. The constructions combine an information-theoretic key encapsulation mechanism (iKEM) with a data encapsulation mechanism that provides certified deletion (DEM-CD) and, respectively, provide {\em information-theoretic certified deletion}, where both confidentiality and deletion properties are provided against a computationally unbounded adversary; and {\em everlasting certified deletion}, where confidentiality is computational before deletion, and upon successful verification of the deletion certificate, the message becomes information-theoretically hidden from an adversary that is computationally unbounded. Our pHE-CD schemes provide IND--CPA notion of security and support encryption of arbitrarily long messages. In the second construction, using a computationally secure DEM-CD that is quantum-safe (i.e. constructed using quantum coding and AES), we obtain quantum-safe security with keys that are significantly shorter than the message. Instantiating the proposed framework using quantum enabled kem (qKEM) as the iKEM, is a future work.
Paper Structure (6 sections, 7 theorems, 14 equations, 5 figures)

This paper contains 6 sections, 7 theorems, 14 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Cryptographic Tools
  4. Hybrid Encryption in with Certified Deletion in Preprocessing Model (pHE-CD)
  5. Constructions
  6. Concluding Remarks

Key Result

Lemma 1

An iKEM iK is $\sigma(\lambda)$-IND-$q_e$-CEA secure if and only if for all computationally unbounded adversary, Here $U_{{iK}.Len(\lambda)}$ is the uniform distribution over $\{0,1\}^{{ iK}.Len(\lambda)}$ and $\sigma(\lambda)$ is a negligible function of $\lambda$.

Figures (5)

  • Figure 1: The distinguishing game $\text{IKIND}^{\text{atk-b}}_{{\sf iK},A}$
  • Figure 2: The distinguishing game $\text{IND}^{\text{atk-b}}_{{\sf D},A}$
  • Figure 3: Hybrid encryption in preprocessing model
  • Figure 4: The distinguishing game $\text{IND}^{\text{atk-b}}_{{\sf pHE},\mathcal{A}}$
  • Figure 5: Hybrid encryption with certified deletion in preprocessing model

Theorems & Definitions (21)

  • Definition 2.1
  • Definition 2.2: Security of iKEM: IND-OT, IND-$q_e$-CEA, IND-$(q_e,q_d)$-CCA sharifian2021information
  • Lemma 1: sharifian2021information
  • Definition 2.3: Data Encapsulation Mechanism (DEM)
  • Definition 2.4: Security of DEM: IND-OT, IND-OTCCA, IND-CPA, IND-CCA1, IND-CCA2 Herranz2006KEMDEMNA
  • Definition 2.5: (Hybrid Encryption in Preprocessing Model (pHE)) sharifian2021information
  • Definition 2.6: (Security of Hybrid Encryption in Preprocessing Model
  • Theorem 2: sharifian2021information
  • Definition 2.7: Syntax
  • Definition 2.8: One-time Everlasting Certified Deletion Security
  • ...and 11 more