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Universal Coding for Shannon Ciphers under Side-Channel Attacks

Yasutada Oohama, Bagus Santoso

TL;DR

This paper advances universal coding for Shannon ciphers under side-channel attacks by proving the existence of encoder/decoder families that achieve reliable decoding for legitimate users while guaranteeing vanishing information leakage for any plaintext distribution and fixed side-channel model. The authors introduce a perfect universality result: for any pair of rates (R_A,R) and any source and channel distributions p_X, p_{KZ}, there exist codes with decoding error decaying exponentially and leakage decaying at a computable exponent G(R_A,R|p_{KZ}). The approach blends information spectrum methods with type-based analysis and introduces a new leakage-bound tool (Upsilon) and a meta-converse lemma, yielding a constructive, distribution-independent coding scheme. These results strengthen the practical relevance of secure source coding under side-channel leakage by guaranteeing robust performance across a wide class of devices and plaintext statistics.

Abstract

We study the universal coding under side-channel attacks posed and investigated by Oohama and Santoso (2022). They proposed a theoretical security model for Shannon cipher system under side-channel attacks, where the adversary is not only allowed to collect ciphertexts by eavesdropping the public communication channel, but is also allowed to collect the physical information leaked by the devices where the cipher system is implemented on such as running time, power consumption, electromagnetic radiation, etc. For any distributions of the plain text, any noisy channels through which the adversary observe the corrupted version of the key, and any measurement device used for collecting the physical information, we can derive an achievable rate region for reliability and security such that if we compress the ciphertext with rate within the achievable rate region, then: (1) anyone with secret key will be able to decrypt and decode the ciphertext correctly, but (2) any adversary who obtains the ciphertext and also the side physical information will not be able to obtain any information about the hidden source as long as the leaked physical information is encoded with a rate within the rate region.

Universal Coding for Shannon Ciphers under Side-Channel Attacks

TL;DR

This paper advances universal coding for Shannon ciphers under side-channel attacks by proving the existence of encoder/decoder families that achieve reliable decoding for legitimate users while guaranteeing vanishing information leakage for any plaintext distribution and fixed side-channel model. The authors introduce a perfect universality result: for any pair of rates (R_A,R) and any source and channel distributions p_X, p_{KZ}, there exist codes with decoding error decaying exponentially and leakage decaying at a computable exponent G(R_A,R|p_{KZ}). The approach blends information spectrum methods with type-based analysis and introduces a new leakage-bound tool (Upsilon) and a meta-converse lemma, yielding a constructive, distribution-independent coding scheme. These results strengthen the practical relevance of secure source coding under side-channel leakage by guaranteeing robust performance across a wide class of devices and plaintext statistics.

Abstract

We study the universal coding under side-channel attacks posed and investigated by Oohama and Santoso (2022). They proposed a theoretical security model for Shannon cipher system under side-channel attacks, where the adversary is not only allowed to collect ciphertexts by eavesdropping the public communication channel, but is also allowed to collect the physical information leaked by the devices where the cipher system is implemented on such as running time, power consumption, electromagnetic radiation, etc. For any distributions of the plain text, any noisy channels through which the adversary observe the corrupted version of the key, and any measurement device used for collecting the physical information, we can derive an achievable rate region for reliability and security such that if we compress the ciphertext with rate within the achievable rate region, then: (1) anyone with secret key will be able to decrypt and decode the ciphertext correctly, but (2) any adversary who obtains the ciphertext and also the side physical information will not be able to obtain any information about the hidden source as long as the leaked physical information is encoded with a rate within the rate region.
Paper Structure (17 sections, 20 theorems, 72 equations, 3 figures)

This paper contains 17 sections, 20 theorems, 72 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Preliminaries
  4. Basic System Description
  5. Security Criterion and Problem Set Up
  6. Previous Results
  7. Strong Converse for Reliable and Secure Rate Region
  8. Direct Coding Theorem
  9. Main Result
  10. Proof of Theorem \ref{['Th:mainth3']}
  11. Types of Sequences and Their Properties
  12. A New Key Proposition
  13. Proof of Property \ref{['pr:pro1']} part b)
  14. Coding Scheme, Reliability and Security Analysis
  15. Proof of Proposition \ref{['pro:UnivCodeBoundA']}
  16. ...and 2 more sections

Key Result

Proposition 1

$\quad$

Figures (3)

  • Figure 1: Side-channel attacks to the source coding with encryption.
  • Figure 2: Shape of the region ${\cal R}(p_{X},p_{KZ})$.
  • Figure 3: Proposed construction of $(\Phi^{(n)},\Psi^{(n)})$.

Theorems & Definitions (27)

  • Remark 1
  • Definition 1
  • Proposition 1
  • Definition 2
  • Definition 3
  • Theorem 1: Oohama and Santoso DBLP:conf/isit/OohamaS22
  • Theorem 2: Oohama and Santoso DBLP:conf/isit/OohamaS22
  • Corollary 1
  • Remark 2
  • Theorem 3
  • ...and 17 more