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On the Semantic Security in the General Bounded Storage Model: A New Proof

Mohammad Moltafet, Hamid R. Sadjadpour, Zouheir Rezki

TL;DR

A new proof of the security of the protocol proposed by Maurer for the general bounded storage model is provided, i.e., the adversary can access all bits of the random string, and store the output of any Boolean function on the string.

Abstract

In the bounded storage model introduced by Maurer, the adversary is computationally unbounded and has a bounded storage capacity. In this model, information-theoretic secrecy is guaranteed by using a publicly available random string whose length is larger than the adversary storage capacity. The protocol proposed by Maurer is simple, from the perspective of implementation, and efficient, from the perspective of the initial secret key size and random string length. However, he provided the proof of the security for the case where the adversary can access a constant fraction of the random string and store only original bits of the random string. In this paper, we provide a new proof of the security of the protocol proposed by Maurer for the general bounded storage model, i.e., the adversary can access all bits of the random string, and store the output of any Boolean function on the string. We reaffirm that the protocol is absolutely semantically secure in the general bounded storage model.

On the Semantic Security in the General Bounded Storage Model: A New Proof

TL;DR

A new proof of the security of the protocol proposed by Maurer for the general bounded storage model is provided, i.e., the adversary can access all bits of the random string, and store the output of any Boolean function on the string.

Abstract

In the bounded storage model introduced by Maurer, the adversary is computationally unbounded and has a bounded storage capacity. In this model, information-theoretic secrecy is guaranteed by using a publicly available random string whose length is larger than the adversary storage capacity. The protocol proposed by Maurer is simple, from the perspective of implementation, and efficient, from the perspective of the initial secret key size and random string length. However, he provided the proof of the security for the case where the adversary can access a constant fraction of the random string and store only original bits of the random string. In this paper, we provide a new proof of the security of the protocol proposed by Maurer for the general bounded storage model, i.e., the adversary can access all bits of the random string, and store the output of any Boolean function on the string. We reaffirm that the protocol is absolutely semantically secure in the general bounded storage model.
Paper Structure (20 sections, 12 theorems, 48 equations, 1 algorithm)

This paper contains 20 sections, 12 theorems, 48 equations, 1 algorithm.

Table of Contents

  1. Introduction
  2. Organization
  3. Notation
  4. The Protocol and Main Results
  5. The Protocol
  6. Attack Model
  7. Proof of Security
  8. Proof of Proposition \ref{['bounded-lemma-1']}
  9. Proof of Theorem \ref{['\u200cBounded-s-th']}
  10. Conclusions
  11. Appendix
  12. Proof of Lemma \ref{['lemma-bou-dv']}
  13. Proof of Lemma \ref{['boundongoodalpha']}
  14. Proof of Lemma \ref{['alphagooddelta']}
  15. Proof of Lemma \ref{['comp-ind-final']}
  16. ...and 5 more sections

Key Result

Theorem 1

For any two equiprobable messages $\mathbf{M}^0$ and $\mathbf{M}^1$ of size $m$, for any recording function $A_1(\boldsymbol\alpha):\{0,1\}^{kn}\rightarrow \{0,1\}^{\beta}$, for any decoding algorithm $A_2$, for $\boldsymbol\alpha\stackrel{R}{\leftarrow}\{0,1\}^{kn}$, and $\mathbf{Z}\stackrel{R}{\le

Theorems & Definitions (32)

  • Remark 1
  • Theorem 1
  • proof
  • Remark 2
  • Remark 3
  • Proposition 1: Bit security
  • Remark 4
  • Definition 1
  • Definition 2
  • Definition 3
  • ...and 22 more