Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Randomized Key Encapsulation/Consolidation

Amir K. Khandani

TL;DR

The paper addresses secure key exchange when common randomness is limited or absent by merging Key Consolidation with randomized Quantum-Safe Key Encapsulation. It introduces a public-key framework $\mathbf{P}=\mathbf{BC}$ with a punctured $\mathbf{C}_1$ and randomized components designed to mask structure from an adversary, while enabling recovery by the legitimate party. Security is formalized with information-theoretic proofs toward a target $\mathsf{SEC}$ (typically $256$ bits), implying an exhaustive search attack over $2^{\mathsf{SEC}}$ possibilities. Compared to McEliece-based quantum-safe KEMs, the approach sacrifices public-key size to gain robustness in the absence or sparsity of common randomness, and it demonstrates compatibility with loop-based common randomness extraction from network RTTs using Reed-Muller component codes. The work emphasizes practical applicability for adaptive secrecy in real-world networks and presents a cohesive fusion of key-consolidation ideas with quantum-safe encapsulation techniques.

Abstract

This article bridges the gap between two topics used in sharing an encryption key: (i) Key Consolidation, i.e., extracting two identical strings of bits from two information sources with similarities (common randomness). (ii) Quantum-safe Key Encapsulation by incorporating randomness in Public/Private Key pairs. In the context of Key Consolidation, the proposed scheme adds to the complexity Eve faces in extracting useful data from leaked information. In this context, it is applied to the method proposed in [1] for establishing common randomness from round-trip travel times in a packet data network. The proposed method allows adapting the secrecy level to the amount of similarity in common randomness. It can even encapsulate a Quantum-safe encryption key in the extreme case that no common randomness is available. In the latter case, it is shown that the proposed scheme offers improvements with respect to the McEliece cryptosystem which currently forms the foundation for Quantum safe key encapsulation. [1] A. K. Khandani, "Looping for Encryption Key Generation Over the Internet: A New Frontier in Physical Layer Security," 2023 Biennial Symposium on Communications (BSC), Montreal, QC, Canada, 2023, pp. 59-64

Randomized Key Encapsulation/Consolidation

TL;DR

The paper addresses secure key exchange when common randomness is limited or absent by merging Key Consolidation with randomized Quantum-Safe Key Encapsulation. It introduces a public-key framework with a punctured and randomized components designed to mask structure from an adversary, while enabling recovery by the legitimate party. Security is formalized with information-theoretic proofs toward a target (typically bits), implying an exhaustive search attack over possibilities. Compared to McEliece-based quantum-safe KEMs, the approach sacrifices public-key size to gain robustness in the absence or sparsity of common randomness, and it demonstrates compatibility with loop-based common randomness extraction from network RTTs using Reed-Muller component codes. The work emphasizes practical applicability for adaptive secrecy in real-world networks and presents a cohesive fusion of key-consolidation ideas with quantum-safe encapsulation techniques.

Abstract

This article bridges the gap between two topics used in sharing an encryption key: (i) Key Consolidation, i.e., extracting two identical strings of bits from two information sources with similarities (common randomness). (ii) Quantum-safe Key Encapsulation by incorporating randomness in Public/Private Key pairs. In the context of Key Consolidation, the proposed scheme adds to the complexity Eve faces in extracting useful data from leaked information. In this context, it is applied to the method proposed in [1] for establishing common randomness from round-trip travel times in a packet data network. The proposed method allows adapting the secrecy level to the amount of similarity in common randomness. It can even encapsulate a Quantum-safe encryption key in the extreme case that no common randomness is available. In the latter case, it is shown that the proposed scheme offers improvements with respect to the McEliece cryptosystem which currently forms the foundation for Quantum safe key encapsulation. [1] A. K. Khandani, "Looping for Encryption Key Generation Over the Internet: A New Frontier in Physical Layer Security," 2023 Biennial Symposium on Communications (BSC), Montreal, QC, Canada, 2023, pp. 59-64
Paper Structure (6 sections, 2 theorems, 10 equations, 4 figures, 1 table)

This paper contains 6 sections, 2 theorems, 10 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Proposed Structure
  3. Construction and Security Level
  4. Encryption and Decryption
  5. Complexity Comparisons
  6. Example for Key Consolidation

Key Result

Theorem 1

Random permutation embedded in $\mathbf{C}_1$ is completely masked by randomness embedded in $\mathbf{B}$.

Figures (4)

  • Figure 1: Structure of the public key: $\mathbf{C}_1$ is formed by puncturing $\mathsf{p+q}$ columns from an $\mathsf{s}\times \mathsf{s}$ random permutation matrix where $\mathsf{s}=\mathsf{m+p+q}$, and $\mathbf{C}_2$ is an $\mathsf{p}\times \mathsf{s}$ random matrix.
  • Figure 2: Structure of the (private to Alice) matrix $\mathbf{A}$ and relevant randomness conditions necessary for key recovery by Alice.
  • Figure 3: Round trip time, namely $TT_3-TT_1$ and $T\!R_3-T\!R_1$, are dependent random variables (since $\epsilon_1+d_2+\epsilon_2+d_3+\epsilon_3+d_4+\epsilon_4$ is in common).
  • Figure 4: Error Rate of a single code-word for different RM codes.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof