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Bridges connecting Encryption Schemes

Mugurel Barcau, Cristian Lupascu, Vicentiu Pasol, George C. Turcas

Abstract

The present work investigates a type of morphisms between encryption schemes, called bridges. By associating an encryption scheme to every such bridge, we define and examine their security. Inspired by the bootstrapping procedure used by Gentry to produce fully homomorphic encryption schemes, we exhibit a general recipe for the construction of bridges. Our main theorem asserts that the security of a bridge reduces to the security of the first encryption scheme together with a technical additional assumption.

Bridges connecting Encryption Schemes

Abstract

The present work investigates a type of morphisms between encryption schemes, called bridges. By associating an encryption scheme to every such bridge, we define and examine their security. Inspired by the bootstrapping procedure used by Gentry to produce fully homomorphic encryption schemes, we exhibit a general recipe for the construction of bridges. Our main theorem asserts that the security of a bridge reduces to the security of the first encryption scheme together with a technical additional assumption.
Paper Structure (21 sections, 5 theorems, 55 equations, 4 figures, 2 tables)

This paper contains 21 sections, 5 theorems, 55 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Finite Distributions
  4. Encryption Schemes and Bridges
  5. The security of a bridge
  6. A general recipe for constructing bridges
  7. On the security of Gentry type bridges
  8. A variant of Gentry's recipe
  9. Conclusions
  10. Examples of Gentry bridges
  11. Description of the CSGN scheme
  12. $1^{\text{st}}$ bridge
  13. $2^{\text{nd}}$ bridge
  14. $3^{\text{rd}}$ bridge
  15. $4^{\text{th}}$ bridge
  16. ...and 6 more sections

Key Result

proposition 1

If a bridge $\mathbf{B}_{\iota, f}$ is IND-CPA secure, then the encryption scheme $\mathscr{S}_1$ is also IND-CPA secure.

Figures (4)

  • Figure 1: Probability distributions for bridges
  • Figure 2: The first and second bridges
  • Figure 3: The third bridge - BGV & BFV
  • Figure 4: Evaluation times for the comparison circuit using GM-SYY bridge

Theorems & Definitions (23)

  • definition 1
  • definition 2
  • remark 1
  • definition 3
  • remark 2
  • definition 4: IND-CPA Security
  • remark 3
  • definition 5
  • remark 4
  • definition 6
  • ...and 13 more