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Tempora-Fusion: Time-Lock Puzzle with Efficient Verifiable Homomorphic Linear Combination

Aydin Abadi

TL;DR

Tempora-Fusion is introduced, a TLP that allows a server to perform homomorphic linear combinations of puzzles from different clients while ensuring verification of computation correctness, thus paving the way for efficient implementations of this scheme in various domains.

Abstract

To securely transmit sensitive information into the future, Time-Lock Puzzles (TLPs) have been developed. Their applications include scheduled payments, timed commitments, e-voting, and sealed-bid auctions. Homomorphic TLP is a key variant of TLP that enables computation on puzzles from different clients. This allows a solver/server to tackle only a single puzzle encoding the computation's result. However, existing homomorphic TLPs lack support for verifying the correctness of the computation results. We address this limitation by introducing Tempora-Fusion, a TLP that allows a server to perform homomorphic linear combinations of puzzles from different clients while ensuring verification of computation correctness. This scheme avoids asymmetric-key cryptography for verification, thus paving the way for efficient implementations. We discuss our scheme's application in various domains, such as federated learning, scheduled payments in online banking, and e-voting.

Tempora-Fusion: Time-Lock Puzzle with Efficient Verifiable Homomorphic Linear Combination

TL;DR

Tempora-Fusion is introduced, a TLP that allows a server to perform homomorphic linear combinations of puzzles from different clients while ensuring verification of computation correctness, thus paving the way for efficient implementations of this scheme in various domains.

Abstract

To securely transmit sensitive information into the future, Time-Lock Puzzles (TLPs) have been developed. Their applications include scheduled payments, timed commitments, e-voting, and sealed-bid auctions. Homomorphic TLP is a key variant of TLP that enables computation on puzzles from different clients. This allows a solver/server to tackle only a single puzzle encoding the computation's result. However, existing homomorphic TLPs lack support for verifying the correctness of the computation results. We address this limitation by introducing Tempora-Fusion, a TLP that allows a server to perform homomorphic linear combinations of puzzles from different clients while ensuring verification of computation correctness. This scheme avoids asymmetric-key cryptography for verification, thus paving the way for efficient implementations. We discuss our scheme's application in various domains, such as federated learning, scheduled payments in online banking, and e-voting.
Paper Structure (45 sections, 5 theorems, 9 equations, 3 figures, 3 tables)

This paper contains 45 sections, 5 theorems, 9 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Our Solutions
  3. Partially Homomorphic TLP.
  4. Applications
  5. Timed Secure Aggregation in Federated Learning.
  6. Transparent Scheduled Payments in Online Banking.
  7. Verifiable E-Voting and Sealed-Bid Auction Systems.
  8. Related Work
  9. Homomorphic Time-lock Puzzles
  10. Verifiable Delay Function (VDF)
  11. Preliminaries
  12. Notations and Informal Threat Model
  13. Pseudorandom Function
  14. Oblivious Linear Function Evaluation
  15. Polynomial Representation of a Message
  16. ...and 30 more sections

Key Result

theorem thmcountertheorem

Let $\bm{\pi}(x)$ be a polynomial of degree $n$ with a random root $\beta$, and $\{(x_{ 1},\pi_{ 1}),\ldots,$$(x_{ l},\pi_{ l})\}$ be point-value representation of $\bm{\pi}(x)$, where $l>n$, ${p}\xspace$ denote a large prime number, $\log_{ 2}({p}\xspace)=\lambda'$ is the security parameter, $\bm{\

Figures (3)

  • Figure 1: Outline of the workflow of $\text{Tempora-Fusion}$. In the figure, $t_{ 0}$ refers to the time when a server receives a puzzle instance from a client, $t'_{ 0}$ is the time when clients delegate the homomorphic linear combination of their puzzles' solutions to the server, $t_{ i}$ is the time when the solution to $Cleint_{ i}$'s puzzle is found, $t'$ is the time when the solution to a puzzle encoding the linear combination is found, $\Delta_{ i}$ is the period after which the solution to $Client_{ i}$'s puzzle is found, and $\Delta$ is the period after which a solution to the puzzle encoding the linear combination is discovered.
  • Figure 2: Performance of polynomial factorizations and $\mathtt{PRF}$. Figure \ref{['fig:sub1']}, depicts the performance of polynomial factorizations across polynomial degrees ranging from $2$ to $10$ over fields of $128$ and $256$ bits, i.e., $\log_{ 2}({p}\xspace)=128$ and $\log_{ 2}({p}\xspace)=256$. Figure \ref{['fig:sub2']}, showcases the performance of $\mathtt{PRF}$ across $2$ to $1024$ invocations, with output sizes of $128$ and $256$ bits.
  • Figure 3: Enhanced Oblivious Linear function Evaluation ($\mathtt{OLE}\xspace^{ +}$) GhoshN19.

Theorems & Definitions (22)

  • theorem thmcountertheorem: Unforgeable Encrypted Polynomial with a Hidden Root
  • definition thmcounterdefinition
  • definition thmcounterdefinition
  • definition thmcounterdefinition: Syntax
  • definition thmcounterdefinition: Privacy
  • definition thmcounterdefinition: Solution-Validity
  • definition thmcounterdefinition: Completeness
  • definition thmcounterdefinition: Efficiency
  • definition thmcounterdefinition: Compactness
  • definition thmcounterdefinition: Security
  • ...and 12 more