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Multi-Message Secure Aggregation with Demand Privacy

Chenyi Sun, Ziting Zhang, Kai Wan, Giuseppe Caire

TL;DR

We study a two-round, dropout-robust secure multi-message aggregation with demand privacy, where the server requests ${\sf K}_{\sf c}$ linear combinations from ${\sf K}$ users and at least ${\sf U}$ users remain. The main approach yields an exact optimal rate region for ${\sf K}_{\sf c}=1$ via multiplicative demand encryption and additive model masking, and an order-optimal scheme (within a factor of 2) for ${\sf 2\le {\sf K}_{\sf c}< {\sf U}}$ using robust symmetric private computation. The results establish exact capacity for ${\sf K}_{\sf c}=1$ and near-optimal performance for larger ${\sf K}_{\sf c}$, with matching converse bounds that bound the first-round rate and the second-round rate. This advances the theory of information-theoretic secure aggregation with demand privacy in the presence of dropouts and suggests directions for exact capacity characterization and key-size minimization in future work.

Abstract

This paper considers a multi-message secure aggregation with privacy problem, in which a server aims to compute $\sf K_c\geq 1$ linear combinations of local inputs from $\sf K$ distributed users. The problem addresses two tasks: (1) security, ensuring that the server can only obtain the desired linear combinations without any else information about the users' inputs, and (2) privacy, preventing users from learning about the server's computation task. In addition, the effect of user dropouts is considered, where at most $\sf{K-U}$ users can drop out and the identity of these users cannot be predicted in advance. We propose two schemes for $\sf K_c$ is equal to (1) and $\sf 2\leq K_c\leq U-1$, respectively. For $\sf K_c$ is equal to (1), we introduce multiplicative encryption of the server's demand using a random variable, where users share coded keys offline and transmit masked models in the first round, followed by aggregated coded keys in the second round for task recovery. For $\sf{2\leq K_c \leq U-1}$, we use robust symmetric private computation to recover linear combinations of keys in the second round. The objective is to minimize the number of symbols sent by each user during the two rounds. Our proposed schemes have achieved the optimal rate region when $ \sf K_c $ is equal to (1) and the order optimal rate (within 2) when $\sf{2\leq K_c \leq U-1}$.

Multi-Message Secure Aggregation with Demand Privacy

TL;DR

We study a two-round, dropout-robust secure multi-message aggregation with demand privacy, where the server requests linear combinations from users and at least users remain. The main approach yields an exact optimal rate region for via multiplicative demand encryption and additive model masking, and an order-optimal scheme (within a factor of 2) for using robust symmetric private computation. The results establish exact capacity for and near-optimal performance for larger , with matching converse bounds that bound the first-round rate and the second-round rate. This advances the theory of information-theoretic secure aggregation with demand privacy in the presence of dropouts and suggests directions for exact capacity characterization and key-size minimization in future work.

Abstract

This paper considers a multi-message secure aggregation with privacy problem, in which a server aims to compute linear combinations of local inputs from distributed users. The problem addresses two tasks: (1) security, ensuring that the server can only obtain the desired linear combinations without any else information about the users' inputs, and (2) privacy, preventing users from learning about the server's computation task. In addition, the effect of user dropouts is considered, where at most users can drop out and the identity of these users cannot be predicted in advance. We propose two schemes for is equal to (1) and , respectively. For is equal to (1), we introduce multiplicative encryption of the server's demand using a random variable, where users share coded keys offline and transmit masked models in the first round, followed by aggregated coded keys in the second round for task recovery. For , we use robust symmetric private computation to recover linear combinations of keys in the second round. The objective is to minimize the number of symbols sent by each user during the two rounds. Our proposed schemes have achieved the optimal rate region when is equal to (1) and the order optimal rate (within 2) when .
Paper Structure (19 sections, 6 theorems, 52 equations, 1 figure)

This paper contains 19 sections, 6 theorems, 52 equations, 1 figure.

Table of Contents

  1. Introduction
  2. System Model and Related Results
  3. System Model
  4. Related Results
  5. Main Results
  6. Achievable Scheme for Theorem \ref{['thm: first result']}
  7. Example: $({\sf K},{\sf U},{\sf K}_{\sf c})=(3,2,1)$
  8. General Scheme
  9. Achievable Scheme for Theorem \ref{['thm: second result']}
  10. Conclusion
  11. Proof of Theorem \ref{['converse of second result']}
  12. Proof of ${\sf R}_1\geq 1$
  13. Proof of ${\sf R}_2\geq \frac{{\sf K}_{\sf c}}{{\sf U}}$
  14. Proof of Security and Privacy in Section \ref{['sec: proof of first result']}
  15. Proof of Security
  16. ...and 4 more sections

Key Result

Theorem 1

For the information theoretic secure aggregation problem with ${\sf K}$ users and at least ${\sf U}$ non-dropped users, where $\sf 1\leq U\leq {K-1}$, the capacity region is

Figures (1)

  • Figure 1: Rate comparison between Theorem \ref{['baseline']} and Theorem \ref{['thm: second result']}

Theorems & Definitions (6)

  • Theorem 1: so2022lightsecagg
  • Theorem 2: zhu2022symmetric
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Theorem 6