{"title":"On the Information Theoretic Secure Aggregation With Uncoded Groupwise Keys","authors":"Kai Wan;Xin Yao;Hua Sun;Mingyue Ji;Giuseppe Caire","doi":"10.1109/TIT.2024.3422087","DOIUrl":null,"url":null,"abstract":"Secure aggregation, which is a core component of federated learning, aggregates locally trained models from distributed users at a central server. The “secure” nature of such aggregation consists of the fact that no information about the local users’ data must be leaked to the server except the aggregated local models. In order to guarantee security, some keys may be shared among the users (this is referred to as the key sharing phase). After the key sharing phase, each user masks its trained model which is then sent to the server (this is referred to as the model aggregation phase). This paper follows the information theoretic secure aggregation problem originally formulated by Zhao and Sun, with the objective to characterize the minimum communication cost from the \n<inline-formula> <tex-math>$\\mathsf K$ </tex-math></inline-formula>\n users in the model aggregation phase. Due to user dropouts, which are common in real systems, the server may not receive all messages from the users. A secure aggregation scheme should tolerate the dropouts of at most \n<inline-formula> <tex-math>${\\mathsf K}-{\\mathsf U}$ </tex-math></inline-formula>\n users, where \n<inline-formula> <tex-math>$\\mathsf U$ </tex-math></inline-formula>\n is a system parameter. The optimal communication cost is characterized by Zhao and Sun, but with the assumption that the keys stored by the users could be any random variables with arbitrary dependency. On the motivation that uncoded groupwise keys are more convenient to be shared and could be used in large range of applications besides federated learning, in this paper we add one constraint into the above problem, namely, that the key variables are mutually independent and each key is shared by a group of \n<inline-formula> <tex-math>$\\mathsf S$ </tex-math></inline-formula>\n users, where \n<inline-formula> <tex-math>$\\mathsf S$ </tex-math></inline-formula>\n is another system parameter. To the best of our knowledge, all existing secure aggregation schemes (with information theoretic security or computational security) assign coded keys to the users. We show that if \n<inline-formula> <tex-math>${\\mathsf S}\\gt {\\mathsf K}-{\\mathsf U}$ </tex-math></inline-formula>\n, a new secure aggregation scheme with uncoded groupwise keys can achieve the same optimal communication cost as the best scheme with coded keys; if \n<inline-formula> <tex-math>${\\mathsf S}\\leq {\\mathsf K}-{\\mathsf U}$ </tex-math></inline-formula>\n, uncoded groupwise key sharing is strictly sub-optimal. Finally, we also implement our proposed secure aggregation scheme into Amazon EC2, which are then compared with the existing secure aggregation schemes with offline key sharing.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 9","pages":"6596-6619"},"PeriodicalIF":2.2000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Information Theory","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10580953/","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
Secure aggregation, which is a core component of federated learning, aggregates locally trained models from distributed users at a central server. The “secure” nature of such aggregation consists of the fact that no information about the local users’ data must be leaked to the server except the aggregated local models. In order to guarantee security, some keys may be shared among the users (this is referred to as the key sharing phase). After the key sharing phase, each user masks its trained model which is then sent to the server (this is referred to as the model aggregation phase). This paper follows the information theoretic secure aggregation problem originally formulated by Zhao and Sun, with the objective to characterize the minimum communication cost from the
$\mathsf K$
users in the model aggregation phase. Due to user dropouts, which are common in real systems, the server may not receive all messages from the users. A secure aggregation scheme should tolerate the dropouts of at most
${\mathsf K}-{\mathsf U}$
users, where
$\mathsf U$
is a system parameter. The optimal communication cost is characterized by Zhao and Sun, but with the assumption that the keys stored by the users could be any random variables with arbitrary dependency. On the motivation that uncoded groupwise keys are more convenient to be shared and could be used in large range of applications besides federated learning, in this paper we add one constraint into the above problem, namely, that the key variables are mutually independent and each key is shared by a group of
$\mathsf S$
users, where
$\mathsf S$
is another system parameter. To the best of our knowledge, all existing secure aggregation schemes (with information theoretic security or computational security) assign coded keys to the users. We show that if
${\mathsf S}\gt {\mathsf K}-{\mathsf U}$
, a new secure aggregation scheme with uncoded groupwise keys can achieve the same optimal communication cost as the best scheme with coded keys; if
${\mathsf S}\leq {\mathsf K}-{\mathsf U}$
, uncoded groupwise key sharing is strictly sub-optimal. Finally, we also implement our proposed secure aggregation scheme into Amazon EC2, which are then compared with the existing secure aggregation schemes with offline key sharing.
期刊介绍:
The IEEE Transactions on Information Theory is a journal that publishes theoretical and experimental papers concerned with the transmission, processing, and utilization of information. The boundaries of acceptable subject matter are intentionally not sharply delimited. Rather, it is hoped that as the focus of research activity changes, a flexible policy will permit this Transactions to follow suit. Current appropriate topics are best reflected by recent Tables of Contents; they are summarized in the titles of editorial areas that appear on the inside front cover.