Due to its provable security and remarkable device-independence,masking has been widely accepted as a noteworthy algorithmic-level countermeasure against side-channel attacks.However,relatively high cost of masking severely limits its applicability.Considering the high tackling complexity of non-linear operations,most masked AES implementations focus on the security and cost reduction of masked S-boxes.In this paper,we focus on linear operations,which seems to be underestimated,on the contrary.Specifically,we discover some security flaws and redundant processes in popular first-order masked AES linear operations,and pinpoint the underlying root causes.Then we propose a provably secure and highly efficient masking scheme for AES linear operations.In order to show its practical implications,we replace the linear operations of state-of-the-art first-order AES masking schemes with our proposal,while keeping their original non-linear operations unchanged.We implement four newly combined masking schemes on an Intel Core i7-4790 CPU,and the results show they are roughly 20％faster than those original ones.Then we select one masked implementation named RSMv2 due to its popularity,and investigate its security and efficiency on an AVR ATMega1 63 processor and four different FPGA devices.The results show that no exploitable first-order side-channel leakages are detected.Moreover,compared with original masked AES implementations,our combined approach is nearly 25％faster on the AVR processor,and at least 70％more efficient on four FPGA devices.