SummaryFog computing is a suitable platform for the Internet of Things (IoT). However, it faces threats that pose security and privacy challenges. This article proposes two new, faster, and more secure schemes based on attribute‐based encryption (ABE) address some security concerns. The new schemes are Cipher text‐policy‐ABE‐anonymous authentication (CP‐ABE‐AA) and key‐policy‐ABE‐anonymous authentication (KP‐ABE‐AA), providing more secure communications and anonymous recognition between servers and users employing registration center (RC). Users and servers register with RC and receive time parameter t and aliases to build an access tree. During the valid time, t a more secure transfer is established. After each t has expired, the servers and users obtain new aliases. RC provides anonymous authentication, and t determines the key's validity period. For simulation, a multi‐paradigm programming language, Rust, was installed on Ubuntu 20. Compared to five existing schemes, the simulation results indicated that, on average, CP‐ABE‐AA has a 5.48% reduction time for key generation but an increased time of 11.28% in encryption and a reduction time of 11.33% in decryption. Also, compared to two other schemes, KP‐ABE‐AA produced an average time increase of 17.31% for key generation, but encryption and decryption times were reduced by 17.31% and 9.57%.