International Association
for Cryptologic Research

Fully homomorphic encryption provides a way to perform computations in a privacy preserving manner. However, despite years of optimization, modern methods may still be too computationally expensive for devices limited by speed or memory constraints. A paradigm that may bridge this gap consists of transciphering: as fully homomorphic schemes can perform most computations obliviously, they can also execute the decryption circuit of any conventional block or stream cipher. Hence, less powerful systems may continue to encrypt their data using classical ciphers that may offer hardware support (e.g., AES) and outsourcing the task of transforming the ciphertexts into their homomorphic equivalent to more powerful systems. In this work, we advance transciphering methods that leverage accumulator-based schemes such as Torus-FHE (TFHE) or FHEW. To this end, we propose a novel method to homomorphically evaluate look-up tables in a setting in which encrypted digits are provided on base 2. At a high level, our method relies on the fact that functions with binary range, i.e., mapping values to {0, 1}, can be evaluated at the same computational cost as negacyclic functions, relying only on the default functionality of accumulator based schemes. To test our algorithm, we implement the AES-128 encryption circuit in OPENFHE and report timings of 67 s for a single block, which is 25% faster than the state of the art and in general, up to 300% faster than other recent works. Furthermore, we achieve this speedup without relying on an instantiation that leverages a power of 2 modulus and can exploit the natural modulo arithmetic of modern processors.

Relay attacks pose a serious security threat to wireless systems, such as, contactless payment systems, keyless entry systems, or smart access control systems. Distance bounding protocols, which allow an entity to not only authenticate another entity but also determine whether it is physically close by, effectively mitigate relay attacks. However, secure implementation of distance bounding protocols, especially of the time critical challenge-response phase, has been a challenging task. In this paper, we design and implement a secure and accurate distance bounding protocol based on Narrow-Band signals, such as Bluetooth Low Energy (BLE), to particularly mitigate relay attacks. Narrow-Band ranging, specifically, phase-based ranging, enables accurate distance measurement, but it is vulnerable to phase rollover attacks. In our solution, we mitigate phase rollover attacks by also measuring time-of-flight (ToF) to detect the delay introduced by such attacks. Therefore, our protocol effectively combines the best of both worlds: phase-based ranging for accuracy and time-of-flight (ToF) measurement for security. To demonstrate the feasibility and practicality of our solution, we prototype it on NXP KW36 BLE chips and evaluate its performance and relay attack resistance. The obtained precision and accuracy of the presented ranging solution are 2.5 cm and 30 cm, respectively, in wireless measurements.