High Precision Arithmetic for Cryptographic Applications

Cryptographic applications require a careful implementation to avoid side-channel attacks that reveal secret information to an attacker (e.g. via run-time measurements). In particular, for floating point arithmetic it is known that the timing of some basic arithmetic operations and functions on some CPUs depends on the input values [1], and thus the timing may leak secret information when the input contains secret values. Constant-time implementation tries to mitigate such run-time timing leakage on typical devices.

Recently, some newer cryptographic applications such as the Latte quantum-safe hierarchical identity-based encryption (HIBE) [2] require higher precision real number arithmetic than the double precision i.e. "double"-type variable in C. However, existing constant-time implementation techniques for real number arithmetic usually focused on the lower precision (typically within the double precision) and/or targetted one specific precision for the target cryptographic application [3,4]. Therefore, it requires extensive work to make high precision real number arithmetic constant-time and adapt the constant-time arithmetic to other cryptographic applications with different precision requirements.