Efficient Masking of ARX-Based Block Ciphers Using Carry-Save Addition on Boolean Shares

Masking is a widely-used technique to protect block ciphers and other symmetric cryptosystems against Differential Power Analysis (DPA) attacks. Applying masking to a cipher that involves both arithmetic and Boolean operations requires a conversion between arithmetic and Boolean masks. An alternative approach is to perform the required arithmetic operations (e.g. modular addition or subtraction) directly on Boolean shares. At FSE 2015, Coron et al. proposed a logarithmic-time algorithm for modular addition on Boolean shares based on the Kogge-Stone carry-lookahead adder. We revisit their addition algorithm in this paper and present a fast implementation for ARM processors. Then, we introduce a new technique for direct modular addition/subtraction on Boolean shares using a simple Carry-Save Adder (CSA) in an iterative fashion. We show that the average complexity of CSA-based addition on Boolean shares grows logarithmically with the operand size, similar to the Kogge-Stone carry-lookahead addition, but consists of only a single AND, an XOR, and a left-shift per iteration. A 32-bit CSA addition~on Boolean shares has an average execution time of 162 clock cycles on an ARM Cortex-M3 processor, which is approximately 43% faster than the Kogge-Stone adder. The performance gain increases to over 55% when comparing the average subtraction times. We integrated both addition techniques into a masked implementation of the block cipher Speck and found that the CSA-based variant clearly outperforms its Kogge-Stone counterpart by a factor of 1.70 for encryption and 2.30 for decryption.