Masking FALCON’s Floating-Point Multiplication in Hardware

Abstract

Floating-point arithmetic is a cornerstone in a wide array of computational domains, and it recently became a building block for the FALCON post-quantum digital signature algorithm. As a consequence, the side-channel security of these operations became under scrutiny. Recent works unveiled the first side-channel attack specifically targeting floating-point multiplication to steal secret cryptographic keys. Despite these new attacks on floating point arithmetic, there is no secure hardware design for side-channel leakage to date. A concurrent work has applied masking of floating-point multiplication in software [CC24], but their empirical validation still demonstrated significant first-order leakages. This paper presents the first hardware masking scheme for floating-point multiplication to mitigate side-channel attacks. Our technique extends the cryptographic masking principles that split all intermediate computations into multiple, random shares while preserving the output functionality. Our innovation also provides a design-time configurable first-order masked multiplier gadget that carries out integer multiplication, which can support future designs. To that end, we propose new hardware gadgets including Integer Multiplier, Carry Calculator, Secure MUX, Zero Check, and Mantissa Selection, and we prove their security in the PINI model. Moreover, we validate the desired firstorder side-channel security of our implementation on a Sakura-X FPGA board using 10 million measurements. We explore the design space with different architectural choices to trade-off performance for the area. Our implementation results show that masking overhead ranges between 5.42x-43.31x in the area and 2x-440x in throughput.

Keywords

• Masking
• Floating-point
• Side-channel Analysis
• FALCON