Provably Secure and Area-Efficient Modular Addition over Boolean Shares

Abstract

Several cryptographic schemes, including lattice-based cryptography and the SHA-2 family of hash functions, involve both integer arithmetic and Boolean logic. Each of these classes of operations, considered separately, can be efficiently implemented under the masking countermeasure when resistance against vertical attacks is required. However, protecting interleaved arithmetic and logic operations is much more expensive, requiring either additional masking conversions to switch between masking schemes, or implementing arithmetic functions as nonlinear operations over a Boolean masking. Both solutions can be achieved by providing masked arithmetic addition over Boolean shares, which is an operation with relatively long latency and usually high area utilization in hardware. A further complication arises when the arithmetic performed by the scheme is over a prime modulus, which is common in lattice-based cryptography. In this work, we propose a first-order masked implementation of arithmetic addition over Boolean shares occupying a very small area, while still having reasonable latency. Our proposal is specifically tuned for efficient addition and subtraction modulo an arbitrary integer, but it can also be configured at runtime for power-of-two arithmetic. To the best of our knowledge, we propose the first such construction whose security is formally proven in the glitch+transition-robust probing model.