Secure addition of floating points

Secure multi-party computation (MPC) and homomorphic encryption are very powerful tools to compute with secret numbers without revealing inputs or any intermediate values. To securely achieve high accuracy with varying number sizes, one needs to work with floating points in the secret (secret-shared or encrypted) domain. The main bottleneck of secure floating points is addition. We improve its efficiency by designing a protocol for multiple additions, using standard building blocks available in most MPC platforms. The more additions n were combined, the larger the relative gain, up to a factor 13 with n = 1,024. Additionally, we introduce a new protocol for securely computing the bitlength (given upper bound M), the first one with linear time complexity and constant round complexity. It reduces secure multiplications with a factor 4 (for the constant-round solution), or the number of communication rounds with a factor M/2 (for the logarithmic-round solution). We evaluate accuracy, execution time and communication complexity of our protocols, and release them open source, such that they can be used to improve the efficiency of secure floating-point arithmetic.