Hybrid Model of Fixed and Floating Point Numbers in Secure Multiparty Computations

Abstract

This paper develops a new hybrid model of floating point numbers suitable for operations in secure multi-party computations. The basic idea is to consider the significand of the floating point number as a fixed point number and implement elementary function applications separately of the significand. This gives the greatest performance gain for the power functions (e.g. inverse and square root), with computation speeds improving up to 18 times in certain configurations. Also other functions (like exponent and Gaussian error function) allow for the corresponding optimisation.We have proposed new polynomials for approximation, and implemented and benchmarked all our algorithms on the Sharemind secure multi-party computation framework.

Preprocessing Based Verification of Multiparty Protocols with Honest Majority

“…We have implemented the verification of computations for the Sharemind protocol set [9,37,39,44]. This set covers integer, fix-and floating point operations, as well as shuffling the arrays.…”

Privacy-Preserving Outsourced Calculation on Floating Point Numbers

“…For example, once a datum needs to be updated, the data owner needs to randomly separated the datum into n shares, encrypts the shares with the corresponding server's public key/session key, and distributes them to the different servers, respectively. Moreover, the data splitting methods in [10], [11] will increase the storage overhead with the number of the servers, while the ciphertext storage overhead will not be affected in [12], [13], [14]. Furthermore, each secret (symmetry) key is preshared between two servers (n(n − 1)/2 are needed) in order to achieve secure communication, which increases the key management cost.…”

“…In the multiple parties storage strategy, n servers (In [12], [13], [14], three servers are needed) are used to storage data, i.e., each datum is randomly separated into n shares using the secret sharing technique, and the each share is distributed to a server for storage, respectively. However, it brings huge computational cost and communication overhead to the data owner for storing and managing the data, especially for updating and synchronizing the data.…”

“…Here, we compare our POCF with the exiting secure computation on floating point numbers scheme, which can be categorized under two strategies: multiple parties storage strategy [10], [11], [12], [13], [14] and outsourcing storage strategy [15]. In the multiple parties storage strategy, n servers (In [12], [13], [14], three servers are needed) are used to storage data, i.e., each datum is randomly separated into n shares using the secret sharing technique, and the each share is distributed to a server for storage, respectively.…”

“…Different from the exiting secure FPN calculation frameworks [10], [11], [12], [13], [14], [15], we regard the challenge issues of our POCF to be five-fold, namely:…”