In this paper, we present new variants of Newton–Raphson-based protocols for the secure computation of the reciprocal and the (reciprocal) square root. The protocols rely on secure fixed-point arithmetic with arbitrary precision parameterized by the total bit length of the fixed-point numbers and the bit length of the fractional part. We perform a rigorous error analysis aiming for tight accuracy claims while minimizing the overall cost of the protocols. Due to the nature of secure fixed-point arithmetic, we perform the analysis in terms of absolute errors. Whenever possible, we allow for stochastic (or probabilistic) rounding as an efficient alternative to deterministic rounding. We also present a new protocol for secure integer division b...
The reciprocal square root is an important computation for which many very sophisticated algorithms...
AbstractThe reciprocal square root calculation α=1/x is very common in scientific computations. Havi...
International audienceSince the introduction of the Fused Multiply and Add (FMA) in the IEEE-754-200...
Implementations of the reciprocal, square root and reciprocal square root often share a common struc...
The square root is an important mathematical primitive whose secure, efficient, distributed computat...
International audienceWe analyze two fast and accurate algorithms recently presented by Borges for c...
International audienceMany numerical problems require a higher computing precision than that offered...
International audienceMany numerical problems require a higher computing precision than the one offe...
This paper describes a study of a class of algorithms for the floating-point divide and square root ...
International audienceWe present the automatic formal verification of a state-of-the-art algorithm f...
Secure Multi-Party Computation (MPC) constructions typically allow computation over a finite field o...
Abstract. The square root is an important mathematical primitive whose secure, efficient, distribute...
Multiplicative Newton–Raphson and Goldschmidt algorithms are widely used in current processors to im...
The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting o...
Quotients, reciprocals, square roots and square root reciprocals all have the property that infinite...
The reciprocal square root is an important computation for which many very sophisticated algorithms...
AbstractThe reciprocal square root calculation α=1/x is very common in scientific computations. Havi...
International audienceSince the introduction of the Fused Multiply and Add (FMA) in the IEEE-754-200...
Implementations of the reciprocal, square root and reciprocal square root often share a common struc...
The square root is an important mathematical primitive whose secure, efficient, distributed computat...
International audienceWe analyze two fast and accurate algorithms recently presented by Borges for c...
International audienceMany numerical problems require a higher computing precision than that offered...
International audienceMany numerical problems require a higher computing precision than the one offe...
This paper describes a study of a class of algorithms for the floating-point divide and square root ...
International audienceWe present the automatic formal verification of a state-of-the-art algorithm f...
Secure Multi-Party Computation (MPC) constructions typically allow computation over a finite field o...
Abstract. The square root is an important mathematical primitive whose secure, efficient, distribute...
Multiplicative Newton–Raphson and Goldschmidt algorithms are widely used in current processors to im...
The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting o...
Quotients, reciprocals, square roots and square root reciprocals all have the property that infinite...
The reciprocal square root is an important computation for which many very sophisticated algorithms...
AbstractThe reciprocal square root calculation α=1/x is very common in scientific computations. Havi...
International audienceSince the introduction of the Fused Multiply and Add (FMA) in the IEEE-754-200...