Through the Looking-Glass: Benchmarking Secure Multi-party Computation Comparisons for ReLU ’s

Aly, Abdelrahaman; Nawaz, Kashif; Salazar, Eugenio; Sucasas, Victor

doi:10.1007/978-3-031-20974-1_3

Cited by 2 publications

(7 citation statements)

References 20 publications

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“…We present our protocols for the secure computation of the reciprocal and the (reciprocal) square root in terms of an arithmetic black box (following, e.g., [9][10][11]). The protocols are specified in pseudocode, using a limited set of operations commonly supported in many MPC frameworks.…”

Section: Secure Computationmentioning

confidence: 99%

“…. , 2 f − 3} and odd f , employing initial approximation (9), and the number of iterations θ is computed with (12), then | θ,n | ≤ δ f +n . In particular, θ,n ∈ {−δ f +n , 0, δ f +n }.…”

Section: Conflicts Of Interestmentioning

confidence: 99%

“…If the Newton-Raphson method is used to compute 1/√b for some b ∈ [0.5, 2), employing initial approximation(9) and with the number of iterations θ computed via(12), then | θ | < σδ f , where σ = 2.71.…”

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confidence: 99%

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Divisions and Square Roots with Tight Error Analysis from Newton–Raphson Iteration in Secure Fixed-Point Arithmetic

Korzilius,

Schoenmakers

2023

Cryptography

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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 based on our protocol for secure fixed-point reciprocals. The resulting protocol is parameterized by the bit length of the inputs and yields exact results for the integral quotient and remainder. The protocol is very efficient, minimizing the number of secure comparisons. Similarly, we present a new protocol for integer square roots based on our protocol for secure fixed-point square roots. The quadratic convergence of the Newton–Raphson method implies a logarithmic number of iterations as a function of the required precision (independent of the input value). The standard error analysis of the Newton–Raphson method focuses on the termination condition for attaining the required precision, assuming sufficiently precise floating-point arithmetic. We perform an intricate error analysis assuming fixed-point arithmetic of minimal precision throughout and minimizing the number of iterations in the worst case.

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Section: Secure Computationmentioning

confidence: 99%

Section: Conflicts Of Interestmentioning

confidence: 99%

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Divisions and Square Roots with Tight Error Analysis from Newton–Raphson Iteration in Secure Fixed-Point Arithmetic

Korzilius,

Schoenmakers

2023

Cryptography

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“…The DL is a queue, represented as [) with back [ and front ) that contains cells' numbers along a multiplication path, i.e., the set of cells that must be multiplied together. In Figure 8, we have the following multiplication paths: (1,4,7,10), (1,4,8,9), (1,5,6), (2,3). For each path, we start with a Algorithm 8 Efficient implementation if 𝛽 = 0 then {AHE Section 6.4} 10: return permute(c) 33: end if list of nodes.…”

Section: Optimized Implementationmentioning

confidence: 99%

“…• Computation of the paths. Using the Illustration in Figure 8, we use a table representation of the tree as explained above and compute the paths: (1, 4, 7, 10), (1,4,8,9), (1,5,6), (2,3). This computation is illustrated in Algorithm 9.…”

Section: B Algorithms For Fhe Instantiationmentioning

confidence: 99%

A Method for Securely Comparing Integers using Binary Trees

Tueno,

Janneck,

Boehm

2023

PoPETs

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In this paper, we propose a new protocol for secure integer comparison which consists of parties having each a private integer. The goal of the computation is to compare both integers securely and reveal to the parties a single bit that tells which integer is larger. Nothing more should be revealed. To achieve a low communication overhead, this can be done by using homomorphic encryption (HE). Our protocol relies on binary decision trees that is a special case of branching programs and can be implemented using HE. We assume a client-server setting where each party holds one of the integers, the client also holds the private key of a homomorphic encryption scheme and the evaluation is done by the server. In this setting, our protocol outperforms the original DGK protocol of Damgård et al. and reduces the running time by at least 45%. In the case where both inputs are encrypted, our scheme reduces the running time of a variant of DGK by 63%.

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Through the Looking-Glass: Benchmarking Secure Multi-party Computation Comparisons for ReLU ’s

Cited by 2 publications

References 20 publications

Divisions and Square Roots with Tight Error Analysis from Newton–Raphson Iteration in Secure Fixed-Point Arithmetic

Divisions and Square Roots with Tight Error Analysis from Newton–Raphson Iteration in Secure Fixed-Point Arithmetic

A Method for Securely Comparing Integers using Binary Trees

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