The TinyTable Protocol for 2-Party Secure Computation, or: Gate-Scrambling Revisited

Damgård, Ivan; Nielsen, Jesper Buus; Nielsen, Mogens Gissel; Ranellucci, Samuel

doi:10.1007/978-3-319-63688-7_6

Cited by 42 publications

(45 citation statements)

References 11 publications

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“…Note that d(C ⊥ ) ≥ min{2 · 2 m 2 +1 , 2 m 1 +1 }. From (10) we conclude that Additionally, when computed these, we can bound the minimum distance directly from (11). This is what we do in Table 1 for the following choices.…”

Section: Constructions From Binary Cyclic Codessupporting

confidence: 58%

Squares of matrix-product codes

Cascudo

Gundersen²,

Ruano

2020

Finite Fields and Their Applications

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The component-wise or Schur product C * C ′ of two linear error-correcting codes C and C ′ over certain finite field is the linear code spanned by all component-wise products of a codeword in C with a codeword in C ′ . When C = C ′ , we call the product the square of C and denote it C * 2 . Motivated by several applications of squares of linear codes in the area of cryptography, in this paper we study squares of so-called matrixproduct codes, a general construction that allows to obtain new longer codes from several "constituent" codes. We show that in many cases we can relate the square of a matrix-product code to the squares and products of their constituent codes, which allow us to give bounds or even determine its minimum distance. We consider the well-known (u, u+v)-construction, or Plotkin sum (which is a special case of a matrix-product code) and determine which parameters we can obtain when the constituent codes are certain cyclic codes. In addition, we use the same techniques to study the squares of other matrix-product codes, for example when the defining matrix is Vandermonde (where the minimum distance is in a certain sense maximal with respect to matrix-product codes).

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Section: Constructions From Binary Cyclic Codessupporting

confidence: 58%

Squares of matrix-product codes

Cascudo

Gundersen²,

Ruano

2020

Finite Fields and Their Applications

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“…Second, some of the currently best alternatives (in terms of communication complexity) for secure multiparty computation protocols for Boolean circuits were given in [14] (known as Min-iMac) and its successor [13] (which uses MiniMac as part of the construction). In MiniMac, a linear binary code C is used, its role basically being to ensure that the parties behave honestly and do not change their private information in the middle of the computation.…”

Section: Applicationsmentioning

confidence: 99%

On Squares of Cyclic Codes

Cascudo

2019

IEEE Trans. Inform. Theory

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The square C * 2 of a linear error correcting code C is the linear code spanned by the component-wise products of every pair of (non-necessarily distinct) words in C. Squares of codes have gained attention for several applications mainly in the area of cryptography, and typically in those applications one is concerned about some of the parameters (dimension, minimum distance) of both C * 2 and C. In this paper, motivated mostly by the study of this problem in the case of linear codes defined over the binary field, squares of cyclic codes are considered. General results on the minimum distance of the squares of cyclic codes are obtained and constructions of cyclic codes C with relatively large dimension of C and minimum distance of the square C * 2 are discussed. In some cases, the constructions lead to codes C such that both C and C * 2 simultaneously have the largest possible minimum distances for their length and dimensions. * Ignacio Cascudo is with the

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“…We implemented the algorithms under study 6 to demonstrate their behavior in practice and compared them to the state of the art implementations of other solutions. In the following SPDZ 2 k refers to a run of a textbook matrix multiplication algorithm performed with the general purpose library SPDZ 2 k [4] 7 , YTP-SS refers to n 2 applications of [11,Algorithm 15]; MP-PDP refers the relaxation and improvement of this algorithm to the current setting; MP-SW refers to our implementation of Protocol 7 using Protocol 5 as a basecase with threshold set to n = 56.…”

Section: Methodsmentioning

confidence: 99%

“…For instance, for a product of dimension 12, with base case dimension b = 3, this gives; L A = L B = L C = (1,2,0,4,5,3,7,8,6,11,9,10) and K A = K B = K C = (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11).…”

Section: Data Layout and Encryptionmentioning

confidence: 99%

“…Then, several MPC implementations are available 4 . Some of them are for two parties only and most of the others are generic and transform programs into circuits or use oblivious transfer [7,26,6,16,23]. For instance the symmetric system solving phase of the Linreg-MPC software is reported in [12] to take about 45 minutes for n = 200, while, in [11], a secure multiparty specific algorithm, YTP-SS, was developed for matrix multiplication requires about a hundred seconds to perform an n = 200 matrix multiplication.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Secure Multiparty Matrix Multiplication Based on Strassen-Winograd Algorithm

Dumas

Lafourcade

Fenner

et al. 2019

Advances in Information and Computer Security

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This paper presents a secure multiparty computation protocol for the Strassen-Winograd matrix multiplication algorithm. We focus on the setting in which any given player knows only one row (or one block of rows) of both input matrices and learns the corresponding row (or block of rows) of the resulting product matrix. Neither the player initial data, nor the intermediate values, even during the recurrence part of the algorithm, are ever revealed to other players. We use a combination of partial homomorphic encryption schemes and additive masking techniques together with a novel schedule for the location and encryption layout of all intermediate computations to preserve privacy. Compared to state of the art protocols, the asymptotic communication volume of our construction is reduced from O(n 3) to O(n 2.81). This improvement in terms of communication volume arises with matrices of dimension as small as n = 96 which is confirmed by experiments.

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The TinyTable Protocol for 2-Party Secure Computation, or: Gate-Scrambling Revisited

Cited by 42 publications

References 11 publications

Squares of matrix-product codes

Squares of matrix-product codes

On Squares of Cyclic Codes

Secure Multiparty Matrix Multiplication Based on Strassen-Winograd Algorithm

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