An OBDD-Based Technique for the Efficient Synthesis of Garbled Circuits

Cimato, Stelvio; Ciriani, Valentina; Damiani, Ernesto; Ehsanpour, Maryam

doi:10.1007/978-3-030-31511-5_10

Cited by 6 publications

(5 citation statements)

References 10 publications

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“…On one hand, several proposed emerging technologies exploit XOR gates [13], [27], [35], [38]. On the other hand, the growing relevance of cryptography-related applications has revived the interest in XOR gates [22], [26], [27], [33], [36], [37], [38]. For example, in high-level cryptography protocols such as secure multiparty computation, processing XOR gates is convenient since their evaluation is possible without any communication cost [28].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we are interested in this second type of XAG applications, where the minimization cost depends only on the number of AND nodes. Therefore, our main aim is the minimization of the number of AND gates in an XAG [22], [36], [37], [38]. The number of AND nodes in an XAG implementation of a function is called the multiplicative complexity of the XAG, while the minimum number of ANDs that are sufficient to represent a function with an XAG defines the multiplicative complexity of the function.…”

Section: Introductionmentioning

confidence: 99%

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Multiplicative Complexity of XOR Based Regular Functions

Bernasconi

Cimato

Ciriani

et al. 2022

IEEE Trans. Comput.

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XOR-AND Graphs (XAGs) are an enrichment of the classical AND-Inverter Graphs (AIGs) with XOR nodes. In particular, XAGs are networks composed by ANDs, XORs, and inverters. Besides several emerging technologies applications, XAGs are often exploited in cryptography-related applications based on the multiplicative complexity of a Boolean function. The multiplicative complexity of a function is the minimum number of AND gates (i.e., multiplications) that are sufficient to represent the function over the basis {AND, XOR, NOT}. In fact, the minimization of the number of AND gates is important for high-level cryptography protocols such as secure multiparty computation, where processing AND gates is more expensive than processing XOR gates. Moreover, it is an indicator of the degree of vulnerability of the circuit, as a small number of AND gates corresponds to a high vulnerability to algebraic attacks. In this paper we study the multiplicative complexity of Boolean functions characterized by two particular regularities, called autosymmetry and D-reducibility. Moreover, we exploit these regularities for decreasing the number of AND nodes in XAGs. The experimental results validate the proposed approaches.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multiplicative Complexity of XOR Based Regular Functions

Bernasconi

Cimato

Ciriani

et al. 2022

IEEE Trans. Comput.

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“…In standard CMOS technology XOR gates are expensive and often considered impractical [28]; they are used only when their presence in a network implementation of a Boolean function guarantees a considerable reduction of some design parameters, usually the area of the network (see [4], [13], [14], [15], [22]). Recently, however, the growing relevance of cryptography-related applications and emerging technologies has revived the interest in XOR gates [12], [18], [19], [25], [26]. For instance, in high-level cryptography protocols such as secure multiparty computation, processing XOR gates is particularly convenient since their evaluation is possible without any interaction between the parties, and then has no communication cost [21] (more details are given in Section II-A).…”

Section: Introductionmentioning

confidence: 99%

Multiplicative Complexity of Autosymmetric Functions: Theory and Applications to Security

Bernasconi

Cimato

Ciriani

et al. 2020

2020 57th ACM/IEEE Design Automation Conference (DAC)

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The multiplicative complexity of a Boolean function is the minimum number of AND gates (i.e., multiplications) that are sufficient to represent the function over the basis {AND, XOR, NOT}. The multiplicative complexity measure plays a crucial role in cryptography-related applications. In fact, the minimization of the number of AND gates is important for high-level cryptography protocols such as secure multiparty computation, where processing AND gates is more expensive than processing XOR gates. Moreover, it is an indicator of the degree of vulnerability of the circuit, as a small number of AND gates corresponds to a high vulnerability to algebraic attacks. In this paper we study a particular structure regularity of Boolean functions, called autosymmetry, and exploit it to decrease the number of ANDs in XOR-AND Graphs (XAGs), i.e., Boolean networks composed by ANDs, XORs, and inverters. The interest in autosymmetric functions is motivated by the fact that a considerable amount of standard Boolean functions of practical interest presents this regularity; indeed, about 24% of the functions in the classical ESPRESSO benchmark suite have at least one autosymmetric output. The experimental results validate the proposed approach.

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“…Thus, many heuristics have been proposed that reduce the MC of an XAG (see, e.g., [7,14,43,55,56]), aiming to arrive at tighter upper bounds on the MC of the function being implemented. Similarly, some heuristics have been proposed that aim to reduce the multiplicative depth [5,11].…”

Section: Introductionmentioning

confidence: 99%

Lowering the T-depth of Quantum Circuits By Reducing the Multiplicative Depth Of Logic Networks

Häner¹,

Soeken²

2020

Preprint

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The multiplicative depth of a logic network over the gate basis {∧, ⊕, ¬} is the largest number of ∧ gates on any path from a primary input to a primary output in the network. We describe a dynamic programming based logic synthesis algorithm to reduce the multiplicative depth in logic networks. It makes use of cut enumeration, tree balancing, and exclusive sum-of-products (ESOP) representations. Our algorithm has applications to cryptography and quantum computing, as a reduction in the multiplicative depth directly translates to a lower T -depth of the corresponding quantum circuit. Our experimental results show improvements in T -depth over state-of-the-art methods and over several hand-optimized quantum circuits for instances of AES, SHA, and floating-point arithmetic.

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An OBDD-Based Technique for the Efficient Synthesis of Garbled Circuits

Cited by 6 publications

References 10 publications

Multiplicative Complexity of XOR Based Regular Functions

Multiplicative Complexity of XOR Based Regular Functions

Multiplicative Complexity of Autosymmetric Functions: Theory and Applications to Security

Lowering the T-depth of Quantum Circuits By Reducing the Multiplicative Depth Of Logic Networks

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