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Explicit construction of q+1 regular local Ramanujan graphs, for all prime-powers q
A constant locality function is one in which each output bit depends on just a constant number of input bits. Viola and Wigderson (2018) gave an...
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AprèsSQI: Extra Fast Verification for SQIsign Using Extension-Field Signing
We optimise the verification of the SQIsign signature scheme. By using field extensions in the signing procedure, we are able to significantly...
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Faster characteristic three polynomial multiplication and its application to NTRU Prime decapsulation
Efficient computation of polynomial multiplication over characteristic three fields is required for post-quantum cryptographic applications which...
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An Alternative Approach for SIDH Arithmetic
In this paper, we present new algorithms for the field arithmetic layers of supersingular isogeny Diffie-Hellman; one of the fifteen remaining...
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E\({^2}\)CSM: efficient FPGA implementation of elliptic curve scalar multiplication over generic prime field GF(p)
Elliptic curve scalar multiplication (ECSM) is the primitive operation that is also the main computational hurdle in almost all protocols based on...
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Finite-Field Parallel Adder Circuit Over Prime Numbers Based on Spiking Neural P Systems
Nowadays, the arithmetic operations precision is one of the most critical aspects in the development of efficient finite-field arithmetic circuits,...
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Improved Polynomial Multiplication Algorithms over Characteristic Three Fields and Applications to NTRU Prime
This paper introduces a new polynomial multiplication algorithm which decreases the arithmetic complexity and another modified algorithm that speeds...
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Automated Verification of Correctness for Masked Arithmetic Programs
Masking is a widely-used effective countermeasure against power side-channel attacks for implementing cryptographic algorithms. Surprisingly, few...
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Lossless FFTs Using Posit Arithmetic
The Fast Fourier Transform (FFT) is required for chemistry, weather, defense, and signal processing for seismic exploration and radio astronomy. It...
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Efficient Extended GCD and Class Groups from Secure Integer Arithmetic
In this paper we first present an efficient protocol for the secure computation of the extended greatest common divisor, assuming basic secure...
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Divisibility, Congruences, and Modular Arithmetic
Modern cryptography is largely based on the mathematicals of modular arithmetic, congruences, and the arithmetic in the integers modulo prime numbers...
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New Approach for Sine and Cosine in Secure Fixed-Point Arithmetic
In this paper we present a new class of protocols for the secure computation of the sine and cosine functions. The precision for the underlying...
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PIE: p-adic Encoding for High-Precision Arithmetic in Homomorphic Encryption
A large part of current research in homomorphic encryption (HE) aims towards making HE practical for real-world applications. In any practical HE, an...
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Second order arithmetic
In the previous chapter, we discussed reducibility notions based on computability theory. Another method for comparing problems relies on...
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Novel Feynman-Based Reversible and Fault-Tolerant Nano-communication Arithmetic Architecture Based on QCA Technology
Quantum-dot cellular automata (QCA) has advantages such as low energy dissipation and high density as a suitable alternative to CMOS technology. The...
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Lower Bounds for Arithmetic Circuits via the Hankel Matrix
We study the complexity of representing polynomials by arithmetic circuits in both the commutative and the non-commutative settings. Our approach...
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MCSat-Based Finite Field Reasoning in the Yices2 SMT Solver (Short Paper)
This system description introduces an enhancement to the Yices2 SMT solver, enabling it to reason over non-linear polynomial systems over finite...
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Basic Arithmetic Foundations
In cryptography, the Integer Factorization Problem (IFP) has significant importance because many cryptosystems with public keys ground their security...
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Montgomery Arithmetic over Gaussian Integers
Up to now, we have demonstrated that Gaussian integers are suitable for RSA and ECC systems. Moreover, we have illustrated that performing complex...
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Field Instruction Multiple Data
Fully homomorphic encryption (FHE) has flourished since it was first constructed by Gentry (STOC 2009). Single instruction multiple data (SIMD) gave...