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Modular Arithmetic
This chapter Modular arithmeticintroduces modular arithmetic and its notation. It also shows how modular arithmetic is used in practice with worked...
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Symbolic Transformation of Expressions in Modular Arithmetic
We present symbolic methods to improve the precision of static analyses of modular integer expressions based on Abstract Interpretation. Like similar...
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Polynomial Analysis of Modular Arithmetic
The modular polynomial abstract domain, MPAD, is proposed, whose invariants are systems of polynomial equations that hold modulo a power of 2. Its...
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A new multimedia cryptosystem using chaos, quaternion theory and modular arithmetic
Based on the combination of quaternion numbers, residual matrices, and chaotic attractors, a new cryptosystem is proposed for multimedia processing...
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Rinocchio: SNARKs for Ring Arithmetic
Succinct non-interactive arguments of knowledge (SNARKs) enable non-interactive efficient verification of NP computations and admit short proofs....
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Efficient Arithmetic in Garbled Circuits
Garbled Circuit (GC) techniques usually work with Boolean circuits. Despite intense interest, efficient arithmetic generalizations of GC were only...
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Montgomery curve arithmetic revisited
A one-third century ago, as a means to speed up the elliptic curve method (ECM) for integer factoring, Montgomery suggested using a special elliptic...
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Big Number and Polynomial Arithmetic
This chapter deals with two related topics that belong to the general area of “computer algebra”: the computation with integer numbers of arbitrary...
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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 Ways to Garble Arithmetic Circuits
The beautiful work of Applebaum, Ishai, and Kushilevitz [FOCS’11] initiated the study of arithmetic variants of Yao’s garbled circuits. An arithmetic...
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Hammering Floating-Point Arithmetic
Sledgehammer, a component of the interactive proof assistant Isabelle/HOL, aims to increase proof automation by automatically discharging proof goals...
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Parameterized Algorithms for Covering by Arithmetic Progressions
An arithmetic progression is a sequence of integers in which the difference between any two consecutive elements is the same. We investigate the...
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Energy efficient triple-modular exponential techniques for batch verification schemes
Most of the authentication protocols have modular multi-exponentiation (MME) as their core operation in the verification step. Triple modular-multi...
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Modular Arithmetic
This chapter introduces modular arithmeticModular arithmetic and its notation. It also shows how modular arithmetic is used in practice with worked...
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Modular Polynomial Multiplication Using RSA/ECC Coprocessor
Modular polynomial multiplication is a core and costly operation of ideal lattice-based schemes. In the context of embedded devices, previous works...
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Finite Field Arithmetic in Large Characteristic for Classical and Post-quantum Cryptography
Both classical and post-quantum cryptography massively use large characteristic finite fields or rings. Consequently, basic arithmetic on these...
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On the Usefulness of Linear Modular Arithmetic in Constraint Programming
Linear modular constraints are a powerful class of constraints that arise naturally in cryptanalysis, checksums, hash functions, and the like. Given...
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How to Garble Mixed Circuits that Combine Boolean and Arithmetic Computations
The study of garbling arithmetic circuits is initiated by Applebaum, Ishai, and Kushilevitz [FOCS’11], which can be naturally extended to mixed...
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Formal Verification of Arithmetic Masking in Hardware and Software
Masking is a popular countermeasure to protect cryptographic implementations against physical attacks like differential power analysis. So far,...