
Automatic Generation of Vectorized Montgomery Algorithm
Modular arithmetic is widely used in crytography and symbolic computatio...
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Why and How to Avoid the Flipped Quaternion Multiplication
Over the last decades quaternions have become a crucial and very success...
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A Multilayer Recursive Residue Number System
We present a method to increase the dynamical range of a Residue Number ...
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On the Decidability of the Ordered Structures of Numbers
The ordered structures of natural, integer, rational and real numbers ar...
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Separation of bounded arithmetic using a consistency statement
This paper proves Buss's hierarchy of bounded arithmetics S^1_2 ⊆ S^2_2 ...
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Computational Flows in Arithmetic
A computational flow is a pair consisting of a sequence of computational...
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Secure Montgomery Multiplication and Repeated Squares for Modular Exponentiation
The BMR16 circuit garbling scheme introduces gadgets that allow for ciph...
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Iterated multiplication in VTC^0
We show that VTC^0, the basic theory of bounded arithmetic corresponding to the complexity class TC^0, proves the IMUL axiom expressing the totality of iterated multiplication satisfying its recursive definition, by formalizing a suitable version of the TC^0 iterated multiplication algorithm by Hesse, Allender, and Barrington. As a consequence, VTC^0 can also prove the integer division axiom, and (by results of Jeřábek) the RSUVtranslation of induction and minimization for sharply bounded formulas. Similar consequences hold for the related theories Δ^b_1CR and C^0_2. As a side result, we also prove that there is a wellbehaved Δ_0 definition of modular powering in IΔ_0+WPHP(Δ_0).
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