Formal Verification of Square Root Algorithms

Formal Verification of Divide and Square Root Algorithms using Series Calculation

Batch Verification of EdDSA Signatures

In AfricaCrypt 2012 and ACNS 2014, several algorithms are proposed for the batch verification of ECDSA signatures. In this paper, we make a comparative study of these methods for the Edwards curve digital signature algorithm (EdDSA). We describe the adaptation of Algorithms N, N′, S2′ and SP for EdDSA signatures. The randomization methods are also explained in detail. More precisely, we study s...

Mechanical Verification of a Square Root Algorithm Using Taylor's Theorem

The IBM Power4 processor uses series approximation to calculate square root. We formally verified the correctness of this algorithm using the ACL2(r) theorem prover. The proof requires the analysis of the approximation error on a Chebyshev series. This is done by proving Taylor’s theorem, and then analyzing the Chebyshev series using Taylor series. Taylor’s theorem is proved by way of non-stand...

Towards platform-independent verification of the standard mathematical functions: the square root function

The paper presents (human-oriented) specification and (penand-paper) verification of the square root function. The function implements Newton method and uses a look-up table for initial approximations. Specification is done in terms of total correctness assertions with use of precise arithmetic and the mathematical square root √ . . ., algorithms are presented in pseudo-code with explicit disti...

Floating Point Division and Square Root Algorithms and Implementation in the AMD-K7 Microprocessor

This paper presents the AMD-K7 IEEE 754 and x87 compliant floating point division and square root algorithms and implementation. The AMD-K7 processor employs an iterative implementation of a series expansion to converge quadratically to the quotient and square root. Highly accurate initial approximations and a high performance shared floating point multiplier assist in achieving low division an...