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More on Squaring and Multiplying Large Integers
IEEE Transactions on Computers
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TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
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TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
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IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
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Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
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We present a formal proof (at the implementation level) of an efficient algorithm proposed by P. Zimmermann in 1999 to compute square roots of arbitrarily large integers. This program, which is part of the GNU Multiple Precision Arithmetic Library, is completely proven within the COQ system. Proofs are developed using the CORRECTNESS tool to deal with imperative features of the program. The formalization is rather large (more than 13,000 lines) and requires some advanced techniques for proof management and reuse.