A Multi-start Heuristic for Multiplicative Depth Minimization of Boolean Circuits

In this work we propose a multi-start heuristic which aims at minimizing the multiplicative depth of boolean circuits. The multiplicative depth objective is encountered in the field of homomorphic encryption where ciphertext size depends on the number of consecutive multiplications. The heuristic is...

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Bibliographic Details
Published inCombinatorial Algorithms Vol. 10765; pp. 275 - 286
Main Authors Carpov, Sergiu, Aubry, Pascal, Sirdey, Renaud
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2018
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Arithmetic Circuits
Boolean Circuit
Ciphertext
Homomorphic Encryption (HE)
Multiplicative Depth
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Summary:In this work we propose a multi-start heuristic which aims at minimizing the multiplicative depth of boolean circuits. The multiplicative depth objective is encountered in the field of homomorphic encryption where ciphertext size depends on the number of consecutive multiplications. The heuristic is based on rewrite operators for multiplicative depth-2 paths. Even if the proposed rewrite operators are simple and easy to understand the experimental results show that they are rather powerful. The multiplicative depth of the benchmarked circuits was hugely improved. In average the obtained multiplicative depths were lower by more than 3 times than the initial ones. The proposed rewrite operators are not limited to boolean circuits and can also be used for arithmetic circuits.
Bibliography:This work has been supported in part by the French’s FUI project CRYPTOCOMP and by the European Union’s H2020 Programme under grant agreement number 727528 (project KONFIDO).
ISBN:3319788248
9783319788241
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-319-78825-8_23