IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Special Section on Discrete Mathematics and Its Applications
The Secure Parameters and Efficient Decryption Algorithm for Multivariate Public Key Cryptosystem EFC
Yacheng WANGYasuhiko IKEMATSUDung Hoang DUONGTsuyoshi TAKAGI
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2019 Volume E102.A Issue 9 Pages 1028-1036

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Abstract

At PQCrypto 2016, Szepieniec et al. proposed a new type of trapdoor called Extension Field Cancellation (EFC) for constructing secure multivariate encryption cryptosystems. They also specifically suggested two schemes EFCp- and EFCpt2- that apply this trapdoor and some modifiers. Although both of them seem to avoid all attacks used for cryptanalysis on multivariate cryptography, their decryption efficiency has room for improvement. On the other hand, their security was analyzed mainly through an algebraic attack of computing the Gröbner basis of the public key, and there possibly exists more effective attacks. In this paper, we introduce a more efficient decryption approach for EFCp- and EFCpt2-, which manages to avoid all redundant computation involved in the original decryption algorithms without altering their public key. In addition, we estimate the secure parameters for EFCp- and EFCpt2- through a hybrid attack of algebraic attack and exhaustive search.

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© 2019 The Institute of Electronics, Information and Communication Engineers
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