Abstract
This chapter deals with the Hidden Field Equations (HFE) cryptosystem and its variants. We start by an introduction of the basic HFE cryptosystem and study its security against direct and rank attacks. Furthermore, we give an overview of the various HFE variants for encryption and digital signatures. In the area of encryption schemes we study here the IPHFE+ and the ZHFE schemes, while, in the area of signature schemes, we analyze the HFEv- signature scheme and its extension Gui, which produces the shortest signatures of all currently existing schemes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The definition holds also for non square transformations \(\mathcal {S}\) and \(\mathcal {T}\) as they are used in variants of MI and HFE. Therefore we speak here of full rank linear transformations.
- 2.
Since we deal with symmetric matrices, each two minors produce the same equation.
References
L. Bettale, J. Faugère, L. Perret, Cryptanalysis of HFE, multi-HFE and variants for odd and even characteristic. Des. Codes Cryptography 69(1), 1–52 (2013)
D. Cabarcas, D. Smith-Tone, J.A. Verbel, Key recovery attack for ZHFE, in The Eighth International Conference on Post-Quantum Cryptography (PQCrypto 2017). Lecture Notes in Computer Science, vol. 10346 (Springer, Berlin, 2017), pp. 289–308
A. Casanova, J. Faugère, G. Macario-Rat, J. Patarin, L. Perret, J. Ryckeghem, GeMSS: a great multivariate short signature. https://csrc.nist.gov/Projects/Post-Quantum-Cryptography/Round-2-Submissions
N. Courtois, Generic attacks and the security of quartz, in International Workshop on Public Key Cryptography (PKC 2003). Lecture Notes in Computer Science, vol. 2567 (Springer, Berlin, 2003), pp. 351–364
J. Ding, D. Schmidt, Cryptanalysis of HFEv and internal perturbation of HFE, in International Workshop on Public Key Cryptography (PKC 2005). Lecture Notes in Computer Science, vol. 3386 (Springer, Berlin, 2005), pp. 288–301
J. Faugère, A. Joux, Algebraic cryptanalysis of hidden field equation (HFE) cryptosystems using gröbner bases, in Annual International Cryptology Conference (CRYPTO 2003). Lecture Notes in Computer Science, vol. 2729 (Springer, Berlin, 2003), pp. 44–60
Y. Ikematsu, D.H. Duong, A. Petzoldt, T. Takagi, An efficient key generation of ZHFE public key cryptosystem. IEICE Trans. 101-A(1), 29–38 (2018)
A. Kipnis, A. Shamir, Cryptanalysis of the HFE public key cryptosystem by relinearization, in Annual International Cryptology Conference (CRYPTO 1999). Lecture Notes in Computer Science, vol. 1666 (Springer, Berlin, 1999), pp. 19–30
M.S.E. Mohamed, J. Ding, J.A. Buchmann, Towards algebraic cryptanalysis of HFE challenge 2, in International Conference on Information Security and Assurance (ISA 2011). Communications in Computer and Information Science, vol. 200 (Springer, Berlin, 2011), pp. 123–131
J. Patarin, Hidden field equations (HFE) and isomorphisms of polynomials (IP): two new families of asymmetric algorithms, in International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT 1996). Lecture Notes in Computer Science, vol. 1070 (Springer, Berlin, 1996), pp. 33–48
A. Petzoldt, M.-S. Chen, B.-Y. Yang, T. Chengdong, J. Ding, Design principles for HFEv- based signature schemes, in International Conference on the Theory and Application of Cryptology and Information Security (ASIACRYPT 2015 - Part I). Lecture Notes in Computer Science, vol. 9452 (Springer, Berlin, 2015), pp. 1–24
J. Porras, J. Baena, J. Ding, ZHFE, a new multivariate public key encryption scheme, in 6th International Workshop Post-quantum Cryptography (PQCrypto 2014). Lecture Notes in Computer Science, vol. 8772 (Springer, Berlin, 2014), pp. 229–245
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Science+Business Media, LLC, part of Springer Nature
About this chapter
Cite this chapter
Ding, J., Petzoldt, A., Schmidt, D.S. (2020). Hidden Field Equations. In: Multivariate Public Key Cryptosystems. Advances in Information Security, vol 80. Springer, New York, NY. https://doi.org/10.1007/978-1-0716-0987-3_4
Download citation
DOI: https://doi.org/10.1007/978-1-0716-0987-3_4
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-0716-0985-9
Online ISBN: 978-1-0716-0987-3
eBook Packages: Computer ScienceComputer Science (R0)