Analysis of the complexity of attacks on multivariate cryptographic transformations using algebraic field structure
DOI:
https://doi.org/10.30837/rt.2021.1.204.06Keywords:
classical and quantum cryptanalysis, differential attacks on the underground, attack analysis, postquantum periodAbstract
In recent years, interest in cryptosystems based on multidimensional quadratic transformations (MQ transformations) has grown significantly. This is primarily due to the NIST PQC competition [1] and the need for practical electronic signature schemes that are resistant to attacks on quantum computers. Despite the fact that the world community has done a lot of work on cryptanalysis of the presented schemes, many issues need further clarification. NIST specialists are very cautious about the standardization process and urge cryptologists [4] in the next 3 years to conduct a comprehensive analysis of the finalists of the NIST PQC competition before their standardization.
One of the finalists is the Rainbow electronic signature scheme [2]. It is a generalization of the UOV (Unbalanced Oil and Vinegar) scheme [3]. Recently, another generalization of this scheme – LUOV (Lifted UOV) [5] was found to attack [6], which in polynomial time is able to recover completely the private key. The peculiarity of this attack is the use of the algebraic structure of the field over which the MQ transformation is given. This line of attack has emerged recently and it is still unclear whether it is possible to use the field structure in the Rainbow scheme.
The aim of this work is to systematize the techniques used in attacks using the algebraic field structure for UOV-based cryptosystems and to analyze the obstacles for their generalization to the Rainbow scheme.
References
NIST Web site/ Електронне посилання: https://csrc.nist.gov/projects/post-quantum-cryptography
Rainbow Web site / Електронне посилання: https://www.pqcrainbow.org/
Wolf, Christopher: Multivariate Quadratic Polynomials in Public Key Cryptography, DIAMANT/EIDMA symposium 2005
NISTIR 8309
Rainbow Web site / Електронне посилання https://www.esat.kuleuven.be/cosic/pqcrypto/luov/
6 Jintai Ding and Joshua Deaton and Vishakha and Bo-Yin Yang The Nested Subset Differential Attack: A Practical Direct Attack Against LUOV which Forges a Signature within 210 Minutes / Електронне посилання: https://eprint.iacr.org/2020/967.pdf
Jintai Ding, Zheng Zhang, Joshua Deaton, Kurt Schmidt, FNU Vishakha New Attacks on Lifted Unbalanced Oil Vinegar, Електронне посилання: https://csrc.nist.gov/CSRC/media/Events/Second-PQC-Standardization Conference/documents/accepted-papers/ding-new-attacks-luov.pdf
Enrico Thomae and Christopher Wolf. Solving underdetermined systems of multivari-ate quadratic equations revisited. In Public Key Cryptography- PKC2012-15th International Conference on Practice and Theory in Public Key Cryptography, Darmstadt, Germany, May21-23, 2012. Proceedings, pages 156–171. Springer, 2012
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