Cryptology ePrint Archive: Report 2021/929

A polynomial time key-recovery attack on the Sidon cryptosystem

Pierre Briaud and Jean-Pierre Tillich and Javier Verbel

Abstract: The Sidon cryptosystem is a new multivariate encryption scheme based on the theory of Sidon spaces which was presented at PKC 2021. As is usual for this kind of schemes, its security relies on the hardness of solving particular instances of the MQ problem and of the MinRank problem. A nice feature of the scheme is that it enjoys a homomorphic property due the bilinearity of its public polynomials. Unfortunately, we will show that the Sidon cryptosystem can be broken by a polynomial time key-recovery attack. This attack relies on the existence of solutions to the underlying MinRank instance which lie in a subfield and which are inherent to the structure of the secret Sidon space. We prove that such solutions can be found in polynomial time. Our attack consists in recovering an equivalent key for the cryptosystem by exploiting these particular solutions, and this task can be performed very efficiently.

Category / Keywords: public-key cryptography / Multivariate cryptography, Encryption scheme, Algebraic attack, MinRank Problem

Date: received 8 Jul 2021, last revised 10 Jul 2021

Contact author: javier verbel at tii ae

Available format(s): PDF | BibTeX Citation

Version: 20210711:043432 (All versions of this report)

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