Structural Collapse of the Amutha-Perumal Scheme Based on Duo Circulant Matrices

Sopan Chavhan; Shrikant Chaudhari

Paper 2026/354

Structural Collapse of the Amutha-Perumal Scheme Based on Duo Circulant Matrices

Sopan Chavhan

, Shri Vyankatesh Arts, Commerce and Science College, Deulgaon Raja, Buldhana, 443204, Maharashtra, India.

Shrikant Chaudhari

, School K.B.C. North Maharashtra University, Umavi Nagar, Jalgaon, 425001, Maharashtra, India.

Abstract

Amutha and Perumal recently proposed a two-party key exchange protocol based on \(\alpha\)-\(v\)-\(w\)-duo circulant matrices over the max-plus semiring, claiming resistance to known tropical attacks and suitability for IoT environments. This paper presents a complete cryptanalysis of this protocol. We uncover a fundamental structural weakness: the construction imposes an affine parameterization on the secret matrices, reducing each matrix to a single integer parameter. Consequently, the public messages become simple shifts of a publicly computable matrix, and the session key reduces to a constant shift of another public matrix. An eavesdropper can recover the shared secret in constant time after a one-time precomputation. The attack is deterministic, succeeds with probability 1, and requires only passive observation. We verify the attack on the authors' own example.

Note: This paper presents a complete cryptanalysis of the Amutha-Perumal two-party key exchange protocol, which is based on duo circulant matrices over the max-plus semiring. We demonstrate that the protocol's construction imposes a severe affine structure on all secret matrices, reducing them to single integer parameters. This structural collapse allows an eavesdropper to recover the shared session key in constant time after a one-time precomputation. The attack is deterministic, succeeds with probability 1, and is verified on the authors' own example, refuting the protocol's claimed security.

Metadata

Available format(s): PDF
Category: Attacks and cryptanalysis
Publication info: Preprint.
Keywords: Cryptanalysis Duo circulant matrices Key exchange Max-plus semiring Structural collapse Tropical cryptography.
Contact author(s): sjchavhanmath17 @ gmail com
drsrchaudhari @ nmu ac in
History: 2026-02-23: approved; 2026-02-22: received; See all versions
Short URL: https://ia.cr/2026/354
License: CC BY

BibTeX

@misc{cryptoeprint:2026/354,
      author = {Sopan Chavhan and Shrikant Chaudhari},
      title = {Structural Collapse of the Amutha-Perumal Scheme Based on Duo Circulant Matrices},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/354},
      year = {2026},
      url = {https://eprint.iacr.org/2026/354}
}