Lightweight Diffusion Layer from the $k^{th}$ root of the MDS Matrix

Souvik Kolay; Debdeep Mukhopadhyay

Paper 2014/498

Lightweight Diffusion Layer from the $k^{th}$ root of the MDS Matrix

Souvik Kolay and Debdeep Mukhopadhyay

Abstract

The Maximum Distance Separable (MDS) mapping, used in cryptography deploys complex Galois field multiplications, which consume lots of area in hardware, making it a costly primitive for lightweight cryptography. Recently in lightweight hash function: PHOTON, a matrix denoted as ‘Serial’, which required less area for multiplication, has been multiplied 4 times to achieve a lightweight MDS mapping. But no efficient method has been proposed so far to synthesize such a serial matrix or to find the required number of repetitive multiplications needed to be performed for a given MDS mapping. In this paper, first we provide an generic algorithm to find out a low-cost matrix, which can be multiplied k times to obtain a given MDS mapping. Further, we optimize the algorithm for using in cryptography and show an explicit case study on the MDS mapping of the hash function PHOTON to obtain the ‘Serial’. The work also presents quite a few results which may be interesting for lightweight implementation.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: MDS Matrix $k^{th}$ Root of a Matrix Lightweight Diffusion Layer
Contact author(s): souvik1809 @ gmail com
History: 2014-06-26: received
Short URL: https://ia.cr/2014/498
License: CC BY

BibTeX

@misc{cryptoeprint:2014/498,
      author = {Souvik Kolay and Debdeep Mukhopadhyay},
      title = {Lightweight Diffusion Layer from the $k^{th}$ root of the {MDS} Matrix},
      howpublished = {Cryptology {ePrint} Archive, Paper 2014/498},
      year = {2014},
      url = {https://eprint.iacr.org/2014/498}
}