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A Small GIFT-COFB: Lightweight Bit-Serial Architectures

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Progress in Cryptology - AFRICACRYPT 2022 (AFRICACRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13503))

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Abstract

GIFT-COFB is a lightweight AEAD scheme and a submission to the ongoing NIST lightweight cryptography standardization process where it currently competes as a finalist. The construction processes 128-bit blocks with a key and nonce of the same size and has a small register footprint, only requiring a single additional 64-bit register. Besides the block cipher, the mode of operation uses a bit permutation and finite field multiplication with different constants. It is a well-known fact that implementing a hardware block cipher in a bit-serial manner, which advances only one bit in the computation pipeline in each clock cycle, results in the smallest circuits. Nevertheless, an efficient bit-serial circuit for a mode of operation that utilizes finite field arithmetic with multiple constants has yet to be demonstrated in the literature.

In this paper, we fill this gap regarding efficient field arithmetic in bit-serial circuits, and propose a lightweight circuit for GIFT-COFB that occupies less than 1500 GE, making it the to-date most area-efficient implementation of this construction. In a second step, we demonstrate how the additional operations in the mode can be executed concurrently with GIFT itself so that the total latency is significantly reduced whilst incurring only a modest area increase. Finally, we propose a first-order threshold implementation of GIFT-COFB, which we experimentally verify resists first-order side-channel analysis. (For the sake of reproducibility, the source code for all proposed designs is publicly available [14]).

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Notes

  1. 1.

    A detailed description of the bit-sliced GIFT representation can be found in the GIFT-COFB white paper [9].

  2. 2.

    Note that there is an equally efficient circuit for the key schedule pipeline. An exact breakdown of all the swaps in the state pipeline is given in Appendix A.

  3. 3.

    The letters S and F in GIFT-COFB-SER-S and GIFT-COFB-SER-F stand for slow and fast respectively.

  4. 4.

    https://satoh.cs.uec.ac.jp/SAKURA/hardware/SAKURA-G.html.

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Acknowledgements

This project is partially supported by the European Union Horizon 2020 research and innovation program under the CPSoSAware project (grant 871738).

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Authors and Affiliations

  1. LASEC, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Andrea Caforio & Daniel Collins

  2. Universita della Svizzera Italiana, Lugano, Switzerland

    Subhadeep Banik & Francesco Regazzoni

  3. University of Amsterdam, Amsterdam, The Netherlands

    Francesco Regazzoni

Authors
  1. Andrea Caforio
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  2. Daniel Collins
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  3. Subhadeep Banik
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  4. Francesco Regazzoni
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Corresponding author

Correspondence to Andrea Caforio .

Editor information

Editors and Affiliations

  1. Radboud University, Nijmegen, The Netherlands

    Lejla Batina

  2. Radboud University, Nijmegen, Gelderland, The Netherlands

    Joan Daemen

Appendices

A Swap-and-Rotate GIFT-128 State Pipeline

In Table 3, we give the exact placement and activation periods of the nine swaps that implement the swap-and-rotate  GIFT-128 permutation \(\varPi \) as specified in the work by Banik et al.  [3].

Table 3. Swap-and-rotate listing of all swaps and their activation cycles.
Full size table

B ANF Equations of the 3-Share GIFT-128 S-Box

Below we list the exact ANF equations for all component functions of the 3-share first-order threshold implementation of the GIFT S-box as proposed in [19].

$$\begin{aligned} \texttt {S}_{G_1}(a_2, b_2, c_2, d_2, a_3, b_3, c_3, d_3)&= a_3 + b_3 + b_2c_2 + b_2c_3 + b_3c_2, \\&\; c_3 + 1, \\&\; b_3 + a_2c_2 + a_2c_3 + a_3c_2, \\&\; a_3 + b_3 + c_3 + d_3 + a_2b_2 + a_2b_3 + a_3b_2; \\ \texttt {S}_{G_2}(a_1, b_1, c_1, d_1, a_3, b_3, c_3, d_3)&= a_1 + b_1 + b_1c_3 + b_3c_1 + b_3c_3, \\&\; c_1, \\&\; b_1 + a_1c_3 + a_3c_1 + a_3c_3, \\&\; a_1 + b_1 + c_1 + d_1 + a_1b_3 + a_3b_1 + a_3b_3; \\ \texttt {S}_{G_3}(a_1, b_1, c_1, d_1, a_2, b_2, c_2, d_2)&= a_2 + b_2 + b_1c_1 + b_1c_2 + b_2c_1 \\&\; c_2, \\&\; b_2 + a_1c_1 + a_1c_2 + a_2c_1, \\&\; a_2 + b_2 + c_2 + d_2 + a_1b_1 + a_1b_2 + a_2b_1; \\ \texttt {S}_{F_1}(a_2, b_2, c_2, d_2, a_3, b_3, c_3, d_3)&= d_3 + a_2b_2 + a_2b_3 + a_3b_2, \\&\; b_3 + c_3 + d_3 + a_2d_2 + a_2d_3 + a_3d_2 + 1, \\&\; a_3 + b_3, \\&\; a_3 + 1; \\ \texttt {S}_{F_2}(a_1, b_1, c_1, d_1, a_3, b_3, c_3, d_3)&= d_1 + a_1b_3 + a_3b_1 + a_3b_3, \\&\; b_1 + c_1 + d_1 + a_1d_3 + a_3d_1 + a_3d_3, \\&\; a_1 + b_1, \\&\; a_1; \\ \texttt {S}_{F_3}(a_1, b_1, c_1, d_1, a_2, b_2, c_2, d_2)&= d_2 + a_1b_1 + a_1b_2 + a_2b_1, \\&\; b_2 + c_2 + d_2 + a_1d_1 + a_1d_2 + a_2d_1, \\&\; a_2 + b_2, \\&\; a_2. \end{aligned}$$

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Caforio, A., Collins, D., Banik, S., Regazzoni, F. (2022). A Small GIFT-COFB: Lightweight Bit-Serial Architectures. In: Batina, L., Daemen, J. (eds) Progress in Cryptology - AFRICACRYPT 2022. AFRICACRYPT 2022. Lecture Notes in Computer Science, vol 13503. Springer, Cham. https://doi.org/10.1007/978-3-031-17433-9_3

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