Abstract
Modular inversion is a very common primitive used for the cryptographic computations. It is the most computation intensive unit which demands more resources as compared to other primitives. Inside the modular inversion arithmetic circuits, considerable speed up with optimized architecture is required. This paper proposes an optimized parallel architecture for Itoh-Tsujii modular inversion algorithm for the field GF(2256) by introducing 23 blocks. The comparative results with conventional architecture show the 30% reduction in LUT requirement with 37% in combinational delay.
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References
Trujillo-Olaya, V., Velasco-Medina, J.: Hardware architectures for inversion in GF (2m) using polynomial and gaussian normal basis. In: ANDESCON IEEE 2010 Conference Publications, pp. 1–5 (2010)
Itoh, T., Tsujii, S.: A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases. Inf. Comput. 78(3), 171–177 (1988)
Dimitrov, V., Järvinen, K.: Another look at inversions over binary fields. In: 2013 IEEE 21st Symposium on Computer Arithmetic, pp. 211–218 (2013)
Roy, S.S., Rebeiro, C., Mukhopadhyay, D.: Theoretical modelling of the Itoh-Tsujii inversion algorithm for enhanced performance on k-LUT based FPGAs. In: Proceedings of the Design, Automation & Test in Europe Conference & Exhibition (DATE), Grenoble, France, vol. 1, pp. 1–6, March 2011
Rebeiro, C., Roy, S.S., Reddy, D.S., Mukhopadhyay, D.: Revisiting the Itoh-Tsujii inversion algorithm for FPGA platforms. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 19(8), 1508–1512 (2011)
Parrilla, L., Lloris, A., Castillo, E., et al.: Minimum-clock-cycle Itoh-Tsujii algorithm hardware implementation for cryptography applications over GF(2m) fields. Electron. Lett. 48(18), 1126–1128 (2012)
Guajardo, J., Paar, C.: Itoh-Tsujii inversion in standard basis and its application in cryptography and codes. Des. Codes Cryptogr. 25(2), 207–216 (2002)
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Zode, P., Deshmukh, R.B., Samad, A. (2017). Fast Architecture of Modular Inversion Using Itoh-Tsujii Algorithm. In: Kaushik, B., Dasgupta, S., Singh, V. (eds) VLSI Design and Test. VDAT 2017. Communications in Computer and Information Science, vol 711. Springer, Singapore. https://doi.org/10.1007/978-981-10-7470-7_5
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DOI: https://doi.org/10.1007/978-981-10-7470-7_5
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