Abstract
In this paper ways to efficiently implement public-key schemes based on ultivariate uadratic polynomials (\(\mathcal{MQ}\)-schemes for short) are investigated. In particular, they are claimed to resist quantum computer attacks. It is shown that such schemes can have a much better time-area product than elliptic curve cryptosystems. For instance, an optimised FPGA implementation of amended TTS is estimated to be over 50 times more efficient with respect to this parameter. Moreover, a general framework for implementing small-field \(\mathcal{MQ}\)-schemes in hardware is proposed which includes a systolic architecture performing Gaussian elimination over composite binary fields.
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Bogdanov, A., Eisenbarth, T., Rupp, A., Wolf, C. (2008). Time-Area Optimized Public-Key Engines: \(\mathcal{MQ}\)-Cryptosystems as Replacement for Elliptic Curves? . In: Oswald, E., Rohatgi, P. (eds) Cryptographic Hardware and Embedded Systems – CHES 2008. CHES 2008. Lecture Notes in Computer Science, vol 5154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85053-3_4
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DOI: https://doi.org/10.1007/978-3-540-85053-3_4
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