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In this paper ways to efficiently implement public-key schemesbased on Multivariate Qua- dratic polynomials (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 im- plementation 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 MQ-schemes in hardware is proposed which includes a systolic architecture performing Gaussian elimination over composite binary fields.

Time-Area Optimized Public-Key Engines: $\mathcal{MQ}$ -Cryptosystems as Replacement for Elliptic Curves?