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The authors propose a new multivariate probabilistic encryption scheme with decryption errors MQQ-ENC that belongs to the family of MQQ-based public key schemes. Similarly to MQQ-SIG, the trapdoor is constructed using quasigroup string transformations with multivariate quadratic quasigroups, and a minus modifier with relatively small and fixed number of removed equations. To make the decryption possible and also efficient, they use a universal hash function to eliminate possibly wrong plaintext candidates. They show that, in this way, the probability of erroneous decryption becomes negligible.
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