In case we use a quantum computer, we have to construct the countermeasure. Due to the high efficiency and fast computation time, the multivariate quadratic public key systems are considered as an alternative to RSA or ECC based systems. However, the large key size is a fatal disadvantage of the multivariate quadratic public key systems. For this reason, the multivariate quadratic public key systems are not widely used. In this paper, we measure how much the private key memory size can be

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... d by using a secure pseudo-random number generator in the UOV scheme. Almost 93% of the private key memory size is reduced. Index Terms-Multivariate quadratic public key system, pseudo-random number generator, UOV scheme. Jihyun Kim received the BSEE degree from Pusan National University, Pusan, Republic of Korea in 2010, and he received the MS degree program in department of Computer Engineering at Pusan National University in 2012. He is Ph. D course in same major and university. His research interests include multivariate quadratic schemes, sensor networks, smart grid and malware protection systems. Howon Kim He received the BSEE degree from Kyungpook National University, Daegu, Republic of Korea, in 1993 and the MS and PhD degrees in electronic and electrical engineering from the Pohang . His research interests include RFID technology, sensor networks, information security, and computer architecture. Currently, his main research focus is on mobile RFID technology and sensor networks, public key cryptosystems, and their security issues. He is a member of the IEEE, and the International Association for Cryptologic Research (IACR).