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A new Multivariate Public-Key Cryptosystem (MPKC) with the security based on the difficulty of the prime factoring is proposed. Unlike conventional cryptosystems such as RSA, most MPKCs are expected secure against quantum computers, and their operation of encryption and decryption is expected quick, because they do not need exponential operation. However, their security against quantum computers is very difficult to prove mathematically. The authors propose a new MPKC based on sequential solution method, assuming the security against von Neumann computers, whose attack seems as difficult as prime factoring. This cryptosystem is applicable to both encryption and signature.
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