It is urgent to develop cryptographic technologies for secure confidential communications of certain types of information, such as genome data in the pharmaceutical and medical fields because their confidentiality needs to be kept for generations over hundreds of years. However, there are concerns that the current cryptographic systems, which rely on computationally complex of factorization of prime numbers or distributed logarithms, may not be able to securely protect confidentiality with the

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... dvent of quantum computers [1]. In addition, the current cryptographic techniques may not be able to secure safety in 30 years due to steadily increasing computational capabilities. On the other hand, lattice-based systems [2][3] are proposed as the most promising quantum-resistant cryptographic systems. However, their performance evaluations are scheduled to be conducted from 2020 to 2022 at the National Institute of Standards and Technology (NIST) [4]. As such, it will take several years before solutions to the safety issues we are currently facing become available. Furthermore, changing cryptographic systems will likely necessitate a change in the length of public keys. We therefore might have to ReReRenRe R 1 P. W. Shor, "Algorithms for quantum computation: Discrete logarithms and factoring, " Proceeding of the 35th Annual Symposimu on Fundations of