CAPTCHA is an authentication test that distinguishes between humans and machines. CAPTCHA is essential to prevent fraudulent account acquisition by BOTs. Conventional CAPTCHAs were based on the assumption that human abilities were superior to BOTs, but with the evolution of AI technology, this assumption no longer holds true. As CAPTCHAs have become more complex, usability has been compromised. The Munker illusion is a visual illusion in which shapes of the same color appear to be different colors to the human eye due to the synergistic effect of color assimilation and color contrast. In this paper, we propose a new CAPTCHA using the Munker illusion.

In 2012, Murakami, Hamasho and Kasahara proposed a knapsack PKC based on the subset sum decision problem. Nagao and Morii proposed an attack which is effective for this type of the knapsack scheme by computing integer solutions of the knapsack problem. This attack is referred to as alternative-solution attack. In 2016, Murakami proposed a new scheme of the knapsack PKCs(M16 schemes) based on the subset sum decision problem. In this paper, we shall evaluate the security of the M16 schemes against the alternative-solution attack by computer experiment. As the result, it is seen that M16 Basic Scheme can be broken with the alternative-solution attack and that M16 Weight-Limited Scheme can not be broken with the alternative-solution attack.

The security of most of the knapsack type public key cryptosystem(PKC) depends on the computational subset sum problem. In 2012, a knapsack PKC based on the subset sum decision problem is proposed by Murakami, Hamasho and Kasahara. An attack against this type of knapsack PKC by computing alternative solutions of the knapsack problem is then proposed by Nagao and Morii. In 2016, a new knapsack PKC(M16 PKC) based on the subset sum decision problem for preventing Nagao and Morii attack is proposed by Murakami. In this paper, we propose the new effective attacks against M16 knapsack PKC. The proposed attacks compute the equivalent secret keys from the public key, and the ciphertext of M16 PKC can be decoded with the equivalent secret keys, in the same way as the decryption with the legitimate secret(decryption) keys.

It is required to invent the public-key cryptosystem(PKC) that is based on an NP-hard problem so that the quantum computer might be realized. The knapsack PKC is based on the subset sum problem which is NP-hard. In this paper, we propose a construction method of knapsack PKC using a linear transformation of the secret sequences over integer ring with the Chinese remainder theorem as the trapdoor. The proposed scheme is secure against Shamir's attack and Adleman's attack and invulnerable to the low-density attack.

The knapsack scheme is expected to be not only a light-weight public-key cryptosystem but also a post quantum cryptosystem. In this paper, we propose a new method for constructing knapsack PKC by using a random sequence. We also give two concrete knapsack schemes based on the proposed method. The scheme constructed the proposed method can be secure against the low-density attack because the density can be made as large as one desires. The scheme constructed the proposed method can be also secure against the attack of computing the secret key, because the public key is almost indistinguishable from a random numbers.