This paper investigates some modular powering functions suitable for cryptography. It is well known that the Rabin encryption function is a 4-to-1 mapping and breaking its one-wayness is secure under the factoring assumption. The previously reported encryption schemes using a powering function are variants of either the 4-to-1 mapping or higher n-to-1 mapping, where n > 4. In this paper, we propose an optimized powering function that is a 3-to-1 mapping using a p2q-type modulus. The one-wayness of the proposed powering function is as hard as the infeasibility of the factoring problem. We present an efficient algorithm for computing the decryption for a p2q-type modulus, which requires neither modular inversion nor division. Moreover, we construct new provably secure digital signatures as an application of the optimized functions. In order to achieve provable security in the random oracle model, we usually randomize a message using random hashing or padding. However, we have to compute the randomization again if the randomized message is a non-cubic residue element--it is inefficient for long messages. We propose an algorithm that can deterministically find the unique cubic residue element for a randomly chosen element.

A digital signature does not allow any alteration of the document to which it is attached. Appropriate alteration of some signed documents, however, should be allowed because there are security requirements other than that for the integrity of the document. In the disclosure of official information, for example, sensitive information such as personal information or national secrets is masked when an official document is sanitized so that its nonsensitive information can be disclosed when it is demanded by a citizen. If this disclosure is done digitally by using the current digital signature schemes, the citizen cannot verify the disclosed information correctly because the information has been altered to prevent the leakage of sensitive information. That is, with current digital signature schemes, the confidentiality of official information is incompatible with the integrity of that information. This is called the digital document sanitizing problem, and some solutions such as digital document sanitizing schemes and content extraction signatures have been proposed. In this paper, we point out that the conventional digital signature schemes are vulnerable to additional sanitizing attack and show how this vulnerability can be eliminated by using a new digitally signed document sanitizing scheme with disclosure condition control.

Today, TLS is widely used for achieving a secure communication system. And TLS is used PKI for server authentication and/or client authentication. However, its PKI environment, which is called as "multiple trust anchors environment," causes the problem that the verifier has to maintain huge number of CA certificates in the ubiquitous network because the increase of terminals connected to the network brings the increase of CAs. However, most of terminals in the ubiquitous network will not have enough memory to hold such huge number of CA certificates. Therefore, another PKI environment, "cross certification environment", is useful for the ubiquitous network. But, because current TLS is designed for the multiple trust anchors model, TLS cannot work efficiently on the cross-certification model. This paper proposes a TLS implementation method to support the cross certification model efficiently. Our proposal reduces the size of exchanged messages between the TLS client and the TLS server during the handshake process. Therefore, our proposal is suitable for implementing TLS in the terminals that do not have enough computing power and memory in ubiquitous network.

The cellular phone ownership rate continues to increase, meaning one person may now own two or more. Meanwhile, a lot of terminals that receive cellular phone services through a mass broadband communication network are being commercialized. When service is received through the cellular phone, the mobile network operator authenticates the subscriber. However, service providers other than the mobile network operators provide communication services and other services through fixed networks. In this situation, if we can use the subscriber authentication that the mobile network operator provide for the fixed network service, fixed mobile convergence (FMC) will be achieved and mobile network operators will be able to better prevent unauthorized users from using their services. In addition, services will become more convenient because users will be authenticated by swiping one cellular phone when switching from using a fixed terminal to another fixed terminal. A mechanism has been developed that allows mobile network operator to authenticate their subscribers' account when using a terminal connected to a fixed network. In addition, services can be easily switched between fixed terminals by using the proposed mechanism. Moreover, a system is constructed on the basis of the proposed mechanism, and its performance is evaluated.