We propose two types of public-key cryptographic schemes based on elliptic curves modulo n, where n is the product of secret large primes p and q. The RSA-type scheme has an encryption function with an odd multiplier. The Rabin-type scheme has an encryption function with a multiplier of 2. The security of the proposed schemes is based on the difficulty of factoring n. Other security characteristics are also discussed. We show some applications to a master key scheme and blind signature scheme.

This paper proposes a new construction of the minimum knowledge undeniable signature scheme which solves a problem inherent in Chaum's scheme. We formulate a new proof system, the minimum knowledge interactive bi-proof system, and a pair of languages, the common witness problem, based on the random self-reducible problem. We show that any common witness problem has the minimum knowledge interactive bi-proof system. A practical construction for undeniable signature schemes is proposed based on such a proof system. These schemes provide signature confirmation and disavowal with the same protocol (or at the same time).

This paper proposes a knowledge-based design method of a protocol of a communication network system based on the knowledge-based design methodology for computer communication systems. In the proposed method, two knowledge models, i.e., the communication network architecture model (CNAM) and the communication protocol architecture model (CPAM), are introduced and a protocol design task is modeled as a successive transformation process of these knowledge models. Giving CNAM which represents the users' requirements concerning a communication network system, the requirements specification of a protocol is derived from CNAM and represented as CPAM. Then, the detailed requirements specification of a protocol is also derived from CPAM and represented by the formal description technique (FDT-Expressions). The derivations of CPAM and FDT-Expressions are executed by the transformation rules which represent the mappings between knowledge models. Due to formally defined knowledge models and mappings, the proposed method provides a framework of a systematic support of knowledge-based protocol design. In this paper, the formal definitions of CNAM and CPAM are given, then the derivation process of FDT-Expressions of a protocol is also formalized based on these knowledge models. Furthermore, a design example is demonstrated by using LOTOS as one of the FDT-Expressions of a protocol.