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Elliptic Curve Cryptosystem

This paper describes elliptic curve cryptosystems (ECCs), which are expected to be-come the next-generation public key cryptosystems, and also describes Fujitsu Labo-ratories’ study of ECCs. | UDC 681.8 Elliptic Curve Cryptosystem Naoya Torii Kazuhiro Yokoyama Manuscript received June 6 2000 This paper describes elliptic curve cryptosystems ECCs which are expected to become the next-generation public key cryptosystems and also describes Fujitsu Laboratories study of ECCs. ECCs require a shorter key length than RSA cryptosystems which are the de facto standards of public key cryptosystems but provide equivalent security levels. Because of the shorter key length ECCs are fast and can be implemented with less hardware. First we outline ECC and describe a typical digital signature algorithm. Then we describe our technology for parameter generation of a secure ECC and the implementation of a fast ECC by software and by a digital signal processor. ECCs are expected to enter widespread use as a base technology of electronic information services. 1. Introduction Various services on open networks for example electronic commerce electronic shops for music video and software and CALS EDI are expected to make life more convenient and efficient. Encryption is a base technology used to realize these services. There are two types of encryption technology secret key cryptosystems and public key cryptosystems. In a secret key cryptosystem a key for encryption and decryption is shared between the sender and the receiver. In a public key cryptosystem the sender and the receiver use different keys. Some commonly used public key cryptosystems are the RSA cryptosystem RSA 1 and the ElGamal cryptosystem 2 these were invented in 1978 and 1984 respectively. The elliptic curve cryptosystem ECC was invented by N. Koblitz3 and by V. Miller4 independently in 1985 and is expected to become the next-generation public key cryptosystem. A lot of work is being done to learn about its security and standardization organizations such as the ISO IEEE ANSI and IETF are actively standardiz ing ECC so it can be put to practical use. 2. Elliptic Curve Cryptosystems ECCs 2.1 Public key .