Cryptography – Particular algorithmic function encoding – Public key
Patent
1995-07-24
1997-05-06
Cain, David S.
Cryptography
Particular algorithmic function encoding
Public key
380 28, 380 23, H04L 926
Patent
active
056278934
DESCRIPTION:
BRIEF SUMMARY
The present invention relates to cryptology and, in particular, to a cryptographic method which can be used for public key encryption and to produce digital signatures.
Cryptographic techniques have become of significant practical importance in the area of digital communications, particularly with the increasing prevalence of digital telecommunications networks. Development has concentrated on schemes which allow message data, often referred to as plaintext, to be encrypted using a key which is available to the public, to produce ciphertext which can only be decrypted using a secret key that is related to the public key but which cannot be derived therefrom. Schemes of this nature were first discussed in W. Diffie and M. E. Hellman, "New Directions in Cryptography", IEEE Transactions on Information Theory, Vol. 22, No. 6, 1976, pp. 644-654, and the first practical implementation was proposed in R. L. Rivest, A. Shamir and L. Adeleman, "A Method for Obtaining Digital Signatures and Public-Key Cryptosystems", Communications of the ACM, Vol. 21, No. 2, 1978, pp. 120-126, and is known as RSA. The schemes can also be used to produce digital signatures, where the plaintext can be signed by encrypting with the secret key, and then read using the public key.
The cryptographic operations performed on the ciphertext and plaintext are best described and defined using mathematical formula and symbols that depict the cryptographic process as being a sequence of mathematical operations on the numerical value represented by the bits of the data forming the plaintext or ciphertext. RSA, for example, involves a sequence of operations which are performed in modulo n arithmetic, where n is part of the public key and is the product of two large primes p and q, that constitute the secret key. The security of RSA relies primarily on the difficulty of factoring the composite number n. Although relatively secure and simple to implement, RSA is susceptible to homomorphic attack, where valid digital signatures can be produced from the combination of previously signed messages that have been recorded.
Elliptic curves over finite fields have also been found to be applicable to cryptology where the points on a curve can form a group and where an initial point can be used to derive other points in the group in a cyclical manner until the initial point of the curve is obtained again. The plaintext can be made a coordinate of a point on an elliptic curve and encrypted by performing the operations on the point to move it to another point within the group. The message can only be retrieved by knowing the characteristics of the curve and the order of the group to which the plaintext belongs. The elliptic curve operations are also performed modulo n, where n is the product of two large primes p and q. The first elliptic curve based scheme which is analogous to RSA is proposed in K. Koyama, U. M. Maurer, T. Okamoto and S. A. Vanstone, "New Public-Key Schemes based on Elliptic Curves over the Ring Zn", CRYPTO '91 Abstracts, Santa Barbara, Calif., pp. 6-1 to 6-7, 11-15 August, 1991. The paper essentially describes two schemes, discussed hereinafter, which can be used for the same applications as RSA, one can only be used to produce digital signatures, while the second scheme can also be used for public key encryption. The latter scheme, however, is restricted in the types of primes, p and q, and the types of elliptic curves which can be used, and a second coordinate needs to be transmitted with the ciphertext to enable decryption. The first scheme has the disadvantages that the digital signatures are roughly twice as long as the message or plaintext and that trial and error is required to locate a point on the elliptic curve corresponding to a plaintext, which involves incrementing the value x of the plaintext.
In accordance with the present invention there is provided a cryptographic method including:
selecting secret keys p and q, being prime numbers greater than 3;
selecting public parameters for a series of data values which belong to one o
REFERENCES:
patent: 4933970 (1990-06-01), Shamir
patent: 4935962 (1990-06-01), Austin
patent: 4944007 (1990-07-01), Austin
patent: 5146500 (1992-09-01), Maurer
patent: 5159632 (1992-10-01), Crandall
patent: 5272755 (1993-12-01), Miyaji et al.
Cain David S.
Engellenner Thomas J.
Laurentano Anthony A.
Telstra Corporation Limited
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