Method and apparatus for use in public-key data encryption system
First Claim
1. For use in connection with an apparatus employing a public key n and a secret key comprising primary factors p and q where n=pq wherein said public key is used for authenticating data, for enciphering data, or for authenticating and enciphering data, and the secret key is used for signing the data, for deciphering the data, or for signing and deciphering the data, apparatus for generating said secret key and said public key such that recovery of said secret key from said public key is computationally infeasible, said apparatus comprising:
- means for establishing a length of said public key;
means for establishing lengths of p-related secondary factors, p-related tertiary factors, q-related secondary factors and q-related tertiary factors which are functions of said secret key p and q;
means for choosing a tentative p value as one of said primary factors;
means for choosing a tentative q value as one of said primary factors;
means for testing said tentative p value for suitability as a part of said secret key based on two p-related secondary factors and two p-related tertiary factors, each one of said p-related tertiary factors and said p-related secondary factors being functions of said tentative p value; and
means for testing said tentative q value for suitability as a part of said secret key based on two q-related secondary factors and two q-related tertiary factors, each one of said q-related tertiary factors and said q-related secondary factors being functions of said tentative q value.
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Accused Products
Abstract
In an encryption scheme based on the use of a public key having secret factors p and q, additional requirements on p and q are invoked in order to ensure a high level of security. In particular, it is additionally required that a value p+1 have a large prime factor r and that the value r-1 also have a large prime factor r'"'"'.
94 Citations
24 Claims
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1. For use in connection with an apparatus employing a public key n and a secret key comprising primary factors p and q where n=pq wherein said public key is used for authenticating data, for enciphering data, or for authenticating and enciphering data, and the secret key is used for signing the data, for deciphering the data, or for signing and deciphering the data, apparatus for generating said secret key and said public key such that recovery of said secret key from said public key is computationally infeasible, said apparatus comprising:
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means for establishing a length of said public key; means for establishing lengths of p-related secondary factors, p-related tertiary factors, q-related secondary factors and q-related tertiary factors which are functions of said secret key p and q; means for choosing a tentative p value as one of said primary factors; means for choosing a tentative q value as one of said primary factors; means for testing said tentative p value for suitability as a part of said secret key based on two p-related secondary factors and two p-related tertiary factors, each one of said p-related tertiary factors and said p-related secondary factors being functions of said tentative p value; and means for testing said tentative q value for suitability as a part of said secret key based on two q-related secondary factors and two q-related tertiary factors, each one of said q-related tertiary factors and said q-related secondary factors being functions of said tentative q value. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13)
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14. For use in connection with an apparatus employing a public key n and a secret key comprising primary factors p and q where n=pq wherein said public key is a digital signal used for authenticating, enciphering, or authenticating and enciphering data and the secret key is used for signing, deciphering, or signing and deciphering the data, a method for generating said secret key and said public key such that recovery of said secret key from said public key is computationally infeasible, said method comprising:
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establishing a length of said public key based on a desired security level; establishing lengths of p-related secondary factors and p-related tertiary factors, q-related secondary factors and q-related tertiary factors which factors are functions of said secret key p and q; choosing a tentative p value as one of said primary factors; choosing a tentative q value as one of said primary factors; testing said tentative p value for suitability as a part of said secret key based on two p-related secondary factors and two p-related tertiary factors, each one of said p-related tertiary factors and said p-related secondary factors being functions of said tentative p value; testing said tentative q value for suitability as a part of secret key based on two q-related secondary factors and two q-related tertiary factors, each one of said q-related tertiary factors and said q-related secondary factors being functions of said tentative q value; and presenting said public key and said secret key as digital electronic signals to an output utilization means. - View Dependent Claims (15, 16, 17, 18, 19, 20, 21, 22, 23, 24)
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Specification