Prime calculation device,method,and key issuing system
First Claim
1. A prime calculating apparatus for calculating a prime candidate N larger than a known prime q and testing primality of the calculated prime candidate N, comprising:
- a prime storage unit storing the known prime q;
a management information storage unit storing unique management information;
a random information generation unit operable to read the management information from the management information storage unit, and generate random information R based on the read management information;
a candidate calculation unit operable to read the prime q from the prime storage unit, and calculate the prime candidate N according to N=2×
random information R×
prime q+1;
a primality testing unit operable to test primality of the calculated prime candidate N; and
an output unit operable to output the calculated prime candidate N as a prime N when the primality of the calculated prime candidate N is determined.
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Accused Products
Abstract
The present invention offers a prime calculating apparatus for achieving prime calculation where producing identical primes is avoided by simple management techniques. The prime calculating apparatus stores a known prime q and management information unique in the use range of primes. The prime calculating apparatus reads the management information; generates random information R based on the read management information; reads prime q; calculates prime candidate N, according to N=2×random information R×prime q+1, using the read prime q and generated random information R; tests whether the calculated prime candidate N is a prime; and outputs the calculated prime candidate N as a prime when the primality of the calculated prime candidate N is determined. Herewith, the prime calculating apparatus is able to calculate prime candidates from unique management information while avoiding producing identical primes.
19 Citations
23 Claims
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1. A prime calculating apparatus for calculating a prime candidate N larger than a known prime q and testing primality of the calculated prime candidate N, comprising:
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a prime storage unit storing the known prime q;
a management information storage unit storing unique management information;
a random information generation unit operable to read the management information from the management information storage unit, and generate random information R based on the read management information;
a candidate calculation unit operable to read the prime q from the prime storage unit, and calculate the prime candidate N according to N=2×
random information R×
prime q+1;
a primality testing unit operable to test primality of the calculated prime candidate N; and
an output unit operable to output the calculated prime candidate N as a prime N when the primality of the calculated prime candidate N is determined. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
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16. A prime calculating apparatus for calculating a prime larger than a known prime, comprising:
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a prime calculation unit operable to calculate an output prime having a bit length twice a bit length of a known input prime;
a prime storage unit storing an initial value of the known prime; and
an iteration control unit operable to control the prime calculation unit to perform the calculation a plurality of iteration rounds, wherein the iteration control unit gives, in a first iteration round, the initial value to the prime calculation unit as the input prime, while giving, in each of the rest of the plurality of iteration rounds, an output prime calculated in an immediately preceding round to the prime calculation unit as the input prime, and in one of the plurality of iteration rounds, the prime calculation unit includes;
a management information storage subunit storing unique management information;
a random information generation subunit operable to read the management information from the management information storage subunit, and generate a random information R based on the read management information;
a candidate calculation subunit operable to receive the input prime, and calculate a prime candidate N according to N=2×
random information R×
the input prime+1;
a primality testing subunit operable to test primality of the calculated prime candidate N;
an output unit operable to output the calculated prime candidate N as the output prime when the primality of the calculated prime candidate N is determined; and
an iteration control subunit operable to control the random information generation subunit, the candidate calculation subunit, and the primality testing subunit to iterate the generation of the random information R, the calculation of the prime candidate N, and the primality testing until the primality of the calculated prime candidate N is determined by the primality testing subunit. - View Dependent Claims (17)
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18. A key issuing system including a terminal and a key issuing server apparatus for generating and issuing a private key and a public key of RSA encryption for the terminal, wherein
the key issuing server apparatus comprises: -
a prime calculation unit operable to calculate a prime N larger than a known prime q;
a public key generation unit operable to generate the public key using the calculated prime N;
a private key generation unit operable to generate the private key using the generated public key;
a key output unit operable to output the generated private key to the terminal; and
a publishing unit operable to publish the generated public key, the prime calculation unit includes;
a prime storage subunit storing the known prime q;
a management information storage subunit storing unique management information;
a random information generation subunit operable to read the management information from the management information storage subunit, and generate random information R based on the read management information;
a candidate calculation subunit operable to read the prime q from the prime storage subunit, and calculate a prime candidate N according to N=2×
random information R×
prime q+1;
a primality testing subunit operable to test primality of the calculated prime candidate N;
an output subunit operable to output the calculated prime candidate N as a prime when the primality of the calculated prime candidate N is determined; and
an iteration control subunit operable to control the random information generation subunit, the candidate calculation subunit, and the primality testing subunit to iterate the generation of the random information R, the calculation of the prime candidate N, and the primality testing until the primality of the calculated prime candidate N is determined by the primality testing subunit, and the terminal includes;
a reception unit operable to receive the private key; and
a key storage unit operable to store the received private key. - View Dependent Claims (19)
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20. A prime calculation method used in a prime calculating apparatus that calculates a prime candidate N larger than a known prime q and tests primality of the calculated prime candidate N, the prime calculating apparatus including:
- a prime storage unit storing the known prime q; and
a management information storage unit storing unique management information, the prime calculation method comprising;
a random number generation step of reading the management information from the management information storage unit and generating random information R based on the read management information;
a candidate calculation step of reading the prime q from the prime storage unit, and calculating the prime candidate N according to N=2×
random information R×
prime q+1;
a primality testing step of testing primality of the calculated prime candidate N; and
an output step of outputting the calculated prime candidate N as a prime when the primality of the calculated prime candidate N is determined.
- a prime storage unit storing the known prime q; and
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21. A prime-calculation computer program used on a prime calculating apparatus that calculates a prime candidate N larger than a known prime q and tests primality of the calculated prime candidate N, the prime calculating apparatus including:
- a prime storage unit storing the known prime q; and
a management information storage unit storing unique management information, the prime-calculation computer program comprising;
a random number generation step of reading the management information from the management information storage unit and generating random information R based on the read management information;
a candidate calculation step of reading the prime q from the prime storage unit, and calculating the prime candidate N according to N=2×
random information R×
prime q+1;
a primality testing step of testing primality of the calculated prime candidate N; and
an output step of outputting the calculated prime candidate N as a prime when the primality of the calculated prime candidate N is determined. - View Dependent Claims (22, 23)
- a prime storage unit storing the known prime q; and
Specification