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Method of generating proven prime numbers suitable for being implemented in a smart card

  • US 9,577,826 B2
  • Filed: 12/12/2012
  • Issued: 02/21/2017
  • Est. Priority Date: 12/15/2011
  • Status: Active Grant
First Claim
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1. A cryptographic method implemented in an electronic device, the method comprising operations of:

  • (a) generating a candidate prime number from another prime number in accordance with;


    Pr=2

    R +
    1,where Pr is the candidate prime number, P is a prime number having a number of bits lower than a desired number of bits of the candidate prime number, and R is an integer, wherein a size in number of bits of the candidate prime number is equal to a margin of one bit to three times a size of the prime number;

    (b) calculating a quotient of an integer division of the integer by the prime number;

    (c) rejecting the generated candidate prime number in response to detecting that the quotient of the integer division of the integer by the prime number is even;

    (d) applying the Pocklington primality test to the candidate prime number;

    (e) storing, in a memory of the electronic device, the candidate prime number as a proven prime number in response to passing the Pocklington primality test, else generating a new candidate prime number and performing operations (b) to (e) again with the new candidate prime number;

    (f) generating, from the proven prime number, a cryptographic key; and

    (g) performing, by the electronic device using the cryptographic key, a cryptographic operation on data, the cryptographic operation being one of an encryption operation, a decryption operation, or a verification of a digital signature included in the data.

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