Ciphering device, cryptographic key generation method and method of managing cryptographic key, and prime number generation device and method therefor

TL;DR: In this paper, the problem of reducing a necessary memory capacity by sequentially generating larger prime numbers based on a prime number not exceeding 2n bits and generating a second prime number having a specified bit length was solved.

Abstract: PROBLEM TO BE SOLVED: To reduce a necessary memory capacity by sequentially generating larger prime numbers based on a prime number not exceeding 2n bits and generating a second prime number having a specified bit length. SOLUTION: A random number generation part 5 generates an odd number having double bit length of a word size, and an arithmetic operation part 4 performs division for trial by using a prime number not larger than word size of the prime number table. When a generated odd number cannot be divided by all the prime numbers in the prime number table, this odd number is judged as a prime number. A parameter (i) of the following processing loop is set to zero (0). Based on a prime number Fi , a random number generation part 5 generates a random number Ri satisfying Ri <Fi to create a prime number candidate Ni expressed as Ni =2Ri Fi +1. If this can be divided by prime numbers in the prime number table, Ni is judged as a composite number, and Ri is re-generated by leaving Fi value at it is for generating a new prime candidate Ni , and it is calculated whether or not a fixed (ai ) satisfies a fixed equation. Ri is increased in the bit length and adjusted, and the prime number Ni is obtained when the prime number candidate Ni has reached a fixed bit length.