New methods of generating primes secure against both P-1 and P+1 methods
Since cryptosystem based on the problem of factoring the composite number N can be attacked with P - 1 and P + 1 methods, it is required that P - 1 and P + 1 should be difficult to be factored into many small primes, where we assume that the P is a factor of N. In this paper, first, we consider the distribution of secure primes against both P - 1 and P + 1 methods. Second, we propose two efficient algorithms for generating secure primes against both P - 1 and P + 1 methods by extending the trial division method.
p+1 method trial division method prime generation p-1 method