Sentence examples for integer factorization from inspiring English sources

In addition, no modification of the original discrete logarithm and integer factorization based cryptosystems is necessary.

The security of this scheme was supposed to be based on the difficulty of integer factorization.

Hashimoto and Sakurai proposed a signature scheme (HS scheme), whose security is based on the difficulty of integer factorization.

Both achieve IND-CPA and are based on the hardness of solving integer factorization and discrete logarithm problems, respectively.

Therefore, the security of the extended HS scheme is no longer based on the difficulty of integer factorization.

Since the security of HS scheme is based on the difficulty of integer factorization, the scheme defined over the ring (mathbb {Z}/Nmathbb {Z}).

It is established on number-theoretic problems allied to the stiffness of integer factoring and computing square roots modulo of composite number, which is straightforward when the factorization is familiar, but very complex when it is concealed.

It is established on number-theoretic problems allied to the stiffness of integer factoring and computing square roots modulo of composite number, which is straight forward when the factorization is familiar, but very composite when it is concealed.

However, Shor showed that factorization of integers and computation of discrete logarithm are done efficiently by using quantum computers [28].

While Deutsch's problem is rather trivial, there now exist several quantum algorithms with interesting applications, notably Shor's factorization algorithm for factoring large composite integers in polynomial time (with direct application to 'public key' cryptography, a widely used classical cryptographic scheme) and Grover's database search algorithm.

If one sets m ( 2 ) = 1 / 2, for notational convenience, then it appears that for any prime factorization of an integer greater than 2, m ( ∏ i = 1 k p i e i ) = ?