They furthermore answer the question of why the quantum algorithm
beats any comparable classical circuit: The quantum algorithm
exploits the non-locality of quantum physics.
However, Shor's quantum algorithm
reveals that the DLP can be solved in polynomial time .
In 1994, mathematician Shor has proposed the quantum algorithm
 by which the integer factorization problem and the discrete logarithm problem can be efficiently solved in polynomial time.
In 1994, Peter Shor invented a fast quantum algorithm
for factoring numbers.
In 1994, Shor first proposed the quantum algorithm
"The massive processing capabilities found in Quantum computers will challenge our current beliefs around complexity and security," said Michael Brown, CTO at ISARA Corporation, posing the case for 'Quantum safe cryptography', which is resistant to quantum algorithm
"A good example of this is giving users the ability to tune the quantum algorithm
to improve application performance."
Shor  proposed the first quantum algorithm
based on the quantum concurrent computation in 1994 and used it to solve the large prime factorization.
can solve some classical nonpolynomial problems in polynomial time and has many advantages of the superposition, coherence, and entanglement of the quantum state.
Recently, a quantum encryption algorithm has been proposed but it has been noticed that the quantum encryption algorithm is very similar to the classical encryption algorithm with the crucial difference that the quantum algorithm
is based on quantum laws whilst the classical algorithms are based on mathematical ones [4-7].
Considering that Shor's quantum algorithm
and its extension work well over some commutative groups, such as the multiplication group [Z.sup.*.sub.n], the multiplication group [F.sup.*.sub.q], and the addition group over elliptic curves on finite field [F.sub.q], and we have already known efficient quantum algorithms
for hidden group problems (HSP) over all commutative groups, a lot of attempts on developing cryptosystems are based on noncommutative algebraic structures.