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 [2].

In 1994, mathematician Shor has proposed the

quantum algorithm [10] 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 [20].

"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 attack.

"A good example of this is giving users the ability to tune the

quantum algorithm to improve application performance."

Shor [17] proposed the first

quantum algorithm based on the quantum concurrent computation in 1994 and used it to solve the large prime factorization.

Quantum algorithm 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.