Quantum key distribution (QKD) uses quantum mechanics to guarantee secure communication. It enables two parties to produce a shared random secret key known only to them, which can then be used to encrypt and decrypt messages. QKD is a research hotspot of international academia in recent years. We introduce some protocols: BB84 protocol, E91 protocol, SARG04 protocol.

In this paper, various polynomial representations of strange classical Lie superalgebras are investigated. It turns out that the representations for the algebras of type P are indecomposable, and we obtain the composition series of the underlying modules. As modules of the algebras of type Q , the polynomial algebras are decomposed into a direct sum of irreducible submodules. superalgebras have attracted a number of mathematicians' attention. Javis and Murray [9] obtained the Casimir invariants, characteristic identities, and tensor operators for the strange Lie superalgebras. Moreover, Nazarov [11] found Yangians of the superalgebras. In [2], Frappat, Sciarrino and Sorba studied Dynkin-like diagrams and a certain representation of the strange superalgebra P (n). In addition, they [3] gave a certain oscillator realization of the strange superalgebras. Medak [13] generalized the Baker-Campbell-Hausdorff formula and used it to examine the so-called BCH-Lie and BCH-invertible subalgebras in the Lie superalgebra P (n). Penkov and Serganova [20] discovered a surprising phenomena that the multiplicity of the highest weight in the finite-dimensional irreducible representations of q(n) is in general greater than 1. Gruson [8] computed the cohomology with trivial coefficients for the strange Lie superalgebras. Palev and Van der Jeugt [19] found a family of nongraded Fock representations of the Lie superalgebra Q(n). Gorelik [5] obtained the center of the universal enveloping algebra of the Lie superalgebra of type P . Serganova [21] determined the center of the quotient algebra of the universal enveloping algebra of the Lie superalgebra of type P by its Jacobson radical and used it to study the typical highest weight modules of the algebra. Medak [14] proved that each maximal invertible subalgebra of P (n) is Z-graded.Moon [15] obtained a "Schur-Weyl duality" for the algebras of type P . Martinez and Zelmanov [12] classified Lie superalgebras graded by P (n) and Q(n). Brundan [1] found a connection between Kazhdan-Lusztig polynomials and character formulas for the Lie superalgebra q(n). Gorelik [6] obtained the Shapovalov determinants of Q-type Lie superalgebras. Stukopin [22] studied the Yangians of the strange Lie superalgebra of type Q by Drinfel'd approach. Gorelik and Serganova [7] investigated the structure of Verma modules over the twisted affine Lie superalgebra q(n) (2) .One way of understanding simple Lie algebras and simple Lie superalgebras is to determine the structure of their natural representations. Canonical polynomial irreducible representations (also known as oscillator representations in physics (e.g., cf. [4])) of finitedimensional simple Lie algebras are very important from application point of view, where both the representation formulas and bases are clear. In [10], we determined the structure of certain noncanonical polynomial representations of classical simple Lie algebras, in particular, their irreducible submodules. In this paper, we want to generalize the above results to the strange simple ...

The Bit Commitment (BC) is an important basic agreement in cryptography . The concept was first proposed by the winner of the Turing Award in 1995 ManuelBlum. Bit commitment scheme can be used to build up zero knowledge proof, verified secret sharing, throwing coins etc agreement.Simultaneously and Oblivious Transfer together constitute the basis of secure multi-party computations. Both of them are hotspots in the field of information security. We investigated unconditional secure Quantum Bit Commitment (QBC) existence. And we constructed a new bit commitment model – double prover bit commitment. The Quantum Bit Commitment Protocol can be resistant to errors caused by noise.