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In order to resist the attack of quantum algorithm and deal with the defect that malicious signers can output multiple signatures using the complete anonymity of ring signature technology to carry out double overhead attack, and to solve the unnecessary waste of system overhead, this paper proposed a new identity-based linkable ring signature scheme form lattice. The scheme takes the approximate shortest vector problem on the lattice as the security basis, reduces the solution of the problem to the solution of the collision problem, generates the signature by using the linear operation between matrix vectors, and combines the identity-based cryptography technology. It solved the problem of system overhead waste, does not involve complex algorithms such as trapdoor generation and Gaussian sampling, improves the signature efficiency and reduces the storage overhead. It is verified that the scheme meets the requirements of complete anonymity and strong unforgeability under the random oracle model. After analysis, the scheme is a secure and efficient ring signature scheme. [ABSTRACT FROM AUTHOR]

In order to solve the problem that the verification key is too large in traditional ring signature scheme over lattice, and the key size varies linearly with the number of ring members. By using the algebraic structure of ideal lattice and MP12 trapdoor derivation technology, this paper constructed an efficient ring signature scheme over lattices. In this scheme, the signature consisted of a single lattice vector, and a relatively small private key, and the verification key size was close to a small constant. In the process of signature operation, this scheme reduces the computational complexity and proves the anonymity and non-forgeability of the scheme under the standard model. [ABSTRACT FROM AUTHOR]

The variational principle and the differential equations of motion for a fractional order system ate studied. The fractional Hamilton principle in terms of Riesz fractional derivatives is established, and the fractional Lagrange equations and the fractional Hamilton canonical equations are derived from the fractional Hamilton principle. In the end, an example is given to illustrate the application of the results. [ABSTRACT FROM AUTHOR]