| 摘要 |
Disclosed are multivariate paraunitary asymmetric cryptographic systems and methods that are based on paraunitary matrices. An algebraic approach is employed in designing the multivariate cryptographic systems and methods. The cryptographic systems and methods are based on formulating a general system of multivariate polynomial equations by paraunitary matrices. These matrices are a family of invertible polynomial matrices that can be completely parameterized and efficiently generated by primitive building blocks. Using a general formulation that involves paraunitary matrices, a one-way function is designed that operates over the fields of characteristic two. To include a trapdoor, approximations are made to the paraunitary matrix. The result is a trapdoor one-way function that is efficient to evaluate, but hard to invert unless secret information about the trapdoor is known. An exemplary implementation operates on the finite field GF(256). In this example, the message block includes 16 to 32 symbols from GF(256), i.e., the block size n is an integer between 16 and 32. The ciphertext block takes its elements from the same field and has at least 10 extra symbols.
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