Public Key Cryptology Based On The Semi-Trapdoor One-way Function

In 1976,Diffie and Hellman published the famous paper "The New Direction of Cryptography" and introduced the concept of "public key cryptography." In 1978,MIT's three scholars Ron Rivest,Adi Shamir,and Leonard Adleman published papers based on this concept,and introduced RSA public key cryptography.At present,supported by financial policies of various countries and governments,quantum computing is developing at a fairly rapid rate.Once quantum computer of the US and Europe has emerged silently,the various cryptographic algorithms currently used in various industries will no longer be secure,cybersecurity in China and other countries will be under invisible threats,and there will be no security at all.This paper first introduces the related concepts of the semi trapdoor one-way function,and the relevant knowledge about how to use the semi-trapdoor one-way function to construct of the password and choose the “Subset Sum Problem” which quantum computing is not good at,by constructing a “semi-super-incremental backpack vector” and using the intractability and solvability of the SSP to take into account “unidirectionality” and “trapdoority” to design the “semi-trapdoor one-way function(STOF,semi-Trapdoor One-way Function)”.In order to ensure the uniqueness of decryption,the vast majority of backpack encryption schemes are based on USSP.In general,the vector in this type of backpack password needs to meet the USS condition and also has a certain backpack density to resist low.Density attack,this article explained the principle of low-density attacks and related issues,and in the later design of backpack passwords,focuses on the backpack password vector density in the program experiments and analysis,and gives experimental data.After discovering that there is a security problem in the scheme of using its "superincremental backpack vector" for its super-incremental construction,wetransformed the vector indefinitely so that it no longer has semi-incrementality.Then give the list of function functions to verify the instance.The improved semi trapdoor one-way function no longer satisfies the uniqueness of inversion.By using a pair of “complementary” semi-trapdoor one-way functions to encrypt messages and then use their complementarity to decrypt the ciphertext we implemented the encryption scheme STOF_A,then we analyzed the correctness and uniqueness of the STOF_A decryption.It is inferred experimentally that when n is large enough,the STOF_A can satisfy the decryption uniqueness.Based on STOF_A,this paper designs another "double backpack" scheme STOF_B.This scheme makes the decryption process orderly,that is,a specific half bit must be solved before the other half bit can be solved.By using a specific half bit,a more random backpack vector is constructed,it greatly increases the difficulty of deciphering the solution.