arXiv subjects

Keum-Bae Cho

Publications and source records attributed to Keum-Bae Cho.

3 recordsLinked to original sources

arXiv2025

Equilibrium SAT based PQC: New aegis against quantum computing

Public-key cryptography algorithms have evolved towards increasing computational complexity to hide desired messages, which is accelerating with the development of the Internet and quantum computing. This paper introduces a novel public-key cryptography algorithm that generates ciphertexts by counting the number of elements in randomly extracted subsets from a multiset. After explaining the novel cryptographic concept, the process of mathematically refining it using satisfiability problems is described. The advantages of the proposed algorithm are: first, it is significantly faster than other public-key algorithms; second, it does not require big numbers, making it executable on any devices; and third, it can be easily extended into a public-key cryptosystem using a single public key and multiple private keys while maintaining quantum resistance.

cs.CR↗

arXiv2018

Indistinguishable binomial decision tree of 3-SAT: Proof of class P is a proper subset of class NP

This paper solves a long standing open problem of whether NP-complete problems could be solved in polynomial time on a deterministic Turing machine by showing that the indistinguishable binomial decision tree can be formed in a 3-SAT instance. This paper describes how to construct the decision tree and explains why 3-SAT has no polynomial-time algorithm when the decision tree is formed in the 3-SAT instance. The indistinguishable binomial decision tree consists of polynomial numbers of nodes containing an indistinguishable variable pair but generates exponentially many paths connecting the clauses to be used for sequences of resolution steps. The number of paths starting from the root node and arriving at a child node forms a binomial coefficient. In addition, each path has an indistinguishable property from one another. Due to the exponential number of paths and their indistinguishability, if an indistinguishable binomial decision tree is constructed in which there exist one or more paths generating an empty clause, the number of calculation steps needed to extract the empty clause is not polynomially bounded. This result leads to the conclusion that class P is a proper subset of class NP.

cs.CC↗

arXiv2018

The number system hidden inside the Boolean satisfiability problem

This paper gives a novel approach to analyze SAT problem more deeply. First, I define new elements of Boolean formula such as dominant variable, decision chain, and chain coupler. Through the analysis of the SAT problem using the elements, I prove that we can construct a k-SAT (k>2) instance where the coefficients of cutting planes take exponentially large values in the input size. This exponential property is caused by the number system formed from the calculation of coefficients. In addition, I show that 2-SAT does not form the number system and Horn-SAT partially forms the number system according to the feasible value of the dominant variable. Whether or not the coefficients of cutting planes in cutting plane proof are polynomially bounded was open problem. Many researchers believed that cutting plane proofs with large coefficients are highly non-intuitive20. However, we can construct a k-SAT (k>2) instance in which cutting planes take exponentially large coefficients by the number system. In addition, this exponential property is so strong that it gives definite answers for several questions: why Horn-SAT has the intermediate property between 2-SAT and 3-SAT; why random-SAT is so easy; and why k-SAT (k>2) cannot be solved with the linear programming technique. As we know, 2-SAT is NL-complete, Horn-SAT is P-complete, and k-SAT (k>2) is NP-complete. In terms of computational complexity, this paper gives a clear mathematical property by which SAT problems in three different classes are distinguished.

cs.CC↗