Formalization of Polynomially Bounded and Negligible Functions Using the Computer-Aided Proof-Checking System Mizar

In recent years, formal verification applications have attracted significant attention. In particular, verification of the security of cryptosystems has been investigated extensively. In this study, we attempt to develop various mathematical libraries for cryptology using the Mizar proof checking system. Polynomially bounded and negligible functions play very important roles in cryptology. Therefore, we introduce formalized definitions of polynomially bounded and negligible functions for formalizing cryptology in Mizar.

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