# A Fuzzy-Fuzzy Vault Scheme

## TL;DR

This paper introduces a fuzzy-fuzzy vault scheme that incorporates fuzzy set theory to enhance security by adding uncertainty and imprecision to the classical fuzzy vault, enabling more robust secret locking and unlocking.

## Contribution

The paper proposes a novel fuzzy-fuzzy vault scheme that extends the classical fuzzy vault with fuzzy set concepts, improving security through uncertainty and imprecision.

## Key findings

- Enhanced security threshold due to fuzzy theory integration
- Use of multi-fuzzy sets and membership functions for locking
- Fuzzy chaff points increase difficulty for unauthorized unlocking

## Abstract

In this paper an enhanced fuzzy vault scheme is proposed which we refer to as fuzzy-fuzzy vault scheme. The proposed scheme builds on the classical fuzzy vault by adding the concept of uncertainty and imprecision to the classical scheme. To lock a secret key K in the classical fuzzy vault the locking and unlocking elements are crisp or real elements and consequently the locking and unlocking operations are strict imperative. In the fuzzy-fuzzy vault scheme, Alice locks the secret key K using a set of fuzzy elements that belong to multi-fuzzy set A~ obtained from a universe public set of fuzzy elements in a multi-fuzzy set F~_q and projecting them on polynomial p. The elements in multi-fuzzy sets F~_q and A~ are fuzzy using m membership functions MF_i, i=1,2,...,m. Alice selects a set k of fuzzy elements fuzzy with a specific membership function MF_K from A~ to lock the vault. To hide the genuine locking points Alice generates a set of fuzzy chaff points that some of them do not lie on polynomial p while the other fuzzy chaff points may lie on polynomial p but fuzzy with different membership functions other than the membership function MF_K used to lock the vault. To unlock the fuzzy-fuzzy vault and retrieve the secret key K , Bob should have a set of unlocking fuzzy elements belonging to multi-fuzzy set B~ which substantially overlap with A~ is required. Then Bob selects t'_(TF_ki) fuzzy elements from B~ which are close to the t_(TF_k) fuzzy elements from A~ used by Alice to lock the vault. We show that adding uncertainty and imprecision by introducing fuzzy theory will enhance the security threshold of the fuzzy vault.

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Source: https://tomesphere.com/paper/1906.03043