## 4 Analysis
### Safety Consideration  
#### 4.3.1 Security against Conspiracy Attacks  
A trusted authority, which securely stores the master key in attribute-based authorization encryption, is an institution that is fully trusted. Proxy is an institution that can be semitrusted. In other words, it is necessary to create a secret key share of the delegated person, generate a re-encryption statement, and distribute it honestly to users. However, it is unreliable in that no information about plaintext should be known.  
Through a security game between an attacker and a user (challenger), an attribute-based authorization delegation encryption technique may know semantic security. Semantic security means that an attacker cannot acquire any information about plaintext when creating a given ciphertext using a ciphertext and a public key.  
Security games have the following requirements. First, it should be possible to prevent conspiracy attacks between users. That is, two or more users should not be able to combine their attribute sets in order to extend their decoding authority. Second, it should be possible to prevent conspiracy attacks by authority reviewers and users. Users and authority reviewers who do not have a secret key satisfying the access policy must not be able to decrypt the ciphertext in malicious cooperation. Finally, the delegated secret key (the secret key created by the delegator for the delegate) should not jeopardize safety. Safety should not be compromised by the delegated secret key, such as deriving the master key of the certification authority using the delegated secret key.  
The most important security feature of attribute-based encryption is the safety against conspiracy attacks. A conspiracy attack is a combination of two or more users' attribute sets to extend their decryption rights.  
For example, there is a ciphertext consisting of the access structure \"A\". The user A's secret key consists of the attribute set \"B\", and the user B's secret key consists of the attribute set \"C\". A public offering attack is to generate a secret key related to \"D\" by combining the secret key of user A and user B to view a ciphertext composed of the access structure \"E\".  
This proposed method is based on the safety of the attribute-based authorization delegation encryption technique against conspiracy attacks. Attribute-based authorization delegation encryption techniques are safe against conspiracy attacks that combine secret keys related to attribute sets. This is because the key generation algorithm generates a unique identifier \"F\" for each user as an arbitrary random number and is inherent in the secret key (e.g., user's secret key share). That is, since each user cannot know \"A\" determined by an arbitrary random number by the certification authority, the secret key cannot be combined for a public offering attack. Therefore, the proposed system is safe from public offering attacks that combine secret keys between users.  
Moreover, it is also safe from conspiracy attacks between the authority reviewer and the user. For example, assuming that user B conspires with a malicious authority reviewer to convert user A's ciphertext into his ciphertext, user A must generate an attribute conversion key \"G\" that delegates access rights to user B in order for [PERSON] to convert the ciphertext. If the attribute conversion key is not generated, re-encryption is not performed. Therefore, the proposed system is also safe against conspiracy attacks between the authority reviewer and the user.