In attribute-based proxy re-encryption (AB-PRE) and attributebased conditional proxy re-encryption (AB-CPRE) systems, the proxy transforms a ciphertext associated with policy f to a ciphertext associated with policy g or transforms a ciphertext for delegator satisfying a fine-grained condition to a ciphertext for delegatee. However, such PRE schemes have found many practical applications requiring fine-grained access control while keeping flexible delegation. Unfortunately, the existing PRE

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... mes are impossible to handle simultaneously with the above scenarios. In this work, we introduce the notion of conditional attribute-based proxy re-encryption (CAB-PRE), which enables a proxy only to transform a ciphertext associated with policy f meeting the special delegation requirements by delegator to a ciphertext associated with policy g. We formalize its honestly re-encryption attacks (HRA) security model that implies CPA-secure, giving a concrete CAB-PRE scheme based on learning with errors (LWE) assumption. Finally, we show that CAB-PRE implies AB-PRE and AB-CPRE notions, and propose their constructions.