Nowadays usage of cloud computing is increasing in popularity and this raises new data protection challenges. In such distributed systems it is unrealistic to assume that the servers are fully trusted in enforcing the access policies. Attribute Based Encryption (ABE) is one of the solutions proposed to tackle these trust problems. In ABE the data is encrypted using the access policy and authorized users can decrypt the data only using a secret key that is associated with their attributes. The secret key is generated by a Key Generation Authority (KGA), which in small systems can be constantly audited, therefore fully trusted. In contrast, in large and distrusted systems, trusting the KGAs is questionable. This paper presents a solution which increases the trust in ABE KGAs. The solution uses several KGAs which issue secret keys only for a limited number of users. One KGA issues a secret key associated with user's attributes and the other authorities issue independently secret keys associated with generalized values of user's attributes. Decryption is possible only if the secret keys associated with the non-generalized and generalized attributes are consistent. This mitigates the risk of unauthorized data disclosure when a couple of authorities are compromised.