This paper presents two fully secure functional encryption schemes: a fully secure attribute-based encryption (ABE) scheme and a fully secure (attribute-hiding) predicate encryption (PE) scheme for inner-product predicates. Both schemes use novel strategies to adapt the dual system encryption methodology introduced by Waters. The ABE scheme is constructed in composite order bilinear groups and is proven secure under three static assumptions. It supports arbitrary monotone access formulas. The PE scheme is constructed using a new approach on bilinear pairings based on the notion of dual pairing vector spaces proposed by Okamoto and Takashima. The ABE scheme is fully secure, supporting arbitrary monotone access formulas, while the PE scheme is fully secure and attribute-hiding, with adaptively secure hierarchical predicate encryption (HPE) for inner-product predicates. The results are proven under non-interactive assumptions and are efficient, comparable to existing selectively-secure schemes. The paper also discusses related work, including identity-based encryption (IBE), hierarchical IBE, and other forms of attribute-based encryption. The security proofs rely on the dual system encryption technique and the notion of dual pairing vector spaces, and the results are proven under three static assumptions. The paper provides a detailed construction of the ABE and PE schemes, including their security proofs and the use of composite order bilinear groups.This paper presents two fully secure functional encryption schemes: a fully secure attribute-based encryption (ABE) scheme and a fully secure (attribute-hiding) predicate encryption (PE) scheme for inner-product predicates. Both schemes use novel strategies to adapt the dual system encryption methodology introduced by Waters. The ABE scheme is constructed in composite order bilinear groups and is proven secure under three static assumptions. It supports arbitrary monotone access formulas. The PE scheme is constructed using a new approach on bilinear pairings based on the notion of dual pairing vector spaces proposed by Okamoto and Takashima. The ABE scheme is fully secure, supporting arbitrary monotone access formulas, while the PE scheme is fully secure and attribute-hiding, with adaptively secure hierarchical predicate encryption (HPE) for inner-product predicates. The results are proven under non-interactive assumptions and are efficient, comparable to existing selectively-secure schemes. The paper also discusses related work, including identity-based encryption (IBE), hierarchical IBE, and other forms of attribute-based encryption. The security proofs rely on the dual system encryption technique and the notion of dual pairing vector spaces, and the results are proven under three static assumptions. The paper provides a detailed construction of the ABE and PE schemes, including their security proofs and the use of composite order bilinear groups.