Formalizing the Relationship Between Commitment and Basic Cryptographic Primitives

Signcryption is a cryptographic primitive which offers the functionality of both digital signature and encryption with lower combined computational cost. On the other hand, commitment scheme allows an entity to commit to a value, where the entity reveals the committed value later during a decommit phase. In this paper, we explore the connection between commitment schemes, public key encryption, digital signatures and signcryption. We establish formal relationship between commitment and the other primitives. Our main result is that we show signcryption can be used as a commitment scheme with appropriate security notions. We show that if the underlying signcryption scheme is IND-CCA2 secure, then the hiding property of the commitment scheme is satisfied. Similarly, we show that if the underlying signcryption scheme is unforgeable, then the relaxed biding property of the commitment scheme is satisfied. Moreover, we prove that if the underlying signcryption scheme is NM-CCA2, then the commitment scheme is non-malleable.