Signcryption is an emerging cryptographic technique provides the functionality of digital signature and encryption with significant less cost. Hyperelliptic curve cryptography is on its way from pure academic interest to industrial applications due to its efficiency and high security per bit. In this book we present six signcryption schemes based on hyperelliptic curve cryptography for confidential and authenticated message delivery. The proposed schemes fulfill all the security parameters of signcryption and equivalent in function to signature-Then-encryption technique with less computation cost and communication overhead. The proposed work is divided in three sections; in section one, proposed schemes fulfill the security parameters of signcryption, in section two proposed schemes have additional feature of forward secrecy and in section three proposed schemes have properties of forward secrecy and direct public verifiability. Proposed schemes have less computation cost, communication overhead and are suitable for restricted computation devices like mobile devices, smart card based applications and many more.