Signcryption is a new paradigm in public key cryptography that simultaneously fulfils both the functions of digital signature and public key encryption in a logically single step, and with a cost significantly lower than that required by the traditional signature and encryption approach. The main disadvantage of this approach is that, digitally signing a message and then encrypting it, consumes more machine cycles and bloats the message by introducing extended bits to it. Hence, decrypting and verifying the message at the receiver?s end, a lot of computational power is used up.

Thus you can say that the cost of delivering a message using signing-then-encryption is in effect the sum of the costs of both digital signatures and public key encryption. Is it possible to send a message of arbitrary length with cost less than that required by signature-then-encryption? Signcryption is a new paradigm in public key cryptography that simultaneously fulfils both the functions of digital signature and public key encryption in a logically single step, and with a cost significantly lower than that required by the traditional signature followed by encryption.This topic has similar mathematical content to the lecture on RSA.It requires a good understanding of the various encryption algorithms like RSA,DES algorithms.
The innovative cryptographic technique of concurrently achieving the signing and encryption with a low cost compared to that of the conventional signature and encryption approach is referred to as signcryption. This method apparently uses the mathematical calculations same as that of the RSA.