AbstractIn a strong designated verifier signature with message recovery (SDVSWMR) scheme, only the designated receiver has the capability to recover and validate the message‐signature pair. In 2015, using the bilinear pairing, Islam and Biswas presented an SDVSWMR scheme (we call it: IsBi‐SDVSWMR) with non‐delegatability, which has better performance than other schemes in terms of communication and computation cost. However, in this study, we address that IsBi‐SDVSWM scheme does not satisfy the security property of non‐delegatability as they claimed and we present two types of delegatability attack to their scheme. We also propose a new and pairing‐free SDVSWMR scheme that possesses the following security requirements: non‐delegatability, unforgeability, non‐transferability and privacy of signer's identity (PrSI). Compared our scheme with other existing related schemes, our scheme obtains better performance; that is, the computational cost is only 58%(lower) of IsBi‐SDVSWM scheme (other schemes), and the communication cost is 800 bits that is only 68%(lower) of IsBi‐SDVSWM scheme (other schemes). Copyright © 2017 John Wiley & Sons, Ltd.