Data hiding is frequently termed steganography, which is very close to cryptography. The purpose of cryptography is to make messages unintelligible so that only the intended receiver who posses the secret keys can recover the messages. Sometimes, it may be desirable to achieve security and privacy by masking the messages instead of encrypting it. This problem is addressed by steganography, which has.been used in spy applications. If Alice (spy in a foreign country) wants to send messages abroad, she will use a local communication channels. On the assumption that the communication channel is monitored all the time hence, sending an encrypted messages would raise suspicion in her. Therefore, Alice would prefer to use steganographic technique rather than a cryptographic one. An embedding algorithm, based on elliptic curve has been presented to provide both data encryption and data hiding in digital images.