# Asymmetric Encryption of Invisible Structured Light 3D Imaging
## 1 Introduction
In this method, the double random phase encryption key is encoded into the encoding key through the Rivest-Shamir-Adelman (RSA) public key encryption algorithm, which is subsequently used to modulate the amplitude of the image for encryption. [PERSON] et al. proposed a hybrid cryptosystem, combining double random phase coding (DRPE) and two-step phase-shifting interferometry (2-PSI) for the encryption of an image into two interferograms, and then used three pairs of public and private keys to encode and decode the session key (geometric parameters, the second random phase mask) and the interferogram [23]. On the other spectrum of encryption, [PERSON] et al. proposed a social network privacy data aggregation encryption method based on matrix decomposition [24]. With this method, the Shamir threshold segmentation scheme is adopted to improve the security of matrix decomposition followed by network user attributes encryption. Similarly, [PERSON] et al. proposed a learning-based reversible encryption network (IENet) for optical image encryption [25]. The method uses IENET for the encryption of the pure phase hologram, which has a large number of key parameters and strong key sensitivity. Compared with the RSA algorithm, the elliptic curve cryptography (ECC) algorithm proposed by [PERSON] [26] and [PERSON] [27] requires a smaller number of parameters with a similar security strength [21; 22]. Specifically, the ECC algorithm with a 600 bit key has the same security level as the 21,000 bit RSA system [21]. Therefore, elliptic curve cryptography is attractive in mobile computing because of its small key. While lightweight in computation, it has been proved that it will take an attacker a significant amount of time to solve the elliptic curve discrete logarithm problem. Because of these advantages, it is not surprising that researchers have used elliptic curve cryptography in optical encryption systems [28; 29; 30]. An evident gap exists regarding the encryption of three-dimensional data. Efforts have been made toward this. [PERSON] et al. proposed a three-dimensional object image encryption system based on the optical heterodyne technology and biological fingerprint key. Using this method, the three-dimensional multi depth object image can be encrypted into a complex encrypted hologram. Then, by associating the encrypted hologram with a set of pinhole holograms, the three-dimensional object image is recovered from the encrypted hologram. The limitation of the method is that the encrypted data is pseudo three-dimensional with different sections. For the encryption of three-dimensional data, structured light projection is an option for realizing the encrypted transmission of real three-dimensional objects [31]. This paper proposes a new imaging method based on the combination of invisible structured light 3D imaging technology and elliptic curve cryptography. This innovative method relies on elliptic curve encryption to ensure the security of three-dimensional object information transmission. This method can effectively suppress the interference from background light by introducing invisible structured light. In the proposed scheme, an invisible structured light is projected on the target plane and three-dimensional object to generate eight fringe patterns. The eight fringe patterns and two random pattern keys are used as the input of the elliptic curve encryption system, which generates eight corresponding ciphertexts. The encryption keys are two random images. The advantage of using elliptic curve cryptography is that it is asymmetric, so the security of the encryption scheme is higher than that of the symmetric encryption scheme. Compared with the traditional structured light 3D imaging system, our imaging system has the following advantages. First, the combination of cryptography and optics provides a new insight for the application of laser 3D imaging technology in information security systems.