Cyphertext-only attack on the double random-phase encryption: Experimental demonstration

Hybrid plaintext attack for a cryptosystem based on interference and the phase-retrieval technique

In this paper, the security strength of an enhanced cryptosystem based on interference and the phase-retrieval technique is evaluated. The security strength of the optical cryptosystem was improved through the phase-retrieval technique used to generate a phase-only mask (POM) as the ciphertext. Due to the complex mathematical model of the phase-retrieval technique, it seems that a silhouette problem existing in the conventional interference-based scheme was removed. However, we noted that the random phase mask (RPM) regarded as the only private key was fixed in the encryption path, which is not related to the plaintext and makes it possible to be recovered using a known-plaintext attack (KPA). Moreover, we also found that the RPM has high key sensitivity, and it should be recovered precisely to retrieve information of plaintexts during the attack. Thus, a hybrid KPA where three pairs of known plaintexts and their ciphertexts are regarded as the amplitude and phase constraints to obtain the precise estimation of the RPM is proposed. Then, with the help of the estimated private key, information of the original plaintexts encoded using the cryptosystem under study could be retrieved from an arbitrarily given ciphertext without any knowledge of the private key. Our cryptoanalysis shows that the cryptosystem based on interference and the phase-retrieval technique is vulnerable to the proposed attack, and there is a security leak in it. Numerical simulations have been carried out to demonstrate the performance of our proposed attack.

Stokes meta-hologram toward optical cryptography

Optical cryptography manifests itself a powerful platform for information security, which involves encrypting secret images into visual patterns. Recently, encryption schemes demonstrated on metasurface platform have revolutionized optical cryptography, as the versatile design concept allows for unrestrained creativity. Despite rapid progresses, most efforts focus on the functionalities of cryptography rather than addressing performance issues, such as deep security, information capacity, and reconstruction quality. Here, we develop an optical encryption scheme by integrating visual cryptography with metasurface-assisted pattern masking, referred to as Stokes meta-hologram. Based on spatially structured polarization pattern masking, Stokes meta-hologram allows multichannel vectorial encryption to mask multiple secret images into unrecognizable visual patterns, and retrieve them following Stokes vector analysis. Further, an asymmetric encryption scheme based on Stokes vector rotation transformation is proposed to settle the inherent problem of the need to share the key in symmetric encryption. Our results show that Stokes meta-hologram can achieve optical cryptography with effectively improved security, and thereby paves a promising pathway toward optical and quantum security, optical communications, and anticounterfeiting.

Achieving optical cryptography scheme with both high capacity and security is highly desirable. Here, authors report a Stokes meta-hologram with a hierarchical encryption strategy that allows vector encryptions to produce depth-masked ciphertexts.

Security analysis on an interference-based optical image encryption scheme

In this paper, the security strength of the improved optical cryptosystem based on interference has been evaluated. Compared to the previous interference-based cryptosystems in which the plaintext is encoded into two phase-only masks (POMs), here the plaintext is encoded into a POM and an amplitude mask (AM). Since the information of the plaintext cannot be recovered directly when one of the masks is released in the decryption process of the improved cryptosystem, it seems that it is free from the silhouette problem. However, we found that the random phase mask (RPM) serving as the encryption key is not related to the plaintext. Thus, it is possible to recover the RPM first by using the known-plaintext attack (KPA). Moreover, the POM and the AM generated in the encryption path only contains the phase and amplitude information, respectively. Thus, these can be utilized as additional constraints in the proposed iterative process. Based on these findings, two kinds of hybrid attacks, including a KPA and the iterative processes with different constraints, are proposed to crack the improved cryptosystem. In the designed KPA with a pair of the known plaintext and its corresponding masks, the RPM is recovered first. With the aid of the recovered RPM, two iterative processes with different released masks are proposed to recover the information of the plaintext without any knowledge of another mask. To the best of our knowledge, this is the first time that the existence of the silhouette problem in the cryptosystem under study has been reported. Numerical simulation has been carried out to validate the feasibility and effectiveness of the proposed hybrid attacks.

Cryptanalysis of an optical cryptosystem with uncertainty quantification in a probabilistic model

In this paper, a modified probabilistic deep learning method is proposed to attack the double random phase encryption by modeling the conditional distribution of plaintext. The well-trained probabilistic model gives both predictions of plaintext and uncertainty quantification, the latter of which is first introduced to optical cryptanalysis. Predictions of the model are close to real plaintexts, showing the success of the proposed model. Uncertainty quantification reveals the level of reliability of each pixel in the prediction of plaintext without ground truth. Subsequent simulation experiments demonstrate that uncertainty quantification can effectively identify poor-quality predictions to avoid the risk of unreliability from deep learning models.

Asymmetric cryptosystem based on optical scanning cryptography and elliptic curve algorithm

We propose an asymmetric cryptosystem based on optical scanning cryptography (OSC) and elliptic curve cryptography (ECC) algorithm. In the encryption stage of OSC, an object is encrypted to cosine and sine holograms by two pupil functions calculated via ECC algorithm from sender’s biometric image, which is sender’s private key. With the ECC algorithm, these holograms are encrypted to ciphertext, which is sent to the receiver. In the stage of decryption, the encrypted holograms can be decrypted by receiver’s biometric private key which is different from the sender’s private key. The approach is an asymmetric cryptosystem which solves the problem of the management and dispatch of keys in OSC and has more security strength than the conventional OSC. The feasibility of the proposed method has been convincingly verified by numerical and experiment results.

Noninvasive imaging of two isolated objects through a thin scattering medium beyond the 3D optical memory effect

A speckle image formed by scattering lights can be decoded by recently invented techniques, owing to the optical memory effect, thereby enabling the observation of a hidden object behind a thin scattering medium. However, the range of three-dimensional OME is typically small; therefore, both the field of view and depth of field are limited. We propose a method that can significantly and simultaneously improve both values for a specific scenario, where one object moves around the other position-fixed object. The effectiveness of the proposed scheme is demonstrated through a set of experiments.

Single-shot three-dimensional imaging with a scattering layer [Invited]

In this paper, we propose a single-shot three-dimensional imaging technique. This is achieved by simply placing a normal thin scattering layer in front of a two-dimensional image sensor, making it a light-field-like camera. The working principle of the proposed technique is based on the statistical independence and spatial ergodicity of the speckle produced by the scattering layer. Thus, the local point responses of the scattering layer should be measured in advance and are used for image reconstruction. We demonstrate the proposed method with proof-of-concept experiments and analyze the factors that affect its performance.

Recovery of the topological charge of a vortex beam propagated through a scattering layer

Coherent vortex beams have shown great potential in many applications including information transmission under non-ideal conditions, as information can be encoded in the orbital angular momentum. However, inhomogeneity of atmosphere tends to scramble the vortex structure and give rise to speckle. It is therefore of great interest to reconstruct the topological charge of a vortex beam after it propagates through a scattering medium. Here, we propose a feasible solution for this. The proposed method measures holographically the scattered field and reconstructs the spiral phase from it by taking advantage of both the deterministic nature and the ergodicity of the scattering process. Our preliminary experiments show promising results and suggest that the proposed method can have great potential in information transmission under non-ideal conditions.

Security-enhanced optical cryptosystem using nonergodic scrambling phase mask

Cryptanalysis revealed a security flaw in the double random phase encoding (DRPE) system, and the original image was recovered via a ciphertext-only attack. In this paper, a nonergodic scrambling phase mask (NESPM) is designed, and a security-enhanced cryptosystem is established by replacing the bonded random phase mask (RPM) in the DRPE system with the designed NESPM. The original image in the security-enhanced cryptosystem is optically scrambled at "macropixel" level by the bonded NESPM, instead of being diffused by the RPM, as in the DRPE system. Due to such a scrambling operation, the ergodic property of the Fourier-plane speckle pattern in the designed cryptosystem is removed, and the original image cannot be recovered via the attack. Experimental results demonstrate that the designed cryptosystem is resistant to the attack. Security enhancement is achieved.

Known-plaintext attack to optical encryption systems with space and polarization encoding

Space-based optical encryption (SBOE) and double random polarization encoding (DRPO) are previously considered to be more secure than common random-phase-encoding-based optical cryptosystems. The known-plaintext attack (KPA) to SBOE and DRPO was seldomly investigated in the past. A matrix regression approach based on training samples is proposed in this paper to crack these two optical cryptosystems. The relationship between plaintexts and ciphertexts is directly modeled by a complex-amplitude weighting matrix, which is optimized by a gradient descent algorithm. This approach has a simple model compared with deep learning and the KPA can be implemented without recovering the exact key. Our proposed KPA schemes reveal the security flaws of SBOE and DRPO, as well as other linear optical cryptosystems.

Chosen-plaintext attack on the double random polarization encryption

Images can be optically encrypted by random encoding in the phase, the polarization, or even the coherence of a light field. It is important for these optical encryption methods to undergo rigorous cryptanalysis. However, only phase-encoding-based encryption has been rigorously analyzed to date. In this manuscript, we demonstrate that the double random polarization encryption (DRPolE) is vulnerable to chosen-plaintext attack (CPA). We show that the keys can be retrieved if one can choose the polarization states of two plaintext images and collect the corresponding cyphertext images. Our study reveals a serious concern regarding the DRPolE that should be addressed in the design of polarization-based optical encryption methods.

Cryptographic key distribution over a public network via variance-based watermarking in compressive measurements

Optical communication has an increasing need for security in public transmission scenarios. Here, we present a protocol for cryptographic key distribution over a public network via a photon-counting compressive imaging system with watermarking, which utilizes a watermarking technique to distribute secure keys, and uses reconstructed images for simultaneous identity authentication and tampering identification. The watermark is embedded in the rearranged compressed measurements of the object, and then the signal is transmitted through a public network. At the receiving terminal, legitimate users can easily extract the watermark as the cryptographic key by using initial keys and the variance characteristic of random measurements. Artificial tampering and attacks can be detected by accurately retrieved images. The realization of this protocol is a step forward toward practical applications, and will be beneficial for the broader fields of optical security in many ways.

Noninvasive three-dimensional imaging through scattering media by three-dimensional speckle correlation

We present a method for noninvasive three-dimensional imaging through scattering media by using a three-dimensional memory effect in scattering phenomena. In the proposed method, an object in a scattering medium is reconstructed from a three-dimensional autocorrelation of speckle images captured by axially scanning an image sensor, based on a three-dimensional phase retrieval algorithm. We experimentally demonstrated our method with a lensless setup by using a three-dimensionally printed object between diffusers.

Cryptoanalysis on optical image encryption systems based on the vector decomposition technique in the Fourier domain

In this paper, the security of optical cryptosystems based on the vector decomposition technique in the Fourier domain is analyzed. Compared to the conventional cryptosystem based on the equal modulus decomposition (EMD) technique, an additional EMD structure is introduced in the cascaded EMD-based cryptosystem; hence, the mask including the phase information of the Fourier spectrum is further encoded in the second EMD structure to enhance the security level. However, it is shown that the number of the private keys has not been increased in the cascaded EMD-based cryptosystem, which makes it possible to crack the cascaded EMD-based cryptosystem. Therefore, a chosen-plaintext attack (CPA) and a special attack with an arbitrarily given private key are proposed to retrieve information from encoded images obtained by the cascaded EMD-based cryptosystem. In addition, the security of the cryptosystem based on the random modulus decomposition (RMD) technique is also analyzed. Compared to the EMD-based cryptosystem in which the Fourier spectrum is decomposed into two vectors with equal moduli, the security level of the cryptosystem has been improved by using the RMD technique to decompose the spectrum into vectors with unequal moduli to decrease the number of the amplitude constraints. However, it is found that the arbitrarily given ciphertext provides the attackers enough information to retrieve the precise information of the plaintext without any knowledge of the private keys. A special attack is proposed to crack the RMD-based cryptosystem. This is the first time to report that these two cryptosystems based on the vector decomposition technique are attacked successfully. Numerical simulation is conducted to validate the feasibility and effectiveness of the proposed attacks.

Image Transmission through Scattering Media Using Ptychographic Iterative Engine

Random scattering media prevent light information from directly transmitting through, them as the photons will deviate from their original propagation directions due to the inhomogeneity of the refractive index distribution in scattering media. Based on recent developed methods, light information transmission through scattering media is realized using a memory effect. However, the memory effect range limits it to a small field of view. To enlarge the field of view, in this article, we propose to use the ptychographic iterative engine to deliver information through scattering media. We experimentally demonstrate that the proposed method can deliver images beyond the memory effect range through the scattering layer with outstanding imaging performance.

Cyphertext-only attack on the joint-transform-correlator-based optical encryption: experimental demonstration

A cyphertext-only attack (COA) on a joint transform correlator encryption system is proposed. Under the proposed COA scheme, the energy spectral density of plaintext can be calculated with cyphertext, and then plaintext information can be recovered by using a phase retrieval algorithm such as the hybrid input-output algorithm. We also numerically and experimentally demonstrate the COA to verify feasibility of the proposed technique.

Hybrid attack on an optical cryptosystem based on phase-truncated Fourier transforms and a random amplitude mask

In this paper, the security of a cryptosystem based on phase-truncated Fourier transforms (PTFTs) and a random amplitude mask (RAM) is evaluated. In the cryptosystem, fake keys used as encryption keys in the second PTFT-based structure are generated by the first PTFT-based structure in which the RAM is encoded by random phase masks (RPMs) used as public keys. Compared to the classical PTFT-based encryption scheme, the security level of the cryptosystem is improved by using cascaded PTFTs to encode the encryption keys and the plaintext simultaneously. However, it is found that a known plaintext-ciphertext pair can provide enough constraints in the iterative process to retrieve the fake keys, which then can be used to retrieve unknown arbitrary plaintext from the corresponding ciphertext. Based on the analysis, we propose a specific attack based on hybrid iterative processes to break the cryptosystem. Two iterative processes with different constraints are involved in the proposed attack. The first known-plaintext-attack (KPA)-based iterative process is used to retrieve two fake keys with the help of two public keys and a known plaintext-ciphertext pair, while the second amplitude-phase retrieval algorithm-based iterative process with a median filter is employed to retrieve the plaintext from the corresponding ciphertext using two retrieval fake keys. To the best of our knowledge, it is the first time that the cryptosystem is attacked by the KPA-based iterative algorithm successfully. Numerical simulation results validate the feasibility and effectiveness of the proposed attack.

Imaging through scattering media with the auxiliary of a known reference object

Imaging through scattering media has been one of the main challenges in optics, and are encountered in many different disciplines of sciences, ranging from biology, mesoscopic physics to astronomy. Recently, various methods have been proposed. In this manuscript, we propose a robust method for imaging through scattering media in a reflective geometry, a scenario widely encountered in non-invasive and marker-free biological imaging. The proposed method relies on the a priori information of a known reference object in the neighborhood of the target, and uses it as an auxiliary to reconstruct the target image. We show that the target image can be analytically reconstructed from the autocorrelation of the recorded speckle if the reference is point-like, otherwise, deconvolution with the reference speckle should be performed. We experimentally demonstrate the proposed method in a proof-of-concept system with an LED illumination through a thick ground glass.

Adaptive lens-free computational coherent imaging using autofocusing quantification with speckle illumination

Multi-distance phase retrieval (MDPR) based lensfree imaging is promising for an aberration free and compact biological imaging system. In the MDPR processing, the measurement uncertainty of the sample-to-sensor distance undermines its imaging quality and imposes a heavy workload to achieve a perfect reconstruction. The optimal distance can be searched by using an image sharpness quantification function with a refocused data set, however, the scanning is sensitive to noise and aliasing artifact for MDPR. In this work, we propose an adaptive imaging scheme with the help of a diffuser inserted in the lensfree system. The optimal sample-to-sensor distance is searched by combing speckle imaging with sharpness quantification function. With this speckle-based auxiliary, intensity patterns under a coherent illumination are directly used to achieve an in-focusing image reconstruction. Experiments are given to demonstrate the stability, imaging resolution and optical sectioning for our scheme. This method provides a simple, stable and robust tool for the auto-focusing imaging.

Special ciphertext-only attack to double random phase encryption by plaintext shifting with speckle correlation

In this paper, a special ciphertext-only attack (COA) scenario to the traditional double random phase encoding (DRPE) technique is proposed based on plaintext shifting. We assume the attacker can illegally manipulate the DRPE system to gain multiple ciphertexts from randomly shifted versions of the same plaintext. The plaintext image can be recovered when our proposed scenario is combined with a speckle correlation attacking method proposed in previous work. Simulation results demonstrate that our proposed scheme can successfully crack the DRPE system even when the speckle correlation method alone fails to work in the conventional single ciphertext scenario due to the small size of the plaintext image. The work in this paper reveals a severe security flaw of DRPE systems when minor position shifting of the plaintext occurs.

Experimental optical encryption of grayscale information

In this paper, we present a new protocol for achieving lower noise and consequently a higher dynamic range in optical encryption. This protocol allows for the securing and optimal recovery of any arbitrary grayscale images encrypted using an experimental double random phase mask encoding (DPRE) cryptosystem. The protocol takes advantage of recent advances that help reduce the noise due to the correlation of random phase mask in the decryption procedure and introduces the use of a "reference mask" as a reference object used to eliminate the noise due to the complex nature of the masks used in experimental DRPE setups. This noise reduction increases the dynamic range of the decrypted data, retaining the grayscale values to a higher extent and opening new possible applications. We detailed the procedure, and we present the experimental results, including an actual experimental video of a grayscale scene, confirming the validity of our proposal.