Novel multiple-image encryption with ultrafast light springs

Abstract

This research proposed a novel multiple-image encryption scheme using ultrafast light springs. The encryption process begins with the random phase encoding of input images, followed by multiplication with distinct orbital angular momentum (OAM) modes. The modulated signals are then processed using a 4-f ultrashort pulse shaper. The dynamic optical amplitude and phase control of the signal was achieved via a liquid crystal–based spatial light modulator (SLM). The resulting light springs, characterized by helical phase and intensity profiles, are generated through the superposition of multiple laser frequency components. The integration of a double random phase encoding (DRPE) with tailored pulse-shaping operations has further converted the encrypted images to ultrashort pulse springs. This approach extends the temporal characteristics of OAM multiplexing encryption, significantly enhancing the system’s encryption capability, key space, and security. The performance of the proposed system is evaluated using multiple security metrics including key sensitive analysis, entropy analysis, correlation analysis, and resistance to attacks. The systematic evaluation demonstrated robustness of this encryption technique and highlighted its potential applications for optical image encryption and real-time secure communication.

Introduction

Optical encryption technology has emerged as a powerful solution for parallel high-dimensional information processing, offering unparalleled advantages in speed and security^1–3. Optical encryption has been benefited from the earlier work of Refregier and Javidi in the 1990s, who demonstrated that double random phase encoding (DRPE) could transform original images into stationary white noise for information encryption⁴. Subsequently, numerous derivative techniques have been proposed including Fresnel transform⁵, fractional Fourier transform⁶, Hartley transform⁷, Gyrator transform⁸, and wavelet domains⁹. Meanwhile, previous research has further explored the use of other imaging system for optical encryption including digital holography¹⁰, optical scanning holography^11,12, ptychography¹³, and ghost imaging¹⁴, which have strengthened the scientific merits of the optical encryption. Although several dynamic encryption schemes based on spatial light modulators (SLM) have been developed to realize video or sequential image encryption^15–18, many conventional optical cryptosystems are still proposed for single-image processing in a single frame, which limits the encryption capacity and efficiency for multi-image parallel tasks required in manufacturing, banking, and medical applications. This limitation therefore motivates our development of a highly efficient multiple-image encryption framework.

Our multiple-image encryption system is motivated by the rich degrees of freedom associated with orbital angular momentum (OAM) of light therefore suitable for optical encryption^19,20. OAM modes offer physically unlimited orthogonal states for information multiplexing characterized by helical wavefronts exp(ilθ), where l and θ denote topological charge and azimuthal angle respectively. This unique property has enabled successful applications in optical communications^21,22 and optical trapping²³. With OAM technique, researchers have developed multiplexing strategies including wavelength²⁴, position²⁵, space²⁶, angular²⁷, phase mask²⁸, and multiplexed holography^29,30. Earlier work has shown the promise for using OAM in multi-image encryption^31–34. Furthermore, the doughnut-shaped intensity profile and helical phase structure of vortex beams provide additional degrees of freedom for mode division multiplexing. Recent innovations include Cheng’s elliptical-channel OAM multiplexing for enhanced data storage³⁰, Zhang’s multi-dimensional holography for capacity expansion³¹, and Yuan’s frequency-shift augmented encryption scheme³². Recently, significant breakthroughs have been achieved in the experimental verification of OAM-based structured light encryption: as the core carrier of OAM technology, vector vortex beams and their arrays are widely used for high-security information encoding, with multiple experimental implementations demonstrating robust performance³⁵ and further confirming OAM’s potential in multi-dimensional multiplexing encryption. Specifically, arrayed vector vortex beams have been experimentally validated for real-time audio encryption via topological charge multiplexing and intensity-based decoding³⁶. Parallelly, single-shot intensity recording based on structured light’s binary polarization states enables experimental color image encryption, offering a cost-effective, speckle-free scheme compatible with partially coherent sources³⁷ that supports the practical application of OAM-based encryption. These developments underscore OAM’s potential for high-security, ultra-large capacity encryption systems. Our research is further motivated by the unique spatial-temporally correlated optical encryption leveraging the emerging feature of the special OAM structural light. For this, the spatio-temporally correlated Light Springs (LS) has been used, which encode frequency correlations through superposed Laguerre-Gaussian (LG) modes^38,39. As a novel class of ultrafast OAM-carrying beams, LS exhibits matched helical structures in both intensity and phase profiles. This distinctive characteristic has enabled breakthroughs in frequency Raman amplification³⁹, super-resolution imaging⁴⁰, and information coding⁴¹. Yang et al. demonstrated that the precise control of LS intensity distribution and azimuth angle could substantially increase information capacity⁴¹, while ultrafast pulse shaping techniques offer additional coding dimensions^42–45. Despite these advances, previous research has not explored the use of LS for large-capacity multiple-image optical encryption, which is a critical gap to be filled by our research.

In this study, we present a novel multiple-image encryption technique that synergistically integrates ultrafast LS with DRPE system. Our approach makes three key contributions. First, we have implementation a novel encryption scheme of leveraging LS parameters (combined with DRPE and pulse shaping) to enhance encryption robustness. Second, we have developed a multi-functional ultrashort pulse shaper capable of simultaneous pulse shaping and image encryption. Third, we have used spatio-temporal light spring to expand the multiplexing encryption capabilities. Simulation validation confirms our system’s ability to achieve parallel encryption of multiple images with exceptional security, noise resistance, and resilience against attacks.

Principle and methods

Principle of LS

Light spring laser is a novel type of spatio-temporally coupled beam generated by the superposition of LG modes, where the azimuthal mode index l is linearly correlated with the frequency ω as

1

where ω₀ is the central frequency corresponding to the modal index l₀, Δω is the spectral width of the pulse, and Δl denotes the variation of the model index across Δω. The spatio-temporal correlation induces a helical beat wave in the intensity profile, with a temporal pitch given by τ_p = 2πΔl/Δω³⁴. The most distinctive feature of an LS is its spiral phase and intensity structure, which introduces a new degree of freedom for optical encoding, offering potential advancements in optical encryption.

The spatio-temporal amplitude of an LS pulse can be expressed as a superposition of N LG modes⁴⁴:

2

3

where B_0j represents the amplitude of each mode, (z) is the beam waist at propagation distance z, z_0j is the Rayleigh length, R(z) is the radius of curvature of wave front, is the frequency and is the topological charge defined by Eq. (1). Assuming an initial transverse waist (z) =, the intensity profile of the LS is illustrated in Fig. 1. For Fig. 1a, the modal indices are l_j = {1, 2, 3} (Δl = 1) with corresponding frequency ω_j ={365, 375, 385}PHz (Δω = 10PHz). In Fig. 1b, the modal indices are l_j = {1, 3, 5} (Δl = 2). The results clearly demonstrate a helical intensity distribution, forming a spring-like spatio-temporal structure. Notably, for Δl = 1, the LS exhibits a single coil, whereas for Δl = 2, two intertwined coils emerge (Fig. 1b). Increasing Δl further enhances the number of coils, while for a fixed Δl, the light field distribution evolves dynamically, rotating in time-highlighting the unique vortex characteristics of LS. Eq. (1) reveals the spectral width Δω, topological charge gap Δl and temporal pitch τ_p collectively introduce an additional degree of freedom, making LS highly suitable for optical encryption. Moreover, the ultrafast LS encompasses a broad spectrum in the frequency domain, superposed with multiple OAM modes l. This property enables ultrahigh-capacity information storage, positioning LS laser as a promising candidate for next-generation optical encryption systems.

Fig. 1.

The spatio-temporal intensity profiles and the corresponding diffraction patterns of the generated LS, (a) and (c) l_i ={1, 2, 3}, Δl = 1, (b) and (d) l_i ={1, 3, 5}, Δl = 2.

4-f pulse shaper with DRPE

The conventional optical setup of DRPE⁴ employs a 4-f system comprising two lenses, L₁ and L₂, with identical focal length f, as illustrated in Fig. 2. In this process, the original image g(x, y) is encoded to a stationary white noise G(x,y) using of two statistically independent random phase keys RPM₁ and RPM₂, positioned on the input and Fourier planes, respectively. Mathematically, RPM₁ and RPM₂ are expressed as exp[i2πP₁(x,y)] and exp[i2πP₂(u,v)], where P₁(x,y) and P₂(u,v) are random functions uniformly distributed over the interval [0, 1]. The DRPE encoding process is described by:

4

Fig. 2.

Optical setup of double random phase encoding (DRPE).

where ℱ⁻¹ and ℱ denote the Fourier transform and inverse Fourier transform, respectively. For a real-valued amplitude input image g(x, y), the ciphertext image can be obtained using the 4-f system with the two random phase masks.

However, utrashort pulsed light springs impose specific constraints on the DRPE method. Due to the broadband nature of the ultrafast pulses, the two Fourier lenses in the DRPE system introduce significant dispersion, distorting the spatiotemporal wave packets carrying OAM. Thus, applying DRPE requires simultaneous consideration of ultrafast optical pulse shaping and OAM encryption. To address this challenge, we have used a novel Fourier-transform pulse shaper with the DRPE system to enable the encryption of images with light springs.

Figure 3a illustrates the proposed Fourier-transform pulse shaping and DRPE setup. The system consists of diffraction gratings G₁ and G₂, parabolic mirrors L₁ and L₂, and random phase masks RPM₁ and RPM₂. RPM₂, generated by a SLM controlled by a personal computer (PC), is positioned into N sub-regions to modulate the amplitude and phase of N LG modes with the distinct OAM values l. The plaintext images are modulated by the input of LS and RPM₁, which is denoted as E_in (r, θ; t). Grating G₁ is placed at the front focal plane of L₁, while G₂ is located at the rear focal plane of L₂. The encrypted output pulses, E_out (r, θ; t), are obtained from G₂.

Fig. 3.

(a) Schematic of a 4-f pulse shaping and DRPE setup, consisting of a pair of diffraction gratings G₁ and G₂, a pair of parabolic mirrors L₁ and L₂, and a space light modulator (SLM). The SLM is divided into N superpixels to load amplitude and phase modulations of N LG modes with different OAM l. (b) The measurement setup of the topological charges of the generated LS. L₃: spherical lens; CL: cylindrical lens; CCD: Charge-Coupled Device.

If we remove the two random phase masks RPM₁ and RPM₂ in Fig. 3a, the proposed Fourier-transform pulse shaping encryption setup can generate ideal LS beam. The spatio-temporal 3D intensity profiles and 2D slice images at different time of LS are shown in Fig. 1. We can easily see that it is a spring-like intensity distribution. And the value of Δl can be deduced from the number of bright spots in 2D slice images, as shown in Fig. 1a Δl = 1 and Fig. 1(b) Δl = 2. The measurement of the topological charges of the LS beam can be conducted using diffraction method. The schematic setup for the detection of their diffraction patterns is shown in Fig. 3(b). The generated LS pulses exiting grating G₂ in Fig. 3a are focused onto grating G₃ using spherical mirror L₃. A cylindrical lens (CL) with focal length f is placed behind the third grating G₃. A CCD camera is placed in the focal plane of this cylindrical lens, which is marked as the observed plane, to measure the diffraction patterns of the LS. Figure 1c and Fig. 1d show the diffraction patterns of the LS after cylindrical lens corresponding to the intensity profiles shown in Fig. 1a and Fig. 1b. A multiple-lobe structures can be observed in the diffraction patterns. For each component of the LS with topological charge l = n, the diffraction pattern has n + 1 lobes. Furthermore, n gaps are found in the diffraction profile, and each gap is caused by a phase winding. From the measured results shown in Fig. 1c, it can be observed that the simulated LS consists of three vortex beams with topological charges of 1, 2, and 3. And Fig. 1(d) shows that the LS consists of three vortex beams with topological charges of 1, 3, and 5. With this diffraction property, each component of the LS with a different topological charge can be detected directly and rapidly using a single diffraction grating and cylindrical lens.

The process of cryptosystem

The overall encryption and decryption process is organized in below. The encryption process consists of two key steps:

1. The first step involves in the generation of controllable OAM modes, where multiple independent OAM modes are generated to modulate the plaintext images, denoted as E_in (r, θ; t).

2. The second step involves the use of the ultrafast pulse shaping and DRPE system, where the ultrashort pulse shaping, DRPE, and coherent superposition are employed to produce the encrypted ultrashort LS and convert plaintext images into ciphertexts.

The novelty of our approach lies in its ability to simultaneously generate ultrafast light springs as information carriers and perform multiple-image encryption with DRPE. More specifically, Fig. 4 illustrates the generation process of E_in (r, θ; t). Here, the N plaintext images g_j(x, y), or equivalently g_j(r, θ) in polar coordinate system, are multiplied by the random phase mask RPM₁. These images are then loaded onto N LG modes with distinct OAM values l and superposed to form E_in (r, θ; t), which is incident on the 4-f ultrashort pulse shaper. Equation (2a) is thus modified as follows,

5

Fig. 4.

The generation process of E_in (r, θ; t).

The encrypted LS E_out (r, θ; t) is generated via the 4-f pulse shaper system and expressed as:

6

The decryption process is shown in Fig. 5. The encrypted LS E_en (r, θ; t) is first spectrally dispersed by a grating G₂, each angularly separated frequency component of E_en is then focused by an off-axis parabolic mirror L₂ onto a specific lateral position in the focal plane of the mirror. The spectrum information corresponding to the ciphertext can be obtained. The space light modulator SLM₁ loaded globally the conjugate of RPM₂ (denoted RPM₂^*) to eliminate the phase distortion introduced by the encryption process. Then, a switching mask M(u,v), which is matched with SLM₁ and partitioned into N sub-regions to modulate the corresponding LG modes with topological charge l, is used to select the effective spectral region corresponding to the topological number l. After effective spectrum filtering, the spatial domain field is obtained by the inverse Fourier transform of the parabolic lens L₁ and grating G₁. The decrypted images from G₁ are imaged onto a CCD camera after multiplying the conjugate of RPM₁ (denoted as RPM₁^*) and amplitude modulation index to eliminate the influence of modal amplitude term B_j(r, t), which can be load by a space light modulator SLM₂. The entire decryption procedure corresponds to the inverse operation of the encryption scheme illustrated in Fig. 5. The decrypted images E_de (r, θ; t) can be expressed as:

7

Fig. 5.

Schematic of the decryption process.

Numerical simulations

Key sensitivity analysis

To demonstrate the effectiveness of the proposed LS-based DRPE method, we conducted numerical simulations using MATLAB (R2024b). The simulations employed a 256 × 256 pixel of original image size, where RPM₁ matches this dimension. The SLM had a resolution of 1920 × 1080 pixels. The LG modes followed the configuration in Fig. 1(b), with N = 3 modes characterized by topological charges l_j ={1, 3, 5} and Δl = 2. Figures 6(a₁)-6(c₁) display the three plaintext images: ‘Baboon’, ‘Cameraman’, and ‘Guang’. The encryption process generated two random phase keys in Fig. 6(a₂) and Fig. 6(b₂), and produced the multiplexed encrypted image shown in Fig. 6(c₂). Successful decryption with all correct keys yielded the reconstructed images in Figs. 6(a₃)-6(c₃). The ciphertext in Fig. 6(c₂) exhibits a pixel distribution statistically equivalent to stationary white noise, confirming the encryption’s effectiveness as no discernible information remains visible.

Fig. 6.

Illustration of plaintext images, encryption keys, encrypted images, and decrypted images. Plaintext images: (a₁) ‘Baboon’, (b₁) ‘Cameraman’, (c₁) ‘Guang’. Encryption keys: (a₂) RPM₁, (b₂) RPM₂. Multiplexed encrypted image: (c₂). Decrypted images: (a₃) ‘Baboon’, (b₃) ‘Cameraman’, (c₃) ‘Guang’.

The correlation coefficient (CC) was used to evaluate the quality of decryption and the CC value of the original image, and the decrypted image is calculated mathematically as shown in the following equation:

8

where A₁(x, y) represents the pixel value of the original image with M×N pixels, A₂(x, y) represents the pixel value in the decrypted image. and represent the average gray values of all pixels in the original and decrypted images. The CC value closer to 1 indicates stronger correlation between the two images while an absolute value closer to 0 indicates weaker correlation. The CC values between Fig. 6(a₁) and Fig. 6(a₃), Fig. 6(b₁) and Fig. 6(b₃), Fig. 6(c₁) and Fig. 6(c₃) are 0.7335, 0.6560 and 0.8570 respectively. These results confirm that the main information of each target image can be effectively recovered and the visual quality of the decrypted images is acceptable. It should be emphasized that the slight residual imprints and the relatively low CC value for the Cameramen image are mainly caused by the inherent cross-talk among different channels in multi-image multiplexing and the numerical errors in calculation. The phenomenon is also attributed to the high sensitivity of complex texture details to nonlinear modulation during encryption. These factors affect only the visual quality rather than the security of the system. The presented results represent the optimal recovery performance that has been achieved through extensive tests and parameter adjustments. Moreover, compared with the limited conventional DRPE method⁵, the LS parameters (including the OAM mode index l, frequency ω, topological charge gap Δl, spectral width Δω, and temporal pitch τ_p) serve as additional physical keys that effectively expand the key space. Any tiny deviation in these highly sensitive parameters will lead to complete decryption failure, which ensures the high security and information capacity of the proposed system.

Analyzing the key sensitivity of the encryption system is crucial. Figure 7 presents the decrypted results when errors are introduced into the random phase decryption key RPM₂^* with corresponding CC values of 0.0751, 0.0097, and 0.1380, as detailed in Table 1. Figure 8 demonstrates the decryption outcomes using correct keys but incorrect LS parameters (from Fig. 1(b)): (a₁)–(a₃) errors in l and Δl (l_j = {3, 6, 9}, Δl = 3); (b₁)–(b₃) errors in Δω (Δω’ = 1.5Δω); and (c₁)–(c₃) errors in τ_p (τ_p’ = 2/3 τ_p). Table 1 lists the CC values for the decrypted images in Figs. 7 and 8 compared to the original images. The results in Figs. 6, 7 and 8 reveal that the original images are reconstructed with high quality only when all decryption keys are correct, as seen in Figs. 6(a₃)–6(c₃). However, even a minor deviation in any security key leads to decryption failure, producing noise-like distributions with CC values near zero, which therefore the high sensitivity of key variation suggesting the strong encryption strength. Through this process, when key is disturbed, the decrypted results contain no discernible features or meaningful information related to the plaintext images. In conclusion, the encryption keys are highly sensitive and secure, ensuring robust encryption.

Fig. 7.

The decrypted images when the decryption key RPM₂^* is wrong: (a) ‘Baboon’, (b) ‘Cameraman’, (c) ‘Guang’.

Table 1.

The correlation coefficient of the decrypted images with wrong keys.

Decrypted images	CC	Decrypted images	CC	Decrypted images	CC
Figure 7(a)	0.0751	Figure 8(a2)	0.1941	Figure 8(b3)	0.1019
Figure 7(b)	0.0097	Figure 8(a3)	0.1566	Figure 8(c1)	0.1420
Figure 7(c)	0.1380	Figure 8(b1)	0.1451	Figure 8(c2)	0.1669
Figure 8(a1)	0.1788	Figure 8(b2)	0.2062	Figure 8(c3)	0.1696

Fig. 8.

Decrypted results with incorrect parameters of LS: (a₁)-(a₃) l and Δl error, l_j ={3, 6, 9}, Δl=3; (b₁)-(b₃) Δω error, ; (c₁)-(c₃) τ_p error, .

Strength of encryption key space

The key space of the encryption system has been rigorously evaluated. To resist brute-force attacks, a robust encryption system requires a key space exceeding 2¹⁰⁰. In this scheme, the key composition includes not only the random phase masks RPM₁ and RPM₂, but also the physical parameters of light springs, such as topological charge l, spectral width , and coil pitch . For an image with 256 × 256 pixels, each pixel value in this mask can range from 1 to 255. This provides a key space of 255^{256 × 256}=255⁶⁵⁵³⁶, which is far larger than the security threshold of 2¹⁰⁰. Combined with additional physical keys including topological charge gap Δl, spectral width , and temporal pitch , the total key space is further enlarged to ensure high security against brute-force attacks.

Noise attack analysis

The encryption system’s resilience against noise attacks was evaluated through Gaussian noise analysis that was applied only to the encrypted ciphertext image. Fig. 9 presents decrypted images affected by varying noise strengths: (a₁)-(a₃) at strength 0.01, (b₁)-(b₃) at 0.2, and (c₁)-(c₃) at 0.4. The corresponding CC values are detailed in Table 2. Results show that decryption quality generally decreases with increasing noise strength, and the slight increase in CC value for the Cameraman image at noise strength 0.01 is due to minor numerical fluctuations during the decryption process while the original plaintext images remain visually identifiable. This demonstrates that the proposed encryption system possesses strong robustness against Gaussian noise interference.

Fig. 9.

The impacts of noises on the quality of decrypted images: (a₁)-(a₃) the noise strength is 0.01; ( b₁)-(b₃)the noise strength is 0.2; (c₁)-(a₃) the noise strength is 0.4.

Table 2.

The correlation coefficient of the decrypted images with different Gaussian types noises.

Noise strength Decrypted images	0.01	0.2	0.4
	CC	CC	CC
“ Baboon ”	0.6029	0.5569	0.4681
“Cameraman”	0.6870	0.5896	0.5257
“Guang”	0.8059	0.7391	0.6091

Attack analysis

Encryption systems often face the risk of being attacked by others, so we have done a security analysis. Existing research has shown that traditional DRPE system is based on the principle of Fourier transform algorithm and its linearity opens avenues of attacks, such as known-plaintext attack (KPA)⁴⁶, chosen-plaintext attack (CPA)⁴⁷, and ciphertext-only attacks (COA)⁴⁸. KPA is where an adversary has a quantity of plaintexts (that cannot be specifically chosen) and the corresponding ciphertexts. CPA is similar to a KPA with the added advantage (for the adversary) to choose plaintexts. In the proposed cryptosystem, although DRPE is a linear operation, the light-springs-related parameters including orbital angular momentum l, topological charge gap Δl, spectral width , and temporal pitch are generated from the dynamic ultrafast pulse shaping system, which involves multiple nonlinear operations and are indirectly dictated by the secret key value. Besides, it is more challenging for an attacker to decipher the cryptosystem because of the existence of spatio-temporal coupling light springs encryption process. That confirms that LS-based DRPE is resistant to the CPA and the KPA.

Ciphertext-only attacks represents the greatest challenge as attackers possess only the ciphertext. To evaluate this critical vulnerability, we conducted a comprehensive COA security analysis. COA assumes that the attacker is very familiar with the proposed encryption system and knows the ciphertext but does not know the keys. By integrating phase retrieval and cryptanalysis techniques, we apply the Hybrid Input-Output (HIO) algorithm to COA⁴⁸. The attack process is shown on Fig. 10. At the beginning, we need to generate an initialized random image as input function in the spatial domain, calculate frequency domain constraint and deduce object domain support from ciphertext. The kth iteration process of the HIO algorithm is described as the following steps:

Fig. 10.

Flow chart of ciphertext-only attack.

Step1: Calculate by Fourier transform the estimation image .

Step2: Preserve the phase but replace the amplitude of with the frequency domain constraint or the ciphertext amplitude and get.

9

Step3: Obtain with the inverse Fourier transform .

Step4: If satisfies the object domain support, accept the update. Otherwise, apply the HIO correlation rule.

10

where represents a point set at which belongs to the object domain support, is an experienced constant value (0.5 in our simulation).

Step5: Compute the correlation coefficient value of the original image and the attacked result, if it meets the threshold condition, output and end the iteration. Otherwise, go back to step (1) and continue the next iteration.

Figure 11(a) plots the correlation coefficient convergence between attacked results and the plaintext images (“Baboon,” “Cameraman,” and “Guang”) versus iteration count. We can see that the three curves of correlation coefficient values are small and keep stabilizing until 300 iterations. Figure 11(b) confirms that no meaningful plaintext information was recovered. These results demonstrate that the proposed encryption system effectively resists COA.

Fig. 11.

The attack result of COA: (a) The relationship curve between the number of attack iterations and CC, (b) the decrypted image.

Conclusions

This study has successfully developed and validated a novel multiple-image encryption framework integrating ultrafast light springs with DRPE architecture. The core innovation of the research is the integration of the orbital angular momentum mode multiplexing, dynamic ultrafast pulse shaping via SLM, and DRPE-based spatial encoding. This approach enables the transformation of plaintext images into light springs-characterized by helical phase-intensity profiles-through superposition of modulated ultrashort pulse components. The integration of tailored pulse-shaping operations with spatial-phase encoding establishes a physically realizable encryption mechanism, with the SLM-based 4-f pulse shaper providing dynamic control over optical amplitudes and phases. Simulation results confirms that the generated light springs effectively obscure plaintext information while maintaining structural stability during transmission. Numerical simulations and security analyses verify the effectiveness of the proposed multi-image encryption method and its strong ability to counteract common attacks. Given its high security threshold, scalable key space, and compatibility with optical communication infrastructures, this light spring-based encryption paradigm shows significant promise for real-time secure image transmission. While the proposed framework demonstrates promising performance for ultrafast LS in the field of multiple-image encryption, more possibilities of generation LS and encryption methods remain to be discovered, such as fractional topological charges, optical frequency comb and asymmetric cryptosystems. In the future, we will explore to establish a physical experimental platform to validate the cryptosystem’s performance and security under rigorous attack scenarios.

Author contributions

A.Y. developed the proposed method and conceived the experiments. D.W. performed the theoretical analysis and prepared the manuscript. H. Z. provided suggestions and participation in the preparation of the manuscript. All authors reviewed the manuscript.

Funding

This work is funded by the National Natural Science Foundation of China (Grant no. 62075134).

Data availability

The datasets used during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.