Multiparty Random Phase Wrapping Secret-Sharing Systems for Visual Data Security

A secret sharing scheme is an important cryptographic procedure that enables the secure distribution of secret information, such as private images, in an untrusted network. However, in all secret sharing schemes, the sizes of the shares increase in proportion to the size of the secret information, because they involve computationally expensive polynomials of degree <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n-1$ </tex-math></inline-formula> (n is total number of shares) and increasingly large modulus of modulo operations for security. Moreover, with large share sizes, it is not easy in practice to encrypt them quickly using block cipher algorithms. Therefore, ensuring the security of secret sharing for large-scale visual data with a reasonable share length and efficiently encrypting n shares properly represents formidable challenges. To overcome these challenges in secret sharing schemes, we propose new multiparty random phase wrapping secret sharing systems for visual datasets. Computational optical imaging enables the acquisition of wrapped phase information, ranging from –<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula>, to be expressed in the form of a complex sinusoidal waveform. The proposed scheme allows for large-scale secret data—such as confidential digital images and visual data, including optical images—to be securely and efficiently shared and distributed to multiple parties or agencies utilizing a digital representation of a complex sinusoidal waveform of the secret information. The proposed scheme can be useful in cryptographic key escrow systems and in use with large-scale secret data.