Abstract The MinRank problem is an NP-complete problem that is prevalent in multivariate cryptography and its goal is to find a non-zero linear combination of given a series of matrices over a ring such that the obtained matrix has a small rank. At Asiacrypt 2001, two Zero-Knowledge Proofs of Knowledge (ZKPoK) for the MinRank problem are proposed, and we call them MRZK and MRZK$^{\dagger }$, respectively. The latter is an improved version of the proof size of the former. However, the efficiency of MRZK$^{\dagger }$ has been open and not analyzed. While the MRZK protocol is secure, it must be repeated many times due to the soundness error $2/3$, which leads to the large proof size. For 128-bit security, the MRZK protocol is executed at least 219 iterations and the proof size is about 32 KB. In this paper, we first show that the efficiency of MRZK$^{\dagger }$ is impractical due to unreasonable parameter size. However, when the parameter size is tuned and the efficiency is improved, an imposter can be efficiently constructed. Then, to alleviate the large proof size of MRZK, inspired by the technique designing ZKPoK (Eurocrypt 2020), we propose a sigma protocol with helper to prove the solution to the MinRank problem. Finally, we transform the sigma protocol with helper into a standard ZKPoK (MRZK$^{\sharp }$) by removing the helper. The MRZK$^{\sharp }$ protocol can achieve any small soundness error and enjoy the proof size of about 15 KB (53% improvement over MRZK).

Image licensing regulates the scope, type, and limitations of using an image through an agreement. However, it is challenging to verify whether an agreement has been fulfilled honestly. Existing techniques, such as watermarking and perceptual hashing, help check image originality and editing operations specified in the agreement, but fail to achieve editor designation. In this paper, we propose a verifiable image licensing system (VILS) which provides an effective solution to verify if a received image is used legally according to its licensing agreement. The core building block of our design is a new kind of cryptographic primitive, called accumulator with a designated entity. The new accumulator helps achieve not only editing restriction, but also editor designation in image authentication. Our VILS has the following two appealing features: (1) Authorization: Only an authorized licensee who edits an image with operations declared in a licensing agreement can produce valid images; (2) Efficiency: The verification of VILS is efficient and independent of the number of operations or image size. Compared with the most relevant schemes from the state-of-the-art, the new design enriches the functionality of image authentication but reduces the verification time by 40%.

Abstract Image authentication is the process of verifying image origin, integrity and authenticity. In many situations, image authentication should allow reasonable image editing, which does not introduce any wrong information against the original one. While it has been studied both extensively and intensively with considerable efforts, there is no satisfactory method supporting region extraction. This paper presents a solution to address the issue of privacy protection in authenticated images. Our scheme allows anyone to extract sub-image blocks from an original image (authenticated by the image producer) and generate a proof tag to prove the credibility of the extracted image blocks. The process of proof tag generation does not require any interaction with the image producer. In addition, the image producer is able to define must-be-preserved image blocks (e.g. producer logo) during the extraction. We define the security property for the authenticated sub-images and give a generic design with two core primitives: an ordinary digital signature scheme and a cryptographic accumulator. The security of our design can be reduced to the underlying cryptographic primitives and its practical performance is demonstrated by a bunch of evaluations. We believe the proposed design, together with other image authentication methods, will further facilitate image relevant services and applications.

Abstract In a digital society, the rapid development of computer science and the Internet has greatly facilitated image applications. However, one of the public network also brings risks to both image tampering and privacy exposure. Image authentication is the most important approaches to verify image integrity and authenticity. However, it has been challenging for image authentication to address both issues of tampering detection and privacy protection. One aspect, image authentication requires image contents not be changed to detect tampering. The other, privacy protection needs to remove sensitive information from images, and as a result, the contents should be changed. In this paper, we propose a practical image authentication scheme constructed from chameleon hashes combined with ordinary digital signatures to make tradeoff between tampering detection and privacy protection. Our scheme allows legitimate users to modify contents of authenticated images with a privacy-aware purpose (for example, cover some sensitive areas with mosaics) according to specific rules and verify the authenticity without interaction with the original authenticator. The security of our scheme is guaranteed by the security of the underlying cryptographic primitives. Experiment results show that our scheme is efficient and practical. We believe that our work will facilitate image applications where both authentication and privacy protection are desirable.