Article

# 2DCrypt: Image Scaling and Cropping in Encrypted Domains

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## Abstract

The evolution of cloud computing and a drastic increase in image size are making the outsourcing of image storage and processing an attractive business model. Although this outsourcing has many advantages, ensuring data confidentiality in the cloud is one of the main concerns. There are state-of-the-art encryption schemes for ensuring confidentiality in the cloud. However, such schemes do not allow cloud datacenters to perform operations over encrypted images. In this paper, we address this concern by proposing 2DCrypt, a modified Paillier cryptosystem-based image scaling and cropping scheme for multi-user settings that allows cloud datacenters to scale and crop an image in the encrypted domain. To anticipate a high storage overhead resulted from the naive per-pixel encryption, we propose a space-efficient tiling scheme that allows tile-level image scaling and cropping operations. Basically, instead of encrypting each pixel individually, we are able to encrypt a tile of pixels. 2DCrypt is such that multiple users can view or process the images without sharing any encryption keys - a requirement desirable for practical deployments in real organizations. Our analysis and results show that 2DCrypt is INDistinguishable under Chosen Plaintext Attack secure and incurs an acceptable overhead. When scaling a 512 × 512 image by a factor of two, 2DCrypt requires an image user to download approximately 5.3 times more data than the un-encrypted scaling and need to work approximately 2.3 s more for obtaining the scaled image in a plaintext.

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... Multiple parties can perform ciphertext calculation, ciphertext search and so on, while protecting privacy data. For instance, Mohanty et al. in [7] proposed a modified Paillier cryptosystem-based image processing scheme, where a image outsourcer, a cloud server and an image user were involved. The cloud server in [7] can perform scaling and cropping operations over encrypted images with the help of the image outsourcer and the image user. ...
... For instance, Mohanty et al. in [7] proposed a modified Paillier cryptosystem-based image processing scheme, where a image outsourcer, a cloud server and an image user were involved. The cloud server in [7] can perform scaling and cropping operations over encrypted images with the help of the image outsourcer and the image user. Ayday et al. in [8] introduced a privacy-preserving disease susceptibility test. ...
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The modified Paillier cryptosystem has become extremely popular and applied in many fields, owning to its additive homomorphism. This cryptosystem provides weak private keys and a strong private key. A weak private key only can decrypt ciphertexts under the corresponding public key. The strong private key can decrypt all ciphertexts even under different public keys. When the modified Paillier cryptosystem is applied in a system, the member, often the system administrator, has the strong private key and can decrypt all ciphertexts. If this system administrator is attacked or compromised, the security of the application system absolutely break down. Thus, it is important to stop the decryption of the strong private key. To address this issue, we propose an restrained version of the modified Paillier cryptosystem (Restrained-Paillier), by endowing the multiplicative homomorphism. We perform the additive encryption on the multiplicative ciphertext and generate the mixed ciphertext, which can not be decrypted by the strong private key. Based on this Restrained-Paillier, we develop two applications. Firstly, we realize access control of common secret of two owners. In our scheme, only one owner cannot access secret. Secondly, we present three protocols for identity distribution and key management, identity authentication and private key recovery. Security analysis shows that the Restrained-Paillier cryptosystem can resist the chosen plaintext attack. The experimental results illustrate the utility and efficiency of the proposed protocols.
... Among the additive homomorphic encryption schemes, Paillier is the widely used for image processing works on encrypted domain [21,25,32]. The basic image scaling and cropping operations in encrypted domain is proposed in [21]. ...
... Among the additive homomorphic encryption schemes, Paillier is the widely used for image processing works on encrypted domain [21,25,32]. The basic image scaling and cropping operations in encrypted domain is proposed in [21]. A reversible data hiding approach based on Paillier scheme, where the hidden data is directly embedded into the encrypted images is proposed in [32]. ...
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... Existing privacy-preserving multimedia computing schemes [15,18,25] primarily use Homomorphic Encryption (HE) for secure data processing. HE is a special form of encryption which allows specific computations to be performed over the encrypted data, such that, the decryption result matches the same operations being performed over the plain data. ...
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... To the best of our knowledge, no previous effort has been made for encrypted domain camera attribution that guarantees both utility and privacy. Some previous works, however, have focused on encrypted domain image processing [30]- [33] using partial homomorphic encryption schemes, such as Shamir's secret sharing and Paillier encryption. ...
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... For multi-user settings Mohanty et al. [19] have presented a 2DCRYPT, a changed Paillier cryptosystem-based image scaling and cropping plan. The main drawback of this method is security and incurs of the acceptable overhead. ...
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Automatic recognition of human faces is becoming increasingly popular in civilian and law enforcement applications that require reliable recognition of humans. However, the rapid improvement and widespread deployment of this technology raises strong concerns regarding the violation of individuals’ privacy. A typical application scenario for privacy-preserving face recognition concerns a client who privately searches for a specific face image in the face image database of a server. In this paper we present a privacy-preserving face recognition scheme that substantially improves over previous work in terms of communication-and computation efficiency: the most recent proposal of Erkin et al. (PETS’09) requires O(logM)\mathcal{O}(\log M) rounds and computationally expensive operations on homomorphically encrypted data to recognize a face in a database of M faces. Our improved scheme requires only O(1)\mathcal{O}(1) rounds and has a substantially smaller online communication complexity (by a factor of 15 for each database entry) and less computation complexity. Our solution is based on known cryptographic building blocks combining homomorphic encryption with garbled circuits. Our implementation results show the practicality of our scheme also for large databases (e.g., for M = 1000 we need less than 13 seconds and less than 4 MByte online communication on two 2.4GHz PCs connected via Gigabit Ethernet).
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In 1998, Blaze, Bleumer, and Strauss (BBS) proposed an application called atomic proxy re-encryption, in which a semi-trusted proxy converts a ciphertext for Alice into a ciphertext for Bob without seeing the underlying plaintext. We predict that fast and secure re-encryption will become increasingly popular as a method for managing encrypted le systems. Although efciently computable, the wide-spread adop- tion of BBS re-encryption has been hindered by considerable security risks. Following recent work of Ivan and Dodis, we present new re-encryption schemes that realize a stronger notion of security and we demonstrate the usefulness of proxy re-encryption as a method of adding access control to the SFS read- only le system. Performance measurements of our experimental le system demonstrate that proxy re-encryption can work effectively in practice.
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An encryption method is presented with the novel property that publicly re- vealing an encryption key does not thereby reveal the corresponding decryption key. This has two important consequences: 1. Couriers or other secure means are not needed to transmit keys, since a message can be enciphered using an encryption key publicly revealed by the intended recipient. Only he can decipher the message, since only he knows the corresponding decryption key. 2. A message can be \signed" using a privately held decryption key. Anyone can verify this signature using the corresponding publicly revealed en- cryption key. Signatures cannot be forged, and a signer cannot later deny the validity of his signature. This has obvious applications in \electronic mail" and \electronic funds transfer" systems. A message is encrypted by representing it as a number M, raising M to a publicly specied
Article
An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. This has two important consequences: Couriers or other secure means are not needed to transmit keys, since a message can be enciphered using an encryption key publicly revealed by the intended recipient. Only he can decipher the message, since only he knows the corresponding decryption key. A message can be “signed” using a privately held decryption key. Anyone can verify this signature using the corresponding publicly revealed encryption key. Signatures cannot be forged, and a signer cannot later deny the validity of his signature. This has obvious applications in “electronic mail” and “electronic funds transfer” systems. A message is encrypted by representing it as a number M, raising M to a publicly specified power e, and then taking the remainder when the result is divided by the publicly specified product, n , of two large secret prime numbers p and q. Decryption is similar; only a different, secret, power d is used, where e * d = 1(mod (p - 1) * (q - 1)). The security of the system rests in part on the difficulty of factoring the published divisor, n .
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In this paper we show how to divide data D into n pieces in such a way that D is easily reconstructable from any k pieces, but even complete knowledge of k - 1 pieces reveals absolutely no information about D. This technique enables the construction of robust key management schemes for cryptographic systems that can function securely and reliably even when misfortunes destroy half the pieces and security breaches expose all but one of the remaining pieces.
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Cited By (since 1996): 131, Export Date: 15 September 2011, Source: Scopus
Conference Paper
It is desirable to store data on data storage servers such as mail servers and file servers in encrypted form to reduce security and privacy risks. But this usually implies that one has to sacrifice functionality for security. For example, if a client wishes to retrieve only documents containing certain words, it was not previously known how to let the data storage server perform the search and answer the query, without loss of data confidentiality. We describe our cryptographic schemes for the problem of searching on encrypted data and provide proofs of security for the resulting crypto systems. Our techniques have a number of crucial advantages. They are provably secure: they provide provable secrecy for encryption, in the sense that the untrusted server cannot learn anything about the plaintext when only given the ciphertext; they provide query isolation for searches, meaning that the untrusted server cannot learn anything more about the plaintext than the search result; they provide controlled searching, so that the untrusted server cannot search for an arbitrary word without the user's authorization; they also support hidden queries, so that the user may ask the untrusted server to search for a secret word without revealing the word to the server. The algorithms presented are simple, fast (for a document of length n, the encryption and search algorithms only need O(n) stream cipher and block cipher operations), and introduce almost no space and communication overhead, and hence are practical to use today
A public key cryptosystem and a signature scheme based on discrete logarithms
Protecting and evaluating genomic privacy in medical tests and personalized medicine
• E Ayday
• J L Raisaro
• J.-P Hubaux
• J Rougemont
E. Ayday, J. L. Raisaro, J.-P. Hubaux, and J. Rougemont, "Protecting and evaluating genomic privacy in medical tests and personalized medicine," in Proceedings of the 12th ACM Workshop on Privacy in the Electronic Society, 2013, pp. 95-106.