Quiz games as a model for information hiding

Bank, Bernd; Heintz, Joos; Matera, Guillermo; Montaña, José Luis; Pardo, Luis Miguel; Paredes, Andres Rojas

doi:10.1016/j.jco.2015.11.005

Cited by 4 publications

(3 citation statements)

References 13 publications

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“…The complexity paradigm arising from these works is that polynomial systems can be solved with a number of arithmetic operations which is polynomial in the Bézout number of the system. This conclusion nearly matches the lower bounds of [5], [15] and [1], under the assumption that the corresponding algorithms are "geometrically robust", namely they are universal and allow the solution of certain "limit" problems.…”

Section: Introductionsupporting

confidence: 71%

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On the bit complexity of polynomial system solving

Giménez¹,

Matera²

2019

Journal of Complexity

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We exhibit a probabilistic algorithm which solves a polynomial system over the rationals defined by a reduced regular sequence. Its bit complexity is roughly quadratic in the Bézout number of the system and linear in its bit size. Our algorithm solves the input system modulo a prime number p and applies p-adic lifting. For this purpose, we establish a number of results on the bit length of a "lucky" prime p, namely one for which the reduction of the input system modulo p preserves certain fundamental geometric and algebraic properties of the original system. These results rely on the analysis of Chow forms associated to the set of solutions of the input system and effective arithmetic Nullstellensätze.

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Section: Introductionsupporting

confidence: 71%

“…Next, the second condition of the lemma can be rephrased by saying that the image J of J in B is not contained in any prime of B of codimension 0. By [10,Corollary 16.20], this is equivalent to (1), which finishes the proof. 2.2.…”

Section: 1mentioning

confidence: 55%

On the bit complexity of polynomial system solving

Giménez¹,

Matera²

2019

Journal of Complexity

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“…Compared with most existing reversible hiding algorithms, the peak value of signal-to-noise ratio of watermark information embedded in image is high. But the embedding capacity is restricted by the maximum size of the histogram, which makes the embedding capacity limited to the original image [3,12]. After the carrier image is encrypted by other two algorithms, in encrypted image, information bits are embedded in the low value, resulting in some block boundary pixels value in the image with watermark information has flipped, after being extracted image cannot be recovered completely, it not only has a large amount of calculation and but also the image quality has been some injury.…”

Section: Xueyan Wumentioning

confidence: 99%

An algorithm for reversible information hiding of encrypted medical images in homomorphic encrypted domain

Wu¹

2019

DCDS-S

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At present, in reversible information hiding algorithm of image, the difference expansion idea is used. After the carrier image encryption, in encrypted image, information bits are embedded in the low value, resulting in the fact that in the image embedded with watermarking information, a part of the boundary pixel value has flipped. After being extracted, the carrier image cannot be recovered completely that is not only a large quantity of calculation, and the image quality has also been some damage. A algorithm for reversible information hiding of encrypted the medical image in the homomorphic encryption domain is proposed. Combining wavelet and fast fuzzy algorithm, the image edge is extracted from the high frequency and low frequency parts of medical image, and the medical image is reconstructed in the compressed boundary part. Combined with the thought of block compressed sensing and block edge pixels, the reconstructed medical image is divided to multiple non-overlapping blocks. The pixel in the right lower edge of the block is made homomorphic encryption operation, the remaining pixels are made compressed sensing operation, and the two parts are combined to a ciphertext to be sent to the owner of the channel According to the information hiding key the secret information is embedded into the ciphertext by the channel owners. The receiver can extract the information and restore the original image based on the encryption key and the information hiding key. The experimental results show that the proposed algorithm has high embedding capacity, the image quality after recovery is high, and the computational complexity is low. 2010 Mathematics Subject Classification. 43A35. Key words and phrases. Homomorphic encrypted domain, encrypted medical image, reversible information hiding algorithm.

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On the Computational Complexity of Information Hiding

Paredes

2018

Electronic Notes in Theoretical Computer Science

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Quiz games as a model for information hiding

Abstract: We present a general computation model inspired in the notion of information hiding in software engineering. This model has the form of a game which we call quiz game. It allows in a uniform way to prove exponential lower bounds for several complexity problems.

Cited by 4 publications

References 13 publications

On the bit complexity of polynomial system solving

On the bit complexity of polynomial system solving

An algorithm for reversible information hiding of encrypted medical images in homomorphic encrypted domain

On the Computational Complexity of Information Hiding

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