Xmark: Dynamic Software Watermarking Using Collatz Conjecture

Ma, Haoyu; Jia, Chunfu; Li, Shijia; Zheng, Wantong; Wu, Dinghao

doi:10.1109/tifs.2019.2908071

Cited by 27 publications

(16 citation statements)

References 37 publications

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“…if right parent exists for m � n − 1/3 then (11) Output m − 1/3 (12) end if (13) end for (14) end if (15) Enter a new value n for a child node (16) end while ALGORITHM 3: Inverse binary tree generation. 8 International Journal of Mathematics and Mathematical Sciences For example, the sequence starting with n � 15 has a maximum value (or peak) of 160 before it reaches 1 on its 17th iteration.…”

Section: Determining Peaks In Collatzmentioning

confidence: 99%

“…Perhaps the proof of this mesmerizing conjecture is so desired because the conjecture itself finds use in various applications. e Collatz conjecture is used in high-uncertainty audio signal encryption [13], image encryption [14], dynamic software watermarking [15], and information discovery [16]. Although the lack of a proof does not preclude applications of the Collatz conjecture, mathematical phenomenon related to the conjecture may be of interest in other applications, such as cryptography or information theory.…”

Section: Introductionmentioning

confidence: 99%

“…Set c 1 � c 0 (13) end if (14) end while (15) Output i, c 0 , c 1 (16) Convert i to bases 2, 3, 4, then output (17) end for ALGORITHM 1: Iteration analysis.…”

mentioning

confidence: 99%

“…Set tmp � 3 * tmp + 1 (9) end if (10) if peak < � tmp then (11) Set peak � tmp (12) end if (13) c � c + 1 (14) end while (15) Output i, peak, c (16) end for ALGORITHM 2: Peak analysis.…”

mentioning

confidence: 99%

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Novel Theorems and Algorithms Relating to the Collatz Conjecture

Schwob

Shiue

Venkat

2021

International Journal of Mathematics and Mathematical Sciences

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Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and algorithms that explore relationships and properties between the natural numbers, their peak values, and the conjecture. These contributions primarily analyze the number of Collatz iterations it takes for a given integer to reach 1 or a number less than itself, or the relationship between a starting number and its peak value.

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Section: Determining Peaks In Collatzmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Set c 1 � c 0 (13) end if (14) end while (15) Output i, c 0 , c 1 (16) Convert i to bases 2, 3, 4, then output (17) end for ALGORITHM 1: Iteration analysis.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Novel Theorems and Algorithms Relating to the Collatz Conjecture

Schwob

Shiue

Venkat

2021

International Journal of Mathematics and Mathematical Sciences

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“…Digital property management and especially counterfeit protection mostly depend on watermarking in a variety of environments [37][38][39]. Digital watermarking has been finding its applications in digital cinema in recent years [40,41].…”

Section: Introductionmentioning

confidence: 99%

A Survey on Piracy Protection Techniques in Digital Cinema Watermarking Schemes

Zolfaghari¹,

Mitra²

2020

Recent Trends in Communication Networks

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Watermarking is used in several areas such as CDNs (Content Delivery Networks), as part of the rights management system for counterfeit prevention. Watermarking schemes need some additional features in order to be used in digital cinema. In fact, extra watermarks are added to movies by cinema projectors in projection time, which help identify the cinema hall in which the illegal copy has been recorded. But distortions caused by hand vibrations and the point of view angle make it difficult to recover the watermark. This makes it necessary to be distortionresistant for the watermarking schemes used in digital cinema. On the other hand, theatre owners would like to locate the camcorder that has recorded the pirate copy. This requires watermarking schemes to be able to estimate the distance and angle using the distributed pirate copy. In this chapter, we present a review on watermarking techniques specifically designed to attack the aforementioned problems.

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