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Now, the attacker hopes that the Hamming distance between the original image and her attacked version will be small also for other keys than the single one used in her attack.
When the hash length is increased to 128 bytes, the attack gets more difficult since a larger share of the bitstream data needs to be exchanged between original and modified versions possibly compromising image quality of the attacked version.
Each experiment consisted of embedding a 50 bit watermark message in each of the images and subsequently trying to extract it from the watermarked and attacked version of the image.
Figure 21 shows an attacked version of the modified Lena image and a histogram of Hamming distances between 50-byte hash strings of the original and attacked images when 100 different random keys are used in authentication (the same key is used for both original and attacked versions).
While the image quality of the attacked version might still be sufficient for some applications, the Hamming distance histograms clearly indicate that the attack is prevented also under these settings (in these experiments, the key used for producing the attacked versions is not included in the keys used for authentication).
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distances between the original and attacked versions are 0.235 and 0.113, This is in contrast to the previous case when originals and slightly modified versions have been considered.
British economist Thomas Malthus, with whom Say was acquainted, attacked this version in the 19th century, as did John Maynard Keynes in the 20th century.
So the Luftwaffe settled on the Focke-Wulf Fw 190 fighter aircraft, with the Fw 190F becoming the ground-attack version.
It delivered the ground attack version the following year for evaluation, although it could be modified as necessary for other roles.
The Suicide Attack (Version 2): Grab a ball and maybe a friend to increase your chances of hitting someone.
In other words, when Amber and her newfound comrades sit around the dorm debating strategy and raging against the machine, they are attacking one version of the American dream while embodying another.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com