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I have been unable to find any mathematical explanations on how TrueCrypt's plausible deniability encryption works, when using TC containers.

Would someone be able to provide a mathematical walkthrough of how it works?

Other encryption systems implementing things in a similar way is outside the scope of my question. Also, whilst I have some experience in the theoretical side of cryptography, the simpler the explanation the better.

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The link https://www.truecrypt71a.com/documentation/plausible-deniability/ says

Although file-hosted TrueCrypt volumes (containers) do not contain any kind of “signature” either (until decrypted, they appear to consist solely of random data), they cannot provide this kind of plausible deniability, because there is practically no plausible explanation for the existence of a file containing solely random data. However, plausible deniability can still be achieved with a file-hosted TrueCrypt volume (container) by creating a hidden volume within it (see above).

which seems to imply that file containers DO NOT provide the absolute plausible deniability claimed for the other use case.

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  • $\begingroup$ I think you are looking into things a bit too deep. TrueCrypt has plausible deniability, which means there is one password but maybe a second secret password. Is there any technical writeup as to how this is possible? I know about plausible deniability from my time playing with the One Time Pad, but I would guess TrueCrypt works differently...? $\endgroup$ Commented Mar 22, 2023 at 22:55

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