@ arkinox

[!NOTE] Definition Anamorphic (adj.): Relating to or involving a form of distortion in which an image or object is only recognizable when viewed from a specific angle or through a specific device, creating an optical illusion.

Anamorphic image encryption is a way of representing an image in cyberspace such that it may only be viewed from a specific location, and the viewed image may not be copied with high fidelity.

The below is theoretical and yet to be implemented in cyberspace. Feedback welcome!

Primitives

The POW action chain serves as a location primitive. If your action chain is valid, your avatar is in a specific location in cyberspace. The validation rules for action chains enable them to serve as a POW-based proof-of-location and a solution to a location "double spend" (being in 2 locations at once).

This location may be reacted to by a nostr bot watching for an action chain to reach a certain coordinate or area. Once reached, the bot can reveal a secret to the avatar (by sending a DM to their pubkey); the secret is necessary to view anamorphic content. This is a gatekeeper primitive.

If we want to make an image available at a specific location, we need to encode it properly.

If you know what a frustum is, skip this paragraph. Imagine a hollow pyramid. You pick it up and point the tip top of the pyramid right at your eyeball (carefully!). The base of the pyramid is parallel to you, away from your face. This shape is a frustum; it is an imaginary space where all of the objects you can see exist within. Our eyes actually see more of a cone, but in computer graphics the frustum is rectangular. Now think about one edge of the pyramid that goes from the tip at your eyeball to the base away from you; this edge is at the very edge of your "vision" or viewport. If you put a lightbulb on this edge and slid it back and forth from tip to the pyramid's base, it would grow and shrink but it would not change position from your perspective.

Kind 1 notes exist in cyberspace as cubes; each cube's location comes from a simhash of its content. The color of this cube is derived from the last 6 digits of the created_at in hex. Using seconds as a hex color means that the full gamut of hex-based colors spans 16777215 seconds (0xffffff) or 194 days or roughly 6.3 months. This serves as a pixel primitive. Cubes can be used as pixels and placed in specific locations in cyberspace by mining a note's content so that the simhash yields the desired location.

To review: - We have a location primitive -- the action chain enables us to be in a location. - We have a gatekeeper primitive -- we can be given access to information at a location. - We have a pixel primitive -- we can create images in space.

Depiction of an Image

However, we don't simply want to create a flat rectangular canvas in space, because that would be too recognizable and too easy to copy. We need more obfuscation if we are going to achieve anamorphic encryption.

Instead of a flat canvas, we can construct an image where each pixel is a random distance between the front and back of the frustum. Viewed form the frustum's perspective, it doesn't matter how far the pixel is from the viewer as long as the pixel stays on the same ray cast from the viewer's eyeball to the base of the frustum. If the pixels are randomly distributed across the 3D space of the frustum, then the image may only be seen from an angle very near the frustum's perspective.

Typically something gets smaller when it gets further away, but the kind 1 cubes as viewed in ONOSENDAI are scaled such that they actually grow in size as the viewer gets further away from them. This is to give an impression of the density of notes from a far distance and to enable the user to select them from a far distance when this would normally not be possible. So the distance to the pixel does not matter for the purpose of displaying the anamorphic image.

Obfuscation of the Pixels

The final piece to this puzzle is a cryptographic obfuscation of the pixels that assemble the image.

The artist should downscale their artwork so that it is low-resolution, such as 800x600 or whatever size is desired. Considerable POW is necessary to create an anamorphically encrypted image, so the size is important.

Then, the location in cyberspace and frustum should be chosen. The frustum can be of any size, although it would be advisable to keep it within 1 sector (2^30 Gibsons) in length (tip to base).

The pixels in the downscaled artwork should be divided into batches; this can be done in any order or direction or spatial arrangement. Each batch will be published by a separate public key in order to obfuscate the image further.

Next, ephemeral keypair 0 ($E0$) is generated to publish the first batch of pixels (kind 1 notes).

A kind 1 note is published to represent the top leftmost pixel. The created_at is set to a time where the last 6 digits of the time in hex equals the color of the pixel in the downscaled art. The content of the note, when simhashed, must yield a coordinate along the top left edge of the frustum. This is where the POW is required to produce an anamorphic encrypted image because many guesses may be required to obtain a good-enough result. Bear in mind that good-enough is permissible; it's up to the taste of the artist. This tolerance may be useful in adjusting the amount of POW necessary to successfully create each pixel.

A batch of kind 1 notes my be published with ephemeral key 0. When batch 0 of pixels is complete, the following should happen: - An even prefix length $L$ should be chosen. This determines the number of leading hex digits need to be matched for subsequent public keys. This prefix length should be the same for all subsequent batches. - A Secret $S$ of 256 random bits should be generated. This secret will also be used for all subsequent batches.

Public key target 1 is derived from $\text{sha256}( S + E0_{pub})$

Public keys are mined until a resulting public key's hex prefix of length $L$ matches Public key target 1's prefix of length $L$.

9884a42bcf930100... < target public key 988456aa3a87e4fb... < mined public key ^^^^ 4-length match

The matching mined keys will serve as ephemeral keypair 1 ($E1$).

[!Tip] Check out Rana for mining keypairs with specific prefixes: https://github.com/grunch/rana

Now, the next batch of pixels can be published with $E1$ until the batch is complete.

To obtain $E2$ for the third batch, derive your target from $\text{sha256}(S + E1_{pub})$. Mine until you find a public key with a prefix matching your target's prefix of $L$ hex digits long. Publish your third batch under that key. Repeat until your whole image is published.

[!Tip] To further obscure the relationship between the kind 1 notes and the pixels in your image, you can add random e/p tags to give the impression that the notes are actually part of a conversation, or other random tags to give the impression that they are used for something else.

Now, the artist must set up a bot that subscribes to cyberspace actions so that if an avatar enters a defined coordinate area, their pubkey will receive: - The first public key $E0_{pub}$ - The Secret $S$ - The prefix length $L$ - Relays to query for the pixels

Viewing the Anamorphically Encrypted Image

When an avatar looks into the void of cyberspace, they will see a lot of note cubes. Even if viewed from the correct location, the notes comprising the pixels of the artwork won't be free from unrelated clutter. Therefore, it's necessary to filter the notes in the interface to only show notes that comprise the image. To construct this filter requires the following steps.

Using the information supplied by the bot in the DM, the avatar can query nostr relays for notes published by $E0$. Then, the avatar may $\text{sha256}(S + E0_{pub})$ to obtain the target. They can get the prefix with target.substring(0, $L$) and then do a partial author query on the obtained prefix to find notes published by public keys matching that prefix.

[!WARNING] Partial queries on pubkeys must be an even number of hex digits. Make sure you choose an even prefix $L$.

This is where it is important to choose a prefix that is long enough to be fairly unique but short enough to not require a lot of extra POW.

Once you query the author prefix and find zero notes, then you have fully reconstructed the image. Until then, the avatar will continue to derive $E1$, $E2$, $E3$, etc. and query the notes they have published.

Now that the notes representing the pixels of the image are obtained, the client must position these notes in cyberspace as per usual, remove notes not matching the filters from view, and then the avatar must be in the correct location and looking toward the frustum.

Now, finally, the avatar may see the image that the artist intended to portray.

Anamorphic Properties

When viewing the image, there are some things to keep in mind: - to view the image, one must know which coordinate to travel to and actually go there with POW - the image is a low-fidelity recreation of the original image, so the full resolution original may not be reconstructed - the representation of the image via note cubes scattered inside a frustum introduces perspective errors into the viewing if the avatar is not perfectly positioned in line with the center of the frustum. This is actually a feature, not a bug. Because it is difficult to obtain an exact location in cyberspace, the subtle movement of the avatar will gradually obfuscate the depiction of the image as a function of distance from that ideal point. This makes screenshots and screen recordings suboptimal to capture the image as it will almost always contain defects and perspective errors. However, the way perception in our brains works tends to smooth over these imperfections in real-time, especially as we move. Think about looking through a smudged window or phone screen -- often you hardly notice it. Or, think about looking at something beyond a wire mesh or fence while moving. It's easier to see when you are moving even if the image is heavily obscured. - the method of batching and publishing the pixels across the frustum with ephemeral keys prevents observers from detecting that an image exists at all, and even if detected, from assembling every pixel due to the necessity of knowing the secret to derive all ephemeral keys. The only way that an image could accidentally be detected would be by accidentally visiting the exact place where the frustum focal point is located and looking in the correct direction, which is about as rare as generating a private key someone else owns.

To summarize, the anamorphic image is better interpreted by our brains than by a screenshot, especially as we move around in cyberspace. It is a way of displaying image content that requires a viewer to be in a place, meet a criteria, and severely limits their ability to take the image with them.

Potential Counters

Now, one way that the image could be copied is by copying the color data from the cubes once the cubes are known from the secrets provided by the gatekeeper. However, unless the cubes are addressed in cyberspace, they hold no pixel position data in themselves. If the note batches are chopped up creatively, it can be reasonably challenging to reassemble the image even if all the data is at hand.

Conclusion

This is a unique method of obfuscating visual content behind proof-of-work. The image may be seen, but only if enough cyberspace proof-of-work is provided. The image may not easily be copied or stolen, and will look better when experienced in cyberspace than any stolen representation will look because of how our brains interpret visual information.