Does publication remove patent protection? I found the following publication: Fast Multiplication on Elliptic Curves over GF(2^m) without Precomputation which describes an algorithm for computing elliptic scalar multiplications on non-supersingular elliptic curves defined over GF(2^m). In the paragraph 4.2 a version using projective coordinates is described to avoid field inversions in GF(2^m) (please refer to the publication for unknown variables). On the other hand, I found the following patent: Accelerated finite field operations on an elliptic curve which presents A method for multiplication of a point P on elliptic curve E by a value k in order to derive a point kP comprises the steps of representing the number k as vector of binary digits stored in a register and forming a sequence of point pairs (P1, P2) wherein the point pairs differed most by P and wherein the successive series of point pairs are selected either by computing $(2mP,(2m+1)P)$ from (mP,(m+1)P) or ((2m+1)P,(2m+2)P) from (mP,(m+1)P). The computations may be performed without using the y-coordinate of the points during the computation while allowing the y-coordinate to be extracted at the end of the computations, thus, avoiding the use of inversion operations during the computation and therefore, speeding up the cryptographic processor functions. From my point of view, the algorithm presented in the publication is a particular case of the invention described in the patent. Plus it is well known that there are a lot of patents about ECC over binary fields. But I have a little doubt because one of the author of the publication (Julio Lopez) is from the same university of the patent authors (university of Waterloo). So my question is the following: Can I use the publication to perform ECC without being under patent protection? More generally, can an academic publication be under patent protection?
To answer the specific questions you asked: Can I use the publication to perform ECC without being under patent protection? Can an academic publication be under patent protection? The answers are: No, that academic paper does not provide any protection from patent litigation. Yes, an academic paper can publish the details of an invention, and that in no way voids the patent. The issue is the timing of the publication; the patent was filed in 1998; the academic paper was published in 2002. Once a patent is filed, the inventors (or anyone else, for that matter) can publish the patent, and that in no way invalidates the patent. To provide any protection against a patent, the prior art needs to be "prior", that is, earlier than the filing date of the patent. Now, this particular issue is made a bit tricky because there does appear to be prior citations of this invention. The whole reason this invention is called the "Montgomery ladder" (not Montgomery multiplication - that's something else) was because it was first published by Peter Montgomery in 1987. One would think that would invalidate the patent. However, I'm not an attorney; I cannot advise you to proceed under that assumption. Instead, I would suggest you follow the advice of Joao; there are plenty of elliptic curve routines out there; use one of them.
No. (Therefore no). Not necessarily. Yes. Is there a fair use for patents? No. "Fair use" is a affirmative defense for copyright infringement. The issue is that patents cover an design, idea or methodology, while copyright covers an "artistic" work. For example, if he were alive and working today, van Gogh would have copyright over his collection of paintings. If he developed a special paintbrush to make his distinctive style, he could patent the design for that brush. There is no obligation to make a patent available, much less at a "fair rate". And there is no obligation for a patent holder to make their patent available (so yes, they can block you directly or indirectly). There are various rationales for this. One is that a patent holder's historical reward for producing a new invention, a furtherance of common knowledge, is that that individual would receive an exclusive monopoly on the manufacture and sale of that invention. Often, this would serve as a way to recoup investment in new development and an incentive to experiment and expand the knowledge base of a country. This arrangement in the modern day is most closely represented by the exclusive license agreement, in which the licensor (in this case the patent holder) agrees to not only give the licensee the legal right to use the patent holder the legal ability to use their patent, but also agrees to limitations in what other people are granted that legal ability, in exchange for compensation.
Not having immediate access to the source doesn't preclude a finding of copyright infringement. If you have seen the source material, subconscious infringement can happen. However, in this example, both the short phrases doctrine and the merger doctrine would likely prevent the is_prime function from having copyright. Words and short phrases are not individually copyrightable, so the name would be free to take. Regarding the implementing code, if it isn't an exact copy (i.e. copy and paste), courts will apply the abstraction-filtration-comparision test. They may find that you took the selection and arrangement of instructions from the original source, albiet using different names. That selection and arrangement would probably be considered a substantial similarity and, if not for the merger doctrine, infringement. However, given the limited number of ways to express the prime-detection algorithm means that the expression of that idea has merged with the idea, and thus is not protected by copyright. (Or in some jurisdictions, merger is a defence to infringement rather than a bar to copyrightability).
There aren't bright line rules in the area of fair use (which is the core issue - you are clearly copying a work that has copyright protected portions, at least - the question is whether fair use provides a defense and whether some portions are not copyright protected). This inquiry is fact specific and driven by general standards. Context such as whether the use would be free or commercial matter as well. For your own notes, anything goes pretty much. This generally wouldn't constitute "publication" of the work and would be for personal educational used by someone who paid for the book anyway. For shared notes - it depends. Also not all kinds of copying is created equal. Some parts of textbooks are themselves in the public domain or not protectable by copyright. For example, even a lengthy quote from a scientific journal article would probably be allowed with attribution. It would also be easier to evaluate based upon the type of textbook. A history textbook can have protection similar to trade non-fiction and can have very original exposition. An algebra textbook, less so. Your question also points to an end run. If the professor is the author of the textbook (many of mine were in something of a racket), you could get permission from the author.
The software being free and open source has no impact on whether it infringes any patents or violates any copyrights. Copyrights attach to fixed representations of creative work in a tangible medium (e.g., the actual code and graphical elements of the software in question). As long as you aren't copying the copyrighted work of someone else, you should be in the clear. So, if you write your own code from scratch, or rely on code that you're allowed to use (e.g., "free" software with a permissive license that allows it to be used freely), you should be fine. On the other hand, if you copy a chunk of code that you aren't allowed to use, and then change the variable names so that it's superficially different, you're likely violating someone's copyright. Patents are a much more difficult question. To determine whether you would infringe any patents, you would have to read the independent claims of every patent that might be related. If you perform all the steps of any one of those claims, then you are infringing that claim (and therefore, the patent in which it is found). Unfortunately, this is much easier said than done. First, it may be difficult to search for all the potentially relevant patents, and once you've found them, there may be far too many to read. Second, claims are written in a type of language that is specific to patents, and someone without experience in patent law may not understand them correctly. Finally, the terms in the claims may not take on their plain English meaning, but rather may have been defined by the language in the rest of that patent, so it's possible that you might incorrectly think you were in the clear based on a misunderstanding arising from that. All that said, it may be best to go ahead with implementing an idea and then waiting to see what happens. Chances are that the implementation will arguably infringe some patent in some way, no matter what's done. But chances are also high that there will never be any worrisome enforcement action taken against it by a patent owner, simply due to the difficulty and expense associated with enforcing patent rights.
Patenting does not require a working product in fields where the performance is predictable before hand. Chemistry and biology do have criteria regarding real results. The description in the patent application needs to be detailed enough that someone of ordinary skill in the field could make and use the invention. After company A gets a patent (might be 3 years or never), it can try to stop company B from making, selling, offering to sell, using, or importing whatever is claimed in the issued patent. You say "does essentially the same thing". If you accomplish the identical goal (speaker identification from noisy audio, for example) but accomplish it by following very different steps, then there may be no infringement at all.
In general, using content provided by another who incorrectly posted it under a permissive license, such as a CC license, does not grant a valid license from the real copyright holder. That is, if A writes some code (or a song, or creates an image, or whatever else), it is protected by copyright. If B then posts it to the web, with a statement that it is released under a particular license, without having obtained permission from A, then B's &quot;release&quot; is of no value, because B had no rights to grant. If C downloads and uses this content, relying on B's license, then A could take legal action against C. C would probably be considered (in the US) an &quot;innocent infringer&quot; which reduces the minimum statutory damage amount, but does not otherwise change C's legal position. A could, if it chose, bring suit and possibly obtain a judgement including some damages. But to return to the practical case of code posted on one of the SE sites. Given the comparatively short code sections usually posted, and that they do not usually form a complete working program, and given further the stated educational purpose of SE, it is likely that in US law such a posting would constitute fair use, and in the law of other countries fall under one or another exception to copyright. That is a general conclusion, the details would matter. I have not heard of a case similar to that suggested in the question. I find it unlikely that an SE poster would post copyright-protected code without permission, that is valuable enough to be worth an infringement suit, and substantial enough and having enough effect on th market for the original to be outside the protection of fair use. Such a situatiion is, of course, possible, even if unlikely. Note that a cease-and-desist letter is not a court order, and is really only a threat of court action. its only legal effect is to put the recipient on notice, so that continued infringement is not without awareness of the copyright claim. To have legal effect the claimant must actually bring an infringement suit, which is not without cost.
There is no case law as yet However, the most likely situation is that there is no copyright in the original works because they are computer-generated. There is certainly copyright in the code that created the art but the output of that code, the art itself, would probably not be subject to copyright. Copyright only exists in art created by humans. The US Ninth Circuit has held that animals cannot create copyrighted works. Subsequently, the US Copyright office has rejected applications for registration (a prerequisite to a suit in the US) of computer-generated art because it “lacks the human authorship necessary to support a copyright claim.” While this position has not been tested in the courts, I don't think they are any more likely to grant copyright to a program than they were to a monkey. What's going on? The OP states that there is litigation: there isn't. What there is, is a DCMA takedown request from Larva Labs. If this is complied with that will be the end of the matter; if it isn't then there may be litigation. However, before Larva Labs could sue CryptoPunks in the US they would first need to get a writ of mandamus to force the USCO to register it. If they try and fail then there will be a legally binding court decision that Larva Labs don't own the copyright in any of their computer-generated art. Which kills their business model and, presumably, them. This would be a very high-risk move. They may choose to sue in a jurisdiction where registration is not a prerequisite, however, that court would still need to be satisfied that there was a copyright that could be breached. So that's just a different take on the same problem. I have ignored the issue of NFTs as these are legally problematic in their own right and irrelevant to the main question. However, the NFT and the artwork are not the same thing.