Such use might well be illegal, and subject the user to tort liability, or possibly even criminal liability.
For this discussion let us call the person or company that developed and wants to protect the information D, the person or company that downloaded and wants to use the information U, and the person who placed the information on the server P.
One possible source of liability is if D considers the information to be a trade-secret. The law on trade secrets varies to some extent in different countries, although there is a general similarity. Since no jurisdiction is specified in the question, I am going to look at the united-states law.
The LII page on "Trade Secrets defines a trade secret under the US Uniform Trade Secrets Act ("UTSA") as:
- "information, including a formula, pattern, compilation, program, device, method, technique, or process that:
- Derives independent economic value, actual or potential, from not being generally known to, and not being readily ascertainable by proper means by, other persons who can obtain economic value from its disclosure or use; and
- Is the subject of efforts that are reasonable under the circumstances to maintain its secrecy.
A similar definition is given by the USPTO page on "trade secret policy".
Prior to the USTA, and still in those US states that have not adopted the USTA, trade secrets were/are protected under the common law. The LII page lists the common law factors, as given by the Restatement of Torts (1939) § 757, comment b:
- The extent to which the information is known outside the claimant's business
- The extent to which it is known by employees and others involved in the business
- The extent of measures taken by the claimant to guard the secrecy of the information
- The value of the information to the business and its competitors
- The amount of effort or money expended by the business in developing the information
- The ease or difficulty with which the information could be properly acquired or duplicated by others
These factors may apply in other common-law countries.
In either case, one must consider how the would-be user came to acquire the information, and thus how it came to be on the server from which it was downloaded. One must also consider whether it was the subject of "reasonable efforts" to protect its secrecy, under the circumstances.
If P was violating an obligation of confidentiality, such as an NDA or a duty as part of an employment relationship, then the placement of the info on the server was improper. In such a case its acquisition by another, such as U might constitute misappropriation. The same would be true if a person under an obligation of confidentiality arranged for the server to be indexed by a search engine, when it should not have been. The case for misappropriation would be stronger if U knew that the information was considered confidential by D, and also if P had informed U about where to find the info, or what search terms would uncover it.
If P was acting with the permission of D, and P or someone else at D simply failed to realize that the server was, or might become, indexed, then the question is whether the steps taken by D to keep the info secret were reasonable. If this a case of "inadvertent disclosure resulting from the trade secret holder's failure to take reasonable protective measures" then there is no misappropriation, and the actions of U are lawful. That will depend of a judgement of whether D's actions were reasonable in light of the value of the info and the overall circumstances.
If the placement of the info on the server is considered to constitute "general publication" of the info, so that it is no longer secret in any meaningful sense, then D may have a claim against P, but not against U unless U acted in collaboration with P.
The documents downloaded from the4 server are almost surely protected by copyright. Directly incorporating them into an open source project without permission from the copyright holder would be copyright infringement, and would subject U to a suit for infringement.
However, copyright does not protect ideas, methods, or facts. If U learns a method or idea from the document, and uses that knowledge without directly copying or closely paraphrasing the document, there is no copyright infringement and no claim under copyright law.
The question does not mention any patents. It is possible that D has patented the method describe in the downloaded documents. If so, and if the patent is valid, any use by U would be patent infringement, and the question of how U learned the info becomes irrelevant. However, most software developments such as data structures are not patented, so this is a somewhat unlikely, albeit possible, case.
Notre that if the information is covered by a patent is is by definition not secret, as all patents must be openly disclosed. But they may not be widely publicized, and if U does not make a patent search, U may not realize that the document includes patented technology.
This possibility is largely incompatible with the trade secret possibility, althogh it is possible to use trade secrets in connection with patented tech.
In short whether U may lawfully use then info, or is subject to a tort claim by D, or even criminal action, depend on the details of the overall facts. U would do well to take legal advice on the matter before proceeding to use the info.