feat(pqid): hybrid post-quantum identity, AGPL-3.0 license

Player identity is now Ed25519 and ML-DSA-65 (NIST FIPS 204) together,
both signatures required. An attacker must break lattice assumptions and
elliptic curves, not either one — which covers both the quantum threat to
Ed25519 and the possibility that a 2024 lattice standard does not hold.

Signatures are domain-separated to this application so one captured from
another ML-DSA protocol cannot be replayed.

Licensed AGPL-3.0: a fork stood up as a service must publish its changes,
which is what keeps a provably-fair platform honest.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

LICENSE

@@ -0,0 +1,661 @@
+                    GNU AFFERO GENERAL PUBLIC LICENSE
+                       Version 3, 19 November 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+                            Preamble
+
+  The GNU Affero General Public License is a free, copyleft license for
+software and other kinds of works, specifically designed to ensure
+cooperation with the community in the case of network server software.
+
+  The licenses for most software and other practical works are designed
+to take away your freedom to share and change the works.  By contrast,
+our General Public Licenses are intended to guarantee your freedom to
+share and change all versions of a program--to make sure it remains free
+software for all its users.
+
+  When we speak of free software, we are referring to freedom, not
+price.  Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
+them if you wish), that you receive source code or can get it if you
+want it, that you can change the software or use pieces of it in new
+free programs, and that you know you can do these things.
+
+  Developers that use our General Public Licenses protect your rights
+with two steps: (1) assert copyright on the software, and (2) offer
+you this License which gives you legal permission to copy, distribute
+and/or modify the software.
+
+  A secondary benefit of defending all users' freedom is that
+improvements made in alternate versions of the program, if they
+receive widespread use, become available for other developers to
+incorporate.  Many developers of free software are heartened and
+encouraged by the resulting cooperation.  However, in the case of
+software used on network servers, this result may fail to come about.
+The GNU General Public License permits making a modified version and
+letting the public access it on a server without ever releasing its
+source code to the public.
+
+  The GNU Affero General Public License is designed specifically to
+ensure that, in such cases, the modified source code becomes available
+to the community.  It requires the operator of a network server to
+provide the source code of the modified version running there to the
+users of that server.  Therefore, public use of a modified version, on
+a publicly accessible server, gives the public access to the source
+code of the modified version.
+
+  An older license, called the Affero General Public License and
+published by Affero, was designed to accomplish similar goals.  This is
+a different license, not a version of the Affero GPL, but Affero has
+released a new version of the Affero GPL which permits relicensing under
+this license.
+
+  The precise terms and conditions for copying, distribution and
+modification follow.
+
+                       TERMS AND CONDITIONS
+
+  0. Definitions.
+
+  "This License" refers to version 3 of the GNU Affero General Public License.
+
+  "Copyright" also means copyright-like laws that apply to other kinds of
+works, such as semiconductor masks.
+
+  "The Program" refers to any copyrightable work licensed under this
+License.  Each licensee is addressed as "you".  "Licensees" and
+"recipients" may be individuals or organizations.
+
+  To "modify" a work means to copy from or adapt all or part of the work
+in a fashion requiring copyright permission, other than the making of an
+exact copy.  The resulting work is called a "modified version" of the
+earlier work or a work "based on" the earlier work.
+
+  A "covered work" means either the unmodified Program or a work based
+on the Program.
+
+  To "propagate" a work means to do anything with it that, without
+permission, would make you directly or secondarily liable for
+infringement under applicable copyright law, except executing it on a
+computer or modifying a private copy.  Propagation includes copying,
+distribution (with or without modification), making available to the
+public, and in some countries other activities as well.
+
+  To "convey" a work means any kind of propagation that enables other
+parties to make or receive copies.  Mere interaction with a user through
+a computer network, with no transfer of a copy, is not conveying.
+
+  An interactive user interface displays "Appropriate Legal Notices"
+to the extent that it includes a convenient and prominently visible
+feature that (1) displays an appropriate copyright notice, and (2)
+tells the user that there is no warranty for the work (except to the
+extent that warranties are provided), that licensees may convey the
+work under this License, and how to view a copy of this License.  If
+the interface presents a list of user commands or options, such as a
+menu, a prominent item in the list meets this criterion.
+
+  1. Source Code.
+
+  The "source code" for a work means the preferred form of the work
+for making modifications to it.  "Object code" means any non-source
+form of a work.
+
+  A "Standard Interface" means an interface that either is an official
+standard defined by a recognized standards body, or, in the case of
+interfaces specified for a particular programming language, one that
+is widely used among developers working in that language.
+
+  The "System Libraries" of an executable work include anything, other
+than the work as a whole, that (a) is included in the normal form of
+packaging a Major Component, but which is not part of that Major
+Component, and (b) serves only to enable use of the work with that
+Major Component, or to implement a Standard Interface for which an
+implementation is available to the public in source code form.  A
+"Major Component", in this context, means a major essential component
+(kernel, window system, and so on) of the specific operating system
+(if any) on which the executable work runs, or a compiler used to
+produce the work, or an object code interpreter used to run it.
+
+  The "Corresponding Source" for a work in object code form means all
+the source code needed to generate, install, and (for an executable
+work) run the object code and to modify the work, including scripts to
+control those activities.  However, it does not include the work's
+System Libraries, or general-purpose tools or generally available free
+programs which are used unmodified in performing those activities but
+which are not part of the work.  For example, Corresponding Source
+includes interface definition files associated with source files for
+the work, and the source code for shared libraries and dynamically
+linked subprograms that the work is specifically designed to require,
+such as by intimate data communication or control flow between those
+subprograms and other parts of the work.
+
+  The Corresponding Source need not include anything that users
+can regenerate automatically from other parts of the Corresponding
+Source.
+
+  The Corresponding Source for a work in source code form is that
+same work.
+
+  2. Basic Permissions.
+
+  All rights granted under this License are granted for the term of
+copyright on the Program, and are irrevocable provided the stated
+conditions are met.  This License explicitly affirms your unlimited
+permission to run the unmodified Program.  The output from running a
+covered work is covered by this License only if the output, given its
+content, constitutes a covered work.  This License acknowledges your
+rights of fair use or other equivalent, as provided by copyright law.
+
+  You may make, run and propagate covered works that you do not
+convey, without conditions so long as your license otherwise remains
+in force.  You may convey covered works to others for the sole purpose
+of having them make modifications exclusively for you, or provide you
+with facilities for running those works, provided that you comply with
+the terms of this License in conveying all material for which you do
+not control copyright.  Those thus making or running the covered works
+for you must do so exclusively on your behalf, under your direction
+and control, on terms that prohibit them from making any copies of
+your copyrighted material outside their relationship with you.
+
+  Conveying under any other circumstances is permitted solely under
+the conditions stated below.  Sublicensing is not allowed; section 10
+makes it unnecessary.
+
+  3. Protecting Users' Legal Rights From Anti-Circumvention Law.
+
+  No covered work shall be deemed part of an effective technological
+measure under any applicable law fulfilling obligations under article
+11 of the WIPO copyright treaty adopted on 20 December 1996, or
+similar laws prohibiting or restricting circumvention of such
+measures.
+
+  When you convey a covered work, you waive any legal power to forbid
+circumvention of technological measures to the extent such circumvention
+is effected by exercising rights under this License with respect to
+the covered work, and you disclaim any intention to limit operation or
+modification of the work as a means of enforcing, against the work's
+users, your or third parties' legal rights to forbid circumvention of
+technological measures.
+
+  4. Conveying Verbatim Copies.
+
+  You may convey verbatim copies of the Program's source code as you
+receive it, in any medium, provided that you conspicuously and
+appropriately publish on each copy an appropriate copyright notice;
+keep intact all notices stating that this License and any
+non-permissive terms added in accord with section 7 apply to the code;
+keep intact all notices of the absence of any warranty; and give all
+recipients a copy of this License along with the Program.
+
+  You may charge any price or no price for each copy that you convey,
+and you may offer support or warranty protection for a fee.
+
+  5. Conveying Modified Source Versions.
+
+  You may convey a work based on the Program, or the modifications to
+produce it from the Program, in the form of source code under the
+terms of section 4, provided that you also meet all of these conditions:
+
+    a) The work must carry prominent notices stating that you modified
+    it, and giving a relevant date.
+
+    b) The work must carry prominent notices stating that it is
+    released under this License and any conditions added under section
+    7.  This requirement modifies the requirement in section 4 to
+    "keep intact all notices".
+
+    c) You must license the entire work, as a whole, under this
+    License to anyone who comes into possession of a copy.  This
+    License will therefore apply, along with any applicable section 7
+    additional terms, to the whole of the work, and all its parts,
+    regardless of how they are packaged.  This License gives no
+    permission to license the work in any other way, but it does not
+    invalidate such permission if you have separately received it.
+
+    d) If the work has interactive user interfaces, each must display
+    Appropriate Legal Notices; however, if the Program has interactive
+    interfaces that do not display Appropriate Legal Notices, your
+    work need not make them do so.
+
+  A compilation of a covered work with other separate and independent
+works, which are not by their nature extensions of the covered work,
+and which are not combined with it such as to form a larger program,
+in or on a volume of a storage or distribution medium, is called an
+"aggregate" if the compilation and its resulting copyright are not
+used to limit the access or legal rights of the compilation's users
+beyond what the individual works permit.  Inclusion of a covered work
+in an aggregate does not cause this License to apply to the other
+parts of the aggregate.
+
+  6. Conveying Non-Source Forms.
+
+  You may convey a covered work in object code form under the terms
+of sections 4 and 5, provided that you also convey the
+machine-readable Corresponding Source under the terms of this License,
+in one of these ways:
+
+    a) Convey the object code in, or embodied in, a physical product
+    (including a physical distribution medium), accompanied by the
+    Corresponding Source fixed on a durable physical medium
+    customarily used for software interchange.
+
+    b) Convey the object code in, or embodied in, a physical product
+    (including a physical distribution medium), accompanied by a
+    written offer, valid for at least three years and valid for as
+    long as you offer spare parts or customer support for that product
+    model, to give anyone who possesses the object code either (1) a
+    copy of the Corresponding Source for all the software in the
+    product that is covered by this License, on a durable physical
+    medium customarily used for software interchange, for a price no
+    more than your reasonable cost of physically performing this
+    conveying of source, or (2) access to copy the
+    Corresponding Source from a network server at no charge.
+
+    c) Convey individual copies of the object code with a copy of the
+    written offer to provide the Corresponding Source.  This
+    alternative is allowed only occasionally and noncommercially, and
+    only if you received the object code with such an offer, in accord
+    with subsection 6b.
+
+    d) Convey the object code by offering access from a designated
+    place (gratis or for a charge), and offer equivalent access to the
+    Corresponding Source in the same way through the same place at no
+    further charge.  You need not require recipients to copy the
+    Corresponding Source along with the object code.  If the place to
+    copy the object code is a network server, the Corresponding Source
+    may be on a different server (operated by you or a third party)
+    that supports equivalent copying facilities, provided you maintain
+    clear directions next to the object code saying where to find the
+    Corresponding Source.  Regardless of what server hosts the
+    Corresponding Source, you remain obligated to ensure that it is
+    available for as long as needed to satisfy these requirements.
+
+    e) Convey the object code using peer-to-peer transmission, provided
+    you inform other peers where the object code and Corresponding
+    Source of the work are being offered to the general public at no
+    charge under subsection 6d.
+
+  A separable portion of the object code, whose source code is excluded
+from the Corresponding Source as a System Library, need not be
+included in conveying the object code work.
+
+  A "User Product" is either (1) a "consumer product", which means any
+tangible personal property which is normally used for personal, family,
+or household purposes, or (2) anything designed or sold for incorporation
+into a dwelling.  In determining whether a product is a consumer product,
+doubtful cases shall be resolved in favor of coverage.  For a particular
+product received by a particular user, "normally used" refers to a
+typical or common use of that class of product, regardless of the status
+of the particular user or of the way in which the particular user
+actually uses, or expects or is expected to use, the product.  A product
+is a consumer product regardless of whether the product has substantial
+commercial, industrial or non-consumer uses, unless such uses represent
+the only significant mode of use of the product.
+
+  "Installation Information" for a User Product means any methods,
+procedures, authorization keys, or other information required to install
+and execute modified versions of a covered work in that User Product from
+a modified version of its Corresponding Source.  The information must
+suffice to ensure that the continued functioning of the modified object
+code is in no case prevented or interfered with solely because
+modification has been made.
+
+  If you convey an object code work under this section in, or with, or
+specifically for use in, a User Product, and the conveying occurs as
+part of a transaction in which the right of possession and use of the
+User Product is transferred to the recipient in perpetuity or for a
+fixed term (regardless of how the transaction is characterized), the
+Corresponding Source conveyed under this section must be accompanied
+by the Installation Information.  But this requirement does not apply
+if neither you nor any third party retains the ability to install
+modified object code on the User Product (for example, the work has
+been installed in ROM).
+
+  The requirement to provide Installation Information does not include a
+requirement to continue to provide support service, warranty, or updates
+for a work that has been modified or installed by the recipient, or for
+the User Product in which it has been modified or installed.  Access to a
+network may be denied when the modification itself materially and
+adversely affects the operation of the network or violates the rules and
+protocols for communication across the network.
+
+  Corresponding Source conveyed, and Installation Information provided,
+in accord with this section must be in a format that is publicly
+documented (and with an implementation available to the public in
+source code form), and must require no special password or key for
+unpacking, reading or copying.
+
+  7. Additional Terms.
+
+  "Additional permissions" are terms that supplement the terms of this
+License by making exceptions from one or more of its conditions.
+Additional permissions that are applicable to the entire Program shall
+be treated as though they were included in this License, to the extent
+that they are valid under applicable law.  If additional permissions
+apply only to part of the Program, that part may be used separately
+under those permissions, but the entire Program remains governed by
+this License without regard to the additional permissions.
+
+  When you convey a copy of a covered work, you may at your option
+remove any additional permissions from that copy, or from any part of
+it.  (Additional permissions may be written to require their own
+removal in certain cases when you modify the work.)  You may place
+additional permissions on material, added by you to a covered work,
+for which you have or can give appropriate copyright permission.
+
+  Notwithstanding any other provision of this License, for material you
+add to a covered work, you may (if authorized by the copyright holders of
+that material) supplement the terms of this License with terms:
+
+    a) Disclaiming warranty or limiting liability differently from the
+    terms of sections 15 and 16 of this License; or
+
+    b) Requiring preservation of specified reasonable legal notices or
+    author attributions in that material or in the Appropriate Legal
+    Notices displayed by works containing it; or
+
+    c) Prohibiting misrepresentation of the origin of that material, or
+    requiring that modified versions of such material be marked in
+    reasonable ways as different from the original version; or
+
+    d) Limiting the use for publicity purposes of names of licensors or
+    authors of the material; or
+
+    e) Declining to grant rights under trademark law for use of some
+    trade names, trademarks, or service marks; or
+
+    f) Requiring indemnification of licensors and authors of that
+    material by anyone who conveys the material (or modified versions of
+    it) with contractual assumptions of liability to the recipient, for
+    any liability that these contractual assumptions directly impose on
+    those licensors and authors.
+
+  All other non-permissive additional terms are considered "further
+restrictions" within the meaning of section 10.  If the Program as you
+received it, or any part of it, contains a notice stating that it is
+governed by this License along with a term that is a further
+restriction, you may remove that term.  If a license document contains
+a further restriction but permits relicensing or conveying under this
+License, you may add to a covered work material governed by the terms
+of that license document, provided that the further restriction does
+not survive such relicensing or conveying.
+
+  If you add terms to a covered work in accord with this section, you
+must place, in the relevant source files, a statement of the
+additional terms that apply to those files, or a notice indicating
+where to find the applicable terms.
+
+  Additional terms, permissive or non-permissive, may be stated in the
+form of a separately written license, or stated as exceptions;
+the above requirements apply either way.
+
+  8. Termination.
+
+  You may not propagate or modify a covered work except as expressly
+provided under this License.  Any attempt otherwise to propagate or
+modify it is void, and will automatically terminate your rights under
+this License (including any patent licenses granted under the third
+paragraph of section 11).
+
+  However, if you cease all violation of this License, then your
+license from a particular copyright holder is reinstated (a)
+provisionally, unless and until the copyright holder explicitly and
+finally terminates your license, and (b) permanently, if the copyright
+holder fails to notify you of the violation by some reasonable means
+prior to 60 days after the cessation.
+
+  Moreover, your license from a particular copyright holder is
+reinstated permanently if the copyright holder notifies you of the
+violation by some reasonable means, this is the first time you have
+received notice of violation of this License (for any work) from that
+copyright holder, and you cure the violation prior to 30 days after
+your receipt of the notice.
+
+  Termination of your rights under this section does not terminate the
+licenses of parties who have received copies or rights from you under
+this License.  If your rights have been terminated and not permanently
+reinstated, you do not qualify to receive new licenses for the same
+material under section 10.
+
+  9. Acceptance Not Required for Having Copies.
+
+  You are not required to accept this License in order to receive or
+run a copy of the Program.  Ancillary propagation of a covered work
+occurring solely as a consequence of using peer-to-peer transmission
+to receive a copy likewise does not require acceptance.  However,
+nothing other than this License grants you permission to propagate or
+modify any covered work.  These actions infringe copyright if you do
+not accept this License.  Therefore, by modifying or propagating a
+covered work, you indicate your acceptance of this License to do so.
+
+  10. Automatic Licensing of Downstream Recipients.
+
+  Each time you convey a covered work, the recipient automatically
+receives a license from the original licensors, to run, modify and
+propagate that work, subject to this License.  You are not responsible
+for enforcing compliance by third parties with this License.
+
+  An "entity transaction" is a transaction transferring control of an
+organization, or substantially all assets of one, or subdividing an
+organization, or merging organizations.  If propagation of a covered
+work results from an entity transaction, each party to that
+transaction who receives a copy of the work also receives whatever
+licenses to the work the party's predecessor in interest had or could
+give under the previous paragraph, plus a right to possession of the
+Corresponding Source of the work from the predecessor in interest, if
+the predecessor has it or can get it with reasonable efforts.
+
+  You may not impose any further restrictions on the exercise of the
+rights granted or affirmed under this License.  For example, you may
+not impose a license fee, royalty, or other charge for exercise of
+rights granted under this License, and you may not initiate litigation
+(including a cross-claim or counterclaim in a lawsuit) alleging that
+any patent claim is infringed by making, using, selling, offering for
+sale, or importing the Program or any portion of it.
+
+  11. Patents.
+
+  A "contributor" is a copyright holder who authorizes use under this
+License of the Program or a work on which the Program is based.  The
+work thus licensed is called the contributor's "contributor version".
+
+  A contributor's "essential patent claims" are all patent claims
+owned or controlled by the contributor, whether already acquired or
+hereafter acquired, that would be infringed by some manner, permitted
+by this License, of making, using, or selling its contributor version,
+but do not include claims that would be infringed only as a
+consequence of further modification of the contributor version.  For
+purposes of this definition, "control" includes the right to grant
+patent sublicenses in a manner consistent with the requirements of
+this License.
+
+  Each contributor grants you a non-exclusive, worldwide, royalty-free
+patent license under the contributor's essential patent claims, to
+make, use, sell, offer for sale, import and otherwise run, modify and
+propagate the contents of its contributor version.
+
+  In the following three paragraphs, a "patent license" is any express
+agreement or commitment, however denominated, not to enforce a patent
+(such as an express permission to practice a patent or covenant not to
+sue for patent infringement).  To "grant" such a patent license to a
+party means to make such an agreement or commitment not to enforce a
+patent against the party.
+
+  If you convey a covered work, knowingly relying on a patent license,
+and the Corresponding Source of the work is not available for anyone
+to copy, free of charge and under the terms of this License, through a
+publicly available network server or other readily accessible means,
+then you must either (1) cause the Corresponding Source to be so
+available, or (2) arrange to deprive yourself of the benefit of the
+patent license for this particular work, or (3) arrange, in a manner
+consistent with the requirements of this License, to extend the patent
+license to downstream recipients.  "Knowingly relying" means you have
+actual knowledge that, but for the patent license, your conveying the
+covered work in a country, or your recipient's use of the covered work
+in a country, would infringe one or more identifiable patents in that
+country that you have reason to believe are valid.
+
+  If, pursuant to or in connection with a single transaction or
+arrangement, you convey, or propagate by procuring conveyance of, a
+covered work, and grant a patent license to some of the parties
+receiving the covered work authorizing them to use, propagate, modify
+or convey a specific copy of the covered work, then the patent license
+you grant is automatically extended to all recipients of the covered
+work and works based on it.
+
+  A patent license is "discriminatory" if it does not include within
+the scope of its coverage, prohibits the exercise of, or is
+conditioned on the non-exercise of one or more of the rights that are
+specifically granted under this License.  You may not convey a covered
+work if you are a party to an arrangement with a third party that is
+in the business of distributing software, under which you make payment
+to the third party based on the extent of your activity of conveying
+the work, and under which the third party grants, to any of the
+parties who would receive the covered work from you, a discriminatory
+patent license (a) in connection with copies of the covered work
+conveyed by you (or copies made from those copies), or (b) primarily
+for and in connection with specific products or compilations that
+contain the covered work, unless you entered into that arrangement,
+or that patent license was granted, prior to 28 March 2007.
+
+  Nothing in this License shall be construed as excluding or limiting
+any implied license or other defenses to infringement that may
+otherwise be available to you under applicable patent law.
+
+  12. No Surrender of Others' Freedom.
+
+  If conditions are imposed on you (whether by court order, agreement or
+otherwise) that contradict the conditions of this License, they do not
+excuse you from the conditions of this License.  If you cannot convey a
+covered work so as to satisfy simultaneously your obligations under this
+License and any other pertinent obligations, then as a consequence you may
+not convey it at all.  For example, if you agree to terms that obligate you
+to collect a royalty for further conveying from those to whom you convey
+the Program, the only way you could satisfy both those terms and this
+License would be to refrain entirely from conveying the Program.
+
+  13. Remote Network Interaction; Use with the GNU General Public License.
+
+  Notwithstanding any other provision of this License, if you modify the
+Program, your modified version must prominently offer all users
+interacting with it remotely through a computer network (if your version
+supports such interaction) an opportunity to receive the Corresponding
+Source of your version by providing access to the Corresponding Source
+from a network server at no charge, through some standard or customary
+means of facilitating copying of software.  This Corresponding Source
+shall include the Corresponding Source for any work covered by version 3
+of the GNU General Public License that is incorporated pursuant to the
+following paragraph.
+
+  Notwithstanding any other provision of this License, you have
+permission to link or combine any covered work with a work licensed
+under version 3 of the GNU General Public License into a single
+combined work, and to convey the resulting work.  The terms of this
+License will continue to apply to the part which is the covered work,
+but the work with which it is combined will remain governed by version
+3 of the GNU General Public License.
+
+  14. Revised Versions of this License.
+
+  The Free Software Foundation may publish revised and/or new versions of
+the GNU Affero General Public License from time to time.  Such new versions
+will be similar in spirit to the present version, but may differ in detail to
+address new problems or concerns.
+
+  Each version is given a distinguishing version number.  If the
+Program specifies that a certain numbered version of the GNU Affero General
+Public License "or any later version" applies to it, you have the
+option of following the terms and conditions either of that numbered
+version or of any later version published by the Free Software
+Foundation.  If the Program does not specify a version number of the
+GNU Affero General Public License, you may choose any version ever published
+by the Free Software Foundation.
+
+  If the Program specifies that a proxy can decide which future
+versions of the GNU Affero General Public License can be used, that proxy's
+public statement of acceptance of a version permanently authorizes you
+to choose that version for the Program.
+
+  Later license versions may give you additional or different
+permissions.  However, no additional obligations are imposed on any
+author or copyright holder as a result of your choosing to follow a
+later version.
+
+  15. Disclaimer of Warranty.
+
+  THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
+APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
+HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
+OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
+THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
+IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
+ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
+
+  16. Limitation of Liability.
+
+  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
+THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
+GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
+USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
+DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
+PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+  17. Interpretation of Sections 15 and 16.
+
+  If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+                     END OF TERMS AND CONDITIONS
+
+            How to Apply These Terms to Your New Programs
+
+  If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+  To do so, attach the following notices to the program.  It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+    <one line to give the program's name and a brief idea of what it does.>
+    Copyright (C) <year>  <name of author>
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Affero General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU Affero General Public License for more details.
+
+    You should have received a copy of the GNU Affero General Public License
+    along with this program.  If not, see <https://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+  If your software can interact with users remotely through a computer
+network, you should also make sure that it provides a way for users to
+get its source.  For example, if your program is a web application, its
+interface could display a "Source" link that leads users to an archive
+of the code.  There are many ways you could offer source, and different
+solutions will be better for different programs; see section 13 for the
+specific requirements.
+
+  You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU AGPL, see
+<https://www.gnu.org/licenses/>.

go.mod

@@ -2,13 +2,17 @@ module github.com/drjones/quantum-arcade
 
 go 1.26.5
 
-require github.com/jackc/pgx/v5 v5.10.0
+require (
+	github.com/cloudflare/circl v1.6.5
+	github.com/coder/websocket v1.8.15
+	github.com/jackc/pgx/v5 v5.10.0
+)
 
 require (
-	github.com/coder/websocket v1.8.15 // indirect
 	github.com/jackc/pgpassfile v1.0.0 // indirect
 	github.com/jackc/pgservicefile v0.0.0-20240606120523-5a60cdf6a761 // indirect
 	github.com/jackc/puddle/v2 v2.2.2 // indirect
 	golang.org/x/sync v0.17.0 // indirect
+	golang.org/x/sys v0.47.0 // indirect
 	golang.org/x/text v0.29.0 // indirect
 )

go.sum

@@ -1,3 +1,5 @@
+github.com/cloudflare/circl v1.6.5 h1:O64F26HEqNhznd/hrC5KZXVKYuKM2rx4deZDTc4ihQA=
+github.com/cloudflare/circl v1.6.5/go.mod h1:h5LNyxAc5nTue9DS5jT+48en2PSDYt3zdGnz5OstK6c=
 github.com/coder/websocket v1.8.15 h1:6B2JPeOGlpff2Uz6vOEH1Vzpi0iUz20A+lPVhPHtNUA=
 github.com/coder/websocket v1.8.15/go.mod h1:NX3SzP+inril6yawo5CQXx8+fk145lPDC6pumgx0mVg=
 github.com/davecgh/go-spew v1.1.0/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38=
@@ -20,6 +22,8 @@ github.com/stretchr/testify v1.11.1 h1:7s2iGBzp5EwR7/aIZr8ao5+dra3wiQyKjjFuvgVKu
 github.com/stretchr/testify v1.11.1/go.mod h1:wZwfW3scLgRK+23gO65QZefKpKQRnfz6sD981Nm4B6U=
 golang.org/x/sync v0.17.0 h1:l60nONMj9l5drqw6jlhIELNv9I0A4OFgRsG9k2oT9Ug=
 golang.org/x/sync v0.17.0/go.mod h1:9KTHXmSnoGruLpwFjVSX0lNNA75CykiMECbovNTZqGI=
+golang.org/x/sys v0.47.0 h1:o7XGOvZQCADBQQ4Y7VNq2dRWQR7JmOUW8Kxx4ZsNgWs=
+golang.org/x/sys v0.47.0/go.mod h1:4GL1E5IUh+htKOUEOaiffhrAeqysfVGipDYzABqnCmw=
 golang.org/x/text v0.29.0 h1:1neNs90w9YzJ9BocxfsQNHKuAT4pkghyXc4nhZ6sJvk=
 golang.org/x/text v0.29.0/go.mod h1:7MhJOA9CD2qZyOKYazxdYMF85OwPdEr9jTtBpO7ydH4=
 gopkg.in/check.v1 v0.0.0-20161208181325-20d25e280405/go.mod h1:Co6ibVJAznAaIkqp8huTwlJQCZ016jof/cbN4VW5Yz0=

pkg/pqid/export_test.go

@@ -0,0 +1,12 @@
+package pqid_test
+
+import (
+	"github.com/cloudflare/circl/sign/mldsa/mldsa65"
+	"github.com/drjones/quantum-arcade/pkg/pqid"
+)
+
+// signWithContext produces an ML-DSA signature under an arbitrary context, so
+// the domain-separation test can prove the production context is enforced.
+func signWithContext(priv *pqid.PrivateKey, msg, ctx, out []byte) error {
+	return mldsa65.SignTo(priv.PQ, msg, ctx, false, out)
+}

pkg/pqid/pqid.go

@@ -0,0 +1,171 @@
+// Package pqid implements hybrid post-quantum player identity.
+//
+// A player's key is two keys: classical Ed25519 and post-quantum ML-DSA-65
+// (NIST FIPS 204). Both signatures are required for every authentication, so
+// the identity holds if *either* algorithm survives:
+//
+//   - Ed25519 alone falls to Shor's algorithm on a sufficiently large quantum
+//     computer.
+//   - ML-DSA is young. Lattice cryptanalysis is an active field, and betting
+//     everything on a 2024 standard would be its own kind of naive.
+//
+// Requiring both is the composition NIST and the IETF recommend: an attacker
+// must break lattice assumptions *and* elliptic curves, not either one.
+//
+// What this does and does not protect:
+//
+//	protected     player identity, session authentication, bet authorisation
+//	protected     round fairness — commit-reveal is SHA-256/HMAC, and Grover
+//	              only halves the security margin, leaving ~128 bits
+//	NOT protected Bitcoin and Lightning settlement, which sign with secp256k1.
+//	              No application-layer choice can change that.
+package pqid
+
+import (
+	"crypto/ed25519"
+	"crypto/sha256"
+	"encoding/hex"
+	"errors"
+	"fmt"
+	"io"
+
+	"github.com/cloudflare/circl/sign/mldsa/mldsa65"
+)
+
+// Sizes of the wire encodings.
+const (
+	EdPublicKeySize = ed25519.PublicKeySize // 32
+	EdSignatureSize = ed25519.SignatureSize // 64
+
+	PQPublicKeySize = mldsa65.PublicKeySize // 1952
+	PQSignatureSize = mldsa65.SignatureSize // 3309
+
+	PublicKeySize = EdPublicKeySize + PQPublicKeySize
+	SignatureSize = EdSignatureSize + PQSignatureSize
+
+	// IDSize is the length of the account identifier derived from a key.
+	IDSize = sha256.Size
+)
+
+// context binds signatures to this application, so a signature produced for
+// some other ML-DSA protocol cannot be replayed here.
+var context = []byte("quantum-arcade/v1")
+
+var (
+	ErrMalformedKey       = errors.New("pqid: malformed public key")
+	ErrMalformedSignature = errors.New("pqid: malformed signature")
+	ErrClassicalFailed    = errors.New("pqid: ed25519 signature did not verify")
+	ErrPostQuantumFailed  = errors.New("pqid: ML-DSA signature did not verify")
+)
+
+// PublicKey is a player's hybrid identity.
+type PublicKey struct {
+	Ed ed25519.PublicKey
+	PQ *mldsa65.PublicKey
+}
+
+// PrivateKey is the matching secret half. Clients hold this; the server never
+// sees it.
+type PrivateKey struct {
+	Ed ed25519.PrivateKey
+	PQ *mldsa65.PrivateKey
+}
+
+// GenerateKey creates a hybrid keypair.
+func GenerateKey(rand io.Reader) (*PublicKey, *PrivateKey, error) {
+	edPub, edPriv, err := ed25519.GenerateKey(rand)
+	if err != nil {
+		return nil, nil, fmt.Errorf("pqid: generating ed25519 key: %w", err)
+	}
+	pqPub, pqPriv, err := mldsa65.GenerateKey(rand)
+	if err != nil {
+		return nil, nil, fmt.Errorf("pqid: generating ML-DSA key: %w", err)
+	}
+	return &PublicKey{Ed: edPub, PQ: pqPub}, &PrivateKey{Ed: edPriv, PQ: pqPriv}, nil
+}
+
+// Bytes encodes the public key as ed25519 || ML-DSA.
+func (p *PublicKey) Bytes() []byte {
+	out := make([]byte, 0, PublicKeySize)
+	out = append(out, p.Ed...)
+	pq, err := p.PQ.MarshalBinary()
+	if err != nil {
+		// MarshalBinary on a valid key cannot fail; a failure here means the
+		// key is corrupt, and silently returning a short key would be worse.
+		panic("pqid: marshalling ML-DSA public key: " + err.Error())
+	}
+	return append(out, pq...)
+}
+
+// Hex renders the public key for transport.
+func (p *PublicKey) Hex() string { return hex.EncodeToString(p.Bytes()) }
+
+// ID is the account identifier: SHA-256 over the whole hybrid key.
+//
+// The ledger keys on this rather than the raw key because the hybrid key is
+// nearly 2KB, and a fixed 32-byte identifier keeps indexes small. Hashing also
+// means the identifier is stable in length no matter how the key evolves.
+func (p *PublicKey) ID() []byte {
+	sum := sha256.Sum256(p.Bytes())
+	return sum[:]
+}
+
+// ParsePublicKey decodes a hybrid public key from its wire encoding.
+func ParsePublicKey(b []byte) (*PublicKey, error) {
+	if len(b) != PublicKeySize {
+		return nil, fmt.Errorf("%w: got %d bytes, want %d",
+			ErrMalformedKey, len(b), PublicKeySize)
+	}
+	ed := ed25519.PublicKey(append([]byte(nil), b[:EdPublicKeySize]...))
+
+	var pq mldsa65.PublicKey
+	if err := pq.UnmarshalBinary(b[EdPublicKeySize:]); err != nil {
+		return nil, fmt.Errorf("%w: %v", ErrMalformedKey, err)
+	}
+	return &PublicKey{Ed: ed, PQ: &pq}, nil
+}
+
+// ParsePublicKeyHex decodes a hex-encoded hybrid public key.
+func ParsePublicKeyHex(s string) (*PublicKey, error) {
+	b, err := hex.DecodeString(s)
+	if err != nil {
+		return nil, fmt.Errorf("%w: not hex", ErrMalformedKey)
+	}
+	return ParsePublicKey(b)
+}
+
+// Sign produces both signatures over the message, concatenated.
+func Sign(priv *PrivateKey, msg []byte) ([]byte, error) {
+	edSig := ed25519.Sign(priv.Ed, msg)
+
+	pqSig := make([]byte, PQSignatureSize)
+	// randomized=false gives deterministic (hedged) signatures, so a bad RNG
+	// on a phone cannot leak the key through signature randomness.
+	if err := mldsa65.SignTo(priv.PQ, msg, context, false, pqSig); err != nil {
+		return nil, fmt.Errorf("pqid: ML-DSA signing: %w", err)
+	}
+
+	out := make([]byte, 0, SignatureSize)
+	out = append(out, edSig...)
+	return append(out, pqSig...), nil
+}
+
+// Verify checks both signatures. Both must pass.
+//
+// It deliberately reports which half failed: a mismatch between the two is
+// diagnostic — it means a client is half-upgraded or something is tampering
+// with one algorithm — and that is worth surfacing rather than flattening into
+// a generic failure. Nothing secret is revealed by saying which one broke.
+func Verify(pub *PublicKey, msg, sig []byte) error {
+	if len(sig) != SignatureSize {
+		return fmt.Errorf("%w: got %d bytes, want %d",
+			ErrMalformedSignature, len(sig), SignatureSize)
+	}
+	if !ed25519.Verify(pub.Ed, msg, sig[:EdSignatureSize]) {
+		return ErrClassicalFailed
+	}
+	if !mldsa65.Verify(pub.PQ, msg, context, sig[EdSignatureSize:]) {
+		return ErrPostQuantumFailed
+	}
+	return nil
+}

pkg/pqid/pqid_test.go

@@ -0,0 +1,210 @@
+package pqid_test
+
+import (
+	"crypto/rand"
+	"errors"
+	"testing"
+
+	"github.com/drjones/quantum-arcade/pkg/pqid"
+)
+
+func newKey(t *testing.T) (*pqid.PublicKey, *pqid.PrivateKey) {
+	t.Helper()
+	pub, priv, err := pqid.GenerateKey(rand.Reader)
+	if err != nil {
+		t.Fatal(err)
+	}
+	return pub, priv
+}
+
+func TestSignAndVerify(t *testing.T) {
+	pub, priv := newKey(t)
+	msg := []byte("authenticate me")
+
+	sig, err := pqid.Sign(priv, msg)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if err := pqid.Verify(pub, msg, sig); err != nil {
+		t.Fatalf("valid hybrid signature rejected: %v", err)
+	}
+}
+
+func TestWrongMessageFails(t *testing.T) {
+	pub, priv := newKey(t)
+	sig, _ := pqid.Sign(priv, []byte("original"))
+	if err := pqid.Verify(pub, []byte("tampered"), sig); err == nil {
+		t.Fatal("signature verified against a different message")
+	}
+}
+
+func TestWrongKeyFails(t *testing.T) {
+	_, priv := newKey(t)
+	other, _ := newKey(t)
+	sig, _ := pqid.Sign(priv, []byte("msg"))
+	if err := pqid.Verify(other, []byte("msg"), sig); err == nil {
+		t.Fatal("signature verified under the wrong key")
+	}
+}
+
+// The whole point of hybrid: forging only the classical half must not
+// authenticate. This is the quantum-adversary scenario — Shor breaks Ed25519,
+// ML-DSA still holds.
+func TestValidClassicalWithBrokenPostQuantumFails(t *testing.T) {
+	pub, priv := newKey(t)
+	msg := []byte("msg")
+	sig, _ := pqid.Sign(priv, msg)
+
+	// Keep the genuine Ed25519 signature, corrupt the ML-DSA half.
+	forged := append([]byte(nil), sig...)
+	forged[pqid.EdSignatureSize+10] ^= 0xff
+
+	err := pqid.Verify(pub, msg, forged)
+	if err == nil {
+		t.Fatal("a broken post-quantum half still authenticated")
+	}
+	if !errors.Is(err, pqid.ErrPostQuantumFailed) {
+		t.Fatalf("got %v, want ErrPostQuantumFailed", err)
+	}
+}
+
+// And the mirror case: if lattice cryptography turns out to be weak, Ed25519
+// must still stand in the way.
+func TestValidPostQuantumWithBrokenClassicalFails(t *testing.T) {
+	pub, priv := newKey(t)
+	msg := []byte("msg")
+	sig, _ := pqid.Sign(priv, msg)
+
+	forged := append([]byte(nil), sig...)
+	forged[5] ^= 0xff // corrupt the Ed25519 half
+
+	err := pqid.Verify(pub, msg, forged)
+	if err == nil {
+		t.Fatal("a broken classical half still authenticated")
+	}
+	if !errors.Is(err, pqid.ErrClassicalFailed) {
+		t.Fatalf("got %v, want ErrClassicalFailed", err)
+	}
+}
+
+func TestSignatureSizeIsExact(t *testing.T) {
+	_, priv := newKey(t)
+	sig, err := pqid.Sign(priv, []byte("msg"))
+	if err != nil {
+		t.Fatal(err)
+	}
+	if len(sig) != pqid.SignatureSize {
+		t.Fatalf("signature is %d bytes, want %d", len(sig), pqid.SignatureSize)
+	}
+}
+
+func TestTruncatedSignatureRejected(t *testing.T) {
+	pub, priv := newKey(t)
+	sig, _ := pqid.Sign(priv, []byte("msg"))
+
+	for _, n := range []int{0, 64, pqid.SignatureSize - 1} {
+		if err := pqid.Verify(pub, []byte("msg"), sig[:n]); !errors.Is(err, pqid.ErrMalformedSignature) {
+			t.Fatalf("signature truncated to %d bytes gave %v", n, err)
+		}
+	}
+}
+
+func TestPublicKeyRoundTrip(t *testing.T) {
+	pub, priv := newKey(t)
+
+	restored, err := pqid.ParsePublicKeyHex(pub.Hex())
+	if err != nil {
+		t.Fatal(err)
+	}
+	// The restored key must verify signatures made by the original.
+	sig, _ := pqid.Sign(priv, []byte("msg"))
+	if err := pqid.Verify(restored, []byte("msg"), sig); err != nil {
+		t.Fatalf("round-tripped key failed to verify: %v", err)
+	}
+	if string(restored.ID()) != string(pub.ID()) {
+		t.Fatal("round-tripped key has a different ID")
+	}
+}
+
+func TestMalformedKeysRejected(t *testing.T) {
+	cases := map[string][]byte{
+		"empty":     {},
+		"too short": make([]byte, pqid.PublicKeySize-1),
+		"too long":  make([]byte, pqid.PublicKeySize+1),
+	}
+	for name, b := range cases {
+		if _, err := pqid.ParsePublicKey(b); !errors.Is(err, pqid.ErrMalformedKey) {
+			t.Errorf("%s: got %v, want ErrMalformedKey", name, err)
+		}
+	}
+	if _, err := pqid.ParsePublicKeyHex("nothex!!"); !errors.Is(err, pqid.ErrMalformedKey) {
+		t.Errorf("non-hex: got %v, want ErrMalformedKey", err)
+	}
+}
+
+func TestIDIsStableAndDistinct(t *testing.T) {
+	a, _ := newKey(t)
+	b, _ := newKey(t)
+
+	if string(a.ID()) != string(a.ID()) {
+		t.Fatal("ID is not stable across calls")
+	}
+	if string(a.ID()) == string(b.ID()) {
+		t.Fatal("two distinct keys produced the same ID")
+	}
+	if len(a.ID()) != pqid.IDSize {
+		t.Fatalf("ID is %d bytes, want %d", len(a.ID()), pqid.IDSize)
+	}
+}
+
+// Signatures must be bound to this application, so one captured from another
+// ML-DSA protocol cannot be replayed here.
+func TestSignaturesAreDomainSeparated(t *testing.T) {
+	pub, priv := newKey(t)
+	msg := []byte("msg")
+	sig, _ := pqid.Sign(priv, msg)
+
+	// Verifying with the correct context succeeds (covered above). Here we
+	// confirm the context is actually in use by checking that a signature made
+	// over the same message still fails if the ML-DSA half is swapped for one
+	// generated under a different context.
+	other := make([]byte, pqid.PQSignatureSize)
+	if err := signWithContext(priv, msg, []byte("some-other-protocol"), other); err != nil {
+		t.Fatal(err)
+	}
+	forged := append(append([]byte(nil), sig[:pqid.EdSignatureSize]...), other...)
+	if err := pqid.Verify(pub, msg, forged); !errors.Is(err, pqid.ErrPostQuantumFailed) {
+		t.Fatalf("signature from another context was accepted: %v", err)
+	}
+}
+
+func BenchmarkSign(b *testing.B) {
+	_, priv, _ := pqid.GenerateKey(rand.Reader)
+	msg := []byte("benchmark message")
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		if _, err := pqid.Sign(priv, msg); err != nil {
+			b.Fatal(err)
+		}
+	}
+}
+
+func BenchmarkVerify(b *testing.B) {
+	pub, priv, _ := pqid.GenerateKey(rand.Reader)
+	msg := []byte("benchmark message")
+	sig, _ := pqid.Sign(priv, msg)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		if err := pqid.Verify(pub, msg, sig); err != nil {
+			b.Fatal(err)
+		}
+	}
+}
+
+func BenchmarkGenerateKey(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		if _, _, err := pqid.GenerateKey(rand.Reader); err != nil {
+			b.Fatal(err)
+		}
+	}
+}