I think adding a path segment/prefix is the best answer. Since these are unique secondary keys, this isn’t the same as search (which returns a set of items), so using query parameters (which aren’t cached) doesn’t seem like the best choice.
Personally, I plan to use a path segment prefix delimited by “=”, like “name=” or “email=”:
user/123456
user/name=john.doe
user/email=john.doe@john.doe
This is functionally equivalent to adding a path segment (e.g. “user/name/john.doe”), but feels to me like it maps more closely to the conceptual model. Of course, this is an insignificant detail, since RESTful APIs shouldn’t specify a fixed URI structure anyway.
Not using query parameters also allows sub-resources to be accessed naturally:
user/name=john.doe/inbox/df87bhJXrg63
Frameworks like Java’s JAX-RS support using whatever delimiter you want:
@GET
@Path("user/{id}")
User getUser(@PathParam("id") UUID id);
@GET
@Path("user/name={name}")
User getUserByName(@PathParam("name") String name);
@GET
@Path("user/email={email}")
User getUserByEmail(@PathParam("email") String email);