Relationship between user name and public key pair in Authentication Protocol

[Miao Fuyou <miaofy%huawei.com@localhost>]

 Hi, Tatu & Tero:
 
 I have a doubt on draft-ietf-secsh-userauth-16.txt.  
 
 In section 2.1, there is: 
"In any case, if the user does not exist, the authentication request
MUST NOT be accepted." 
 
In section 4, there is a sentence like: 
"When the server receives this message, it MUST check whether the
supplied key is acceptable for authentication, and if so, it MUST check
whether the signature is correct." 

Now the question is: Is there any RELATIONSHIP between the user name and
the public key? For example, public key K1 is only used by user U1.  

If there is relationship, what is it? 1:1, 1:n, n:1 or m:n? I prefer to
1:1 and 1:n because n:1 and m:n have serious security problem.  

Looking forward to your response!

Yours  
Miao