# Patent

## Title
Distributed single sign on technologies including privacy protection and proactive updating

## Abstract

Technologies for distributed single sign-on operable to provide user access to a plurality of services via authentication to a single entity. The distributed single sign-on technologies provide a set of authentication servers and methods for privacy protection based on splitting secret keys and user profiles into secure shares and periodically updating shares among the authentication servers without affecting the underlying secrets. The correctness of the received partial token or partial profiles can be verified with non-interactive zero-knowledge proofs.

## Background
BACKGROUND
Conventional single sign on (“SSO”) technologies have been used to enable users to log into different service providers via a single sign on. With such technologies, a user need only authenticate to a single entity in order to obtain access to a plurality of associated service providers or the like. Such is particularly helpful with the ever increasing number of web and other services requiring user authentication that a user may wish to access. Various SSO technologies are currently available including Kerberos and Microsoft's .NET Passport or Live ID. While Kerberos may be useful for a single domain environment, it is not considered suitable for use in untrusted environment such as the Internet. Technologies such as Live ID have greatly increased the availability of single sign on services for the Internet, but security issues remain. For example, compromising a single authentication server would jeopardize the whole system since replicas of credentials and profiles tend to be stored in the compromised server. Various distributed SSO systems attempt to address these and related issues. In one example, a plurality of authentication servers may return an encrypted partial ticket to a user that may be used to reconstruct a complete ticket useful for service access. Other techniques for such “secret splitting” methods may alternatively be used. But active attacks tend to not be considered in such schemes. That is, a compromised authentication server of a plurality of such servers may send out incorrect partial tickets or the like, resulting in incorrect tickets and resultant denial of access. Several other problems also exist with conventional distributed SSO technologies.
SUMMARY
The following presents a simplified summary of the disclosure in order to provide a basic understanding to the reader. This summary is not an extensive overview of the disclosure and it does not identify key/critical elements of the invention or delineate the scope of the invention. Its sole purpose is to present some concepts disclosed herein in a simplified form as a prelude to the more detailed description that is presented later.
The present examples provide for distributed single sign-on technologies operable to provide user access to a plurality of services via authentication to a single entity. The distributed single sign-on technologies provide a set of authentication servers and methods to split secret keys and user profiles into secure shares and to periodically update the shares among the authentication servers without changing the underlying secrets.
The foregoing summary is provided solely for the convenience of the Examiner. Accordingly, it should be appreciated that each of the claims may not be limited in the manner described in the summary above. Therefore, the Examiner is requested to not rely upon the summary above for determining whether each of the claims distinguishes over any prior art of record. Many of the attendant features of the claimed invention will be more readily appreciated as the same become better understood by reference to the following detailed description considered in connection with the accompanying drawings.



DESCRIPTION OF THE DRAWINGS
The present description will be better understood from the following detailed description considered in connection with the accompanying drawings, wherein:
FIG. 1 is a block diagram showing an example distributed SSO (“DSSO”) service or system A along with example user U and example service provider S.
FIG. 2 is a block diagram showing an example method for setting up a DSSO system.
FIG. 3 is a block diagram showing an example method for setting up a service provider S for operation with a DSSO system.
FIG. 4 is a block diagram showing an example method for setting up a user U for operation with a DSSO system.
FIG. 5 is a block diagram showing an example method for registering and authenticating a user U to authentication servers in set A.
FIG. 6 is an example method showing the operation of an example distributed single sign-on protocol in which no user profile information is sent to a service provider.
FIG. 7 is an example method 700 showing the operation of an example distributed single sign-on protocol in which user profile information is sent to a service provider.
FIG. 8 is a block diagram showing an example method for updating shares of secrets, such as secret key shares and user profile shares, without affecting the underlying secrets.
FIG. 9 is a block diagram showing an example computing environment in which the technologies described herein may be implemented.



Like reference numerals are used to designate like parts in the accompanying drawings.
DETAILED DESCRIPTION
The detailed description provided below in connection with the accompanying drawings is intended as a description of the present examples and is not intended to represent the only forms in which the present examples may be constructed or utilized. The description sets forth at least some of the functions of the examples and/or the sequence of steps for constructing and operating examples. However, the same or equivalent functions and sequences may be accomplished by different examples.
Although the present examples are described and illustrated herein as being implemented in a computing and networking environment, the environment(s) described is provided as an example and not a limitation. As those skilled in the art will appreciate, the present examples are suitable for application in a variety of different types of computing and networking systems and environments.
Table 1 generally defines notation used herein to describe the present invention.







TABLE 1





Notation
















S
A participating service provider.


U
A participating user who requests access to



a service provided by S.


Ai
The i-th authentication server which



provides SSO service.


UID
A unique ID for user U.


SID
A unique ID for service provider S.


AIDi
A unique ID for the i-th authentication



server Ai.


KS
A secret key generated by and known only



to S.


KSi
The i-th partial share of KS generated



with a threshold scheme.


KUi
A secret key for U to authenticate to the i-th



authentication server Ai.


p, q
Two large prime numbers with p = 2q + 1.


Gq
A subgroup with order q of the multiplicative



group Zp*.


xi
A unique public number in Zq\ {0}



associated with the i-th authentication server.


g
A generator in Gq.


SKU, Ai
A session key between a user U and the i-th



authentication server Ai.


(m)k
A message m encrypted with a symmetric cipher



and a key k.


n
The number of shares a secret or profile



is split into.


t
A valid token or profile can not been constructed



unless there are at least t arbitrary partial tokens



or profiles available.


Nsalt
A salt.


nX
Nonce generated by entity X.


rX
A random number generated by entity X,



1 < rX < q − 1.


[.]
Optional part in describing a protocol. 


Hash(.)
Cryptographic hash function.


 1(.),
Two cryptographic hash functions mapping


 2(.)
arbitrary binary string into Gq.


 (.)
Reconstruction function to combine independent partial values.



In this paper, the reconstruction function   is defined as







  
    
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Note that number p is a conventional large prime number as those known to those of ordinary skill in the art. In one example, q is chosen as the Euler totient function of p, denoted as φ(p), which is the number of integers in the interval [1, p] which are relatively prime to p. In another example, p and q are chosen as large prime numbers such that p=2q+1, as shown in Table 1. A more general selection is that q is a large prime number that divides φ(p).
FIG. 1 is a block diagram showing an example distributed SSO (“DSSO”) service or system A 150 along with example user U 110 and example service provider S 140. User 110, service provider 140, and DSSO system 150 are typically coupled via network 130 and links such as link 120. In one example, network 130 is the Internet. In other examples, network 130 may be any network or combination of networks or the like. User 110 typically represents a computing device or environment, such as that described in connection with FIG. 9, or any other type of computing device or system or the like. Such a device may be operated by a human, or operate standalone or as part of a larger system. Service provider 140 typically represents any type of electronic service or the like including network services, Internet or Web services, or any other such service or combination of services that is associated with DSSO system 150. DSSO system 150 is also referred to herein as a set of authentication servers. Example set 150 is shown including authentication servers 150a, 150b, 150c, and 150d, but may in practice include any number n of such servers where each authentication server is represented as an i-th authentication server {Ai|1≦i≦n.} Further, such servers may be physically located proximate to each other or be distributed over a large geographic area. Such servers are typically coupled via one or more networks or the like, not shown in FIG. 1.
FIG. 2 is a block diagram showing an example method 200 for setting up a DSSO system 150. Block 210 typically indicates setup of service provider S, such as service provider 140 of FIG. 1, for operation with a DSSO system, such as DSSO system 150 of FIG. 1. Such setup typically includes S generating a secret key, splitting it into n shares, and distributing a distinct one of the secret key shares to each of the n authentication servers in set A. Thus each authentication server in set A receives a unique share of the split secret key. Such service provider setup is described further in connection with FIG. 3.
Block 220 typically indicates setup of user U, such as user 110 of FIG. 1, for operation with a DSSO system, such as DSSO system 150 of FIG. 1. Such setup typically includes splitting a user profile corresponding to U into n shares, and distributing a distinct one of the user profile shares to each of the n authentication servers in set A. Thus each authentication server in set A receives a unique share of the split user profile. Such user setup is described further in connection with FIG. 4.
Block 230 typically indicates U, such as user 110 of FIG. 1, registering authentication credentials with A, such as DSSO system 150 of FIG. 1, and authenticating to A. In general, user U needs to authenticate to authentication servers A before receiving DSSO services. Such registering and authenticating are described further in connection with FIG. 5.
Block 240 typically indicates U, such as user 110 of FIG. 1, authenticating to S, such as service provider 140 of FIG. 1, in order to access the services offered by S. When user U wants to access a service provided by S, U typically receives partial tokens and profiles from t of the set of authentication servers A (where 1≦t≦n), and constructs a token and a profile that only the designated service provider S can verify or view. The token is used to authenticate U to S, and the profile is used to provide the U's information to S. Such authenticating is described further in connection with FIG. 6 and FIG. 7.
Block 250 typically indicates periodically updating secret key shares and/or user profile shares such as those described in connection with blocks 210 and 220. Such updating is further described in connection with FIG. 8.
FIG. 3 is a block diagram showing an example method 300 for setting up a service provider S, such as service provider 140 of FIG. 1, for operation with a DSSO system, such as DSSO system 150 of FIG. 1.
Block 310 typically indicates service provider S generating a secret key KS. In this example, the secret key KS is a number where 1<KS<q−1. Once the secret key is generated, then method 300 typically continues at block 320.
Block 320 typically indicates service provider S selecting a random polynomial f(x)=KS+a1x+a2x2+ . . . +at−1xt−1 of order t−1 with random coefficients ai in Zq: {ai ∈ Zq} except the constant which is set to KS, where Zq is a set of integers from 0 to q−1, as shown in block 320, the random polynomial being used to split the secret key KS generated at block 310 into n distinct shares KSi=f(xi), {xi ∈ Zq\{0}}, 1≦i≦n, each distinct share KSi associated with the related authentication server Ai of set A. In this example, any t shares (where 1≦t≦n) of KS can be used to reconstruct the value of KS. Once secret key KS has been split into n shares, method 300 typically continues at block 330.
Block 330 typically indicates service provider S sending a distinct secret key share KSi to each authentication server Ai in set A. The sending to each authentication server Ai typically includes a unique identifier SID of service provider S as shown in block 330. The sending to each authentication server Ai may also include values ga1, . . . , gat−1, gKS as shown in block 330. Once the sending is completed, method 300 typically continues at block 340.
Block 340 typically indicates each authentication server Ai storing the secret key share KSi, the SID value, and the optional values, and verifying the secret key share sent from service provider S and acknowledging the verification to service provider S. Each authentication server Ai may verify the sent secret key share KSi using the optional values ga1, . . . , gat−1, gKS by checking whether the following equation holds:

gKSi=gKS(ga1)xi . . . (ga1)xit−1.

If, using the foregoing equation and the sent optional values, it is determined that the sent secret key share KSi is valid, then the authentication server Ai generally sends a “Success” indication back to service provider S. Otherwise a “Failure” indication may be sent back to service provider S. Once the sent values are stored, the secret key share is verified, and a verification indication is sent back to service provider S, then method 300 is typically complete.
Overall, knowledge of any t shares (where 1≦t≦n) of secret key KS can be used to reconstruct the value of secret key KS. But knowledge of any t−1 or fewer shares of secret key KS and all the values ga1, . . . , gat−1, gKS are not sufficient to deduce secret key KS.
FIG. 4 is a block diagram showing an example method 400 for setting up a user U, such as user 110 of FIG. 1, for operation with a DSSO system, such as DSSO system 150 of FIG. 1. In some examples, a service provider, such as service provider S or service provider 140 of FIG. 1, may need to know some information about a user to which it grants access. A user may have several user profiles comprising personal information or the like of different levels of sensitivity. For example, one such profile may comprise only basic personal information such as a user identifier (“ID”) and email address or the like. Another user profile may comprise more sensitive information such as a credit card number or the like. Different service providers may receive user profiles of differing levels of sensitivity from an authentication server.
Like a secret key KS, user profiles may also benefit from being protected. In one example, protection may be provided by splitting a user profile into n shares that are then distributed to the n authentication servers in set A. Each authentication server stores a share of the user profile but cannot deduce the content of the user profile unless there are t or more colluding authentication servers, each with a unique valid share of the user profile.
Block 410 typically indicates user U generating a secret number ΓU. In this example, the secret number ΓU is a number where 1<ΓU<q−1. Further, user U generally calculates ΓU−1 mod q. Once the secret number is generated and the calculation is complete, then method 400 typically continues at block 420.
Block 420 typically indicates user U selecting a random polynomial w(x)=ΓU+b1x+b2x2+ . . . . +bt−1xt−1 of order t−1 with random coefficients bi in Zq: {bi ∈ Zq}, and with a constant ΓU as shown in block 420, the random polynomial being used to split the secret number ΓU generated at block 410 into n shares PUi=w(xi), 1≦i≦n and then calculates an encrypted user profile Pf,Γ=(Pf)ΓU−1, where Pf is a user profile mapping, i.e., a number in Gq: Pf ∈ Gq that a user profile is one-to-one mapped to. An example of mapping for the case that q and p=2q+1 are two prime number is as follows: if a user profile can be represented by a bit-string less than q, denoted as Profile, then a mapping from Profile to Pf ∈ Gq can be:

Pf=2*Profile+1, if 2*Profile+1 is a quadratic residue mod q. 

Pf=q−2*Profile−1, if 2*Profile+1 is not a quadratic residue mod q. 

Recall that an integer X, 0≦X<q, is called a quadratic residue mod q if and only if there is an integer Y such that Y2=X mod q. If a user profile is too long such that it cannot be represented by a bit-string less than q then, in one example, Pf is an encryption key belonging to Gq that is used to encrypt a user profile with a symmetric encryption primitive such as the Advanced Encryption Standard (“AES”). In this case, Pf,Γ=(Pf)ΓU−1 is an encrypted version of the symmetric encryption key Pf instead of an encrypted version of the user profile mapping. In addition, the encrypted user profile is typically sent along with Pf,Γ, and a service provider S calculates Pf and then uses it to decrypt the received encrypted user profile sent to it together with Pf,Γ to obtain the user profile. In this example, any t shares (where 1≦t≦n) of the split user profile can be used to reconstruct the use profile. Once secret number ΓU has been split into n shares and the user profiles shares calculated, method 400 typically continues at block 430.

Block 430 typically indicates user U sending a distinct secret share PUi together with the encrypted user profile Pf,Γ to each authentication server Ai in set A. The sending to each authentication server Ai typically includes a unique identifier UID of the user U as shown in block 430. The sending to each authentication server Ai may also include optional values gb1, . . . , gbt−1, gΓU as shown in block 430. Once the sending is completed, method 400 typically continues at block 440.
Block 440 typically indicates each authentication server Ai calculating a user profile share Pf,Γi=Pf,ΓPUi from the received PUi and Pf,Γ and storing Pf,Γi, Pf,Γ, the UID value, and the optional values, and verifying the user profile share sent from user U and acknowledging the reception back to user U. Each authentication server Ai may verify the sent user secret share PUi using the optional values gb1, . . . , gbt−1, gΓU by checking whether the following equation holds:

gPUi=gΓU(gb1)xi . . . (gb1)xit−1.

If, using the foregoing equation and the sent optional values, it is determined that the sent user secret share PUi is valid, then the authentication server Ai generally sends a “Success” indication back to service provider S. Otherwise a “Failure” indication may be sent back to service provider S. Once the sent values are stored, the secret key share is verified, and a verification indication is sent back to service provider S, then method 400 is typically complete.
Overall, knowledge of any t shares (where 1≦t≦n) of the user profile can be used to reconstruct the user profile. But knowledge of any t−1 or fewer shares of the user profile and all the values gb1, . . . , gbt−1, gΓU are not sufficient to deduce the user profile.
FIG. 5 is a block diagram showing an example method 500 for registering and authenticating a user U, such as user 110 of FIG. 1, to authentication servers in set A, such as set 150 of FIG. 1. In general, a user of a DSSO system, such as DSSO system 150 of FIG. 1, needs to authenticate to authentication servers in set A before receiving services of the system. Such authentication may typically be based on any authentication scheme, including a conventional scheme such as password-based authentication. In one example, each authentication server Ai in set A operates and authenticates users independently. Each authentication server Ai in set A uses the same user ID for a particular user, but uses a different password in authenticating the user. To the user, authentication appears to be conventional: that is, a user only needs to provide a single user ID and password. A portion (typically a client-side portion or a web browser plug-in or the like) of DSSO system 150, responsive to the user-provided password, manages the complexity of generating a unique password registered with each authentication server Ai in set A.
Block 510 typically indicates a user U, such as user 110 of FIG. 1, generating a unique user ID and a user password. Further, a random number Nsalt of high entropy is generated. In this example, user U may refer to a human or system user, and/or to a portion of a DSSO system with which a user interacts, such as a client portion or a web browser plug-in or the like. Once the user ID and such are generated, method 500 typically continues at block 520.
Block 520 typically indicates user U computing an authentication password KUi for each authentication server Ai in set A where 1≦i≦n and where n is the number of authentication servers in set A. In this example, each of the n authentication passwords is computed as KUi=Hash(UID, Password, AIDi, Nsalt), 1≦i≦n where Hash( ) is a hash function usable for generating a high entropy password, and where UID is the user ID of block 510, and where Password is the user password of block 510, and where AIDi is a unique identifier for the i-th authentication server Ai in set A, and where Nsalt is the high-entropy random number of block 510. In this example, the salt value Nsalt is not a secret, but is generally kept from the authentication servers. Once the authentication passwords have been computed, method 500 typically continues at block 530.
Block 530 typically indicates user U sending each authentication password KUi and the user ID to the corresponding authentication server Ai in set A. Once the authentication passwords are sent to their corresponding authentication servers, method 500 typically continues at block 540.
Block 540 typically indicates each authentication server Ai in set A returning a “Success” indication upon successfully receiving an authentication password from user U. Otherwise a “Failure” indication may be sent back to user U. Further, each authentication server typically stores the authentication password and corresponding user ID for later use, such as for user authentication. At this point user U is registered with each authentication server Ai in set A and method 500 is typically complete.
Once registered, in order to receive DSSO system services, a user generally needs to authenticate to the system. Any suitable authentication protocol may be used. In one example, a simple challenge/response protocol that makes use of the user ID, user password, and authentication passwords generated by method 500 or the like is suitable. The authentication protocol is typically used to authenticate the user to each authentication server Adj where 1≦j≦t and where t is the number of secret key shares and/or user profile shares. Once authenticated to the DSSO system a session key SKU,Adj is typically returned to user U for each authentication server Adj. The session keys are typically used to establish a secure communications channel between user U and each authentication server Adj, the secure communication channels usable to provide DSSO system single sign-on services to user U.
In one example, a single sign-on protocol of a DSSO system, such as DSSO system 150 of FIG. 1, makes use of two non-interactive zero-knowledge proofs, denoted as DLEQ and DLEQ2:

DLEQ(g1,h1,g2,h2) is a pair (c,s) used to prove that logg1h1=logg2h2 for g1,h1,g2,h2 ∈ Gq, where c=Hash(g1, h1,g2,h2,g1sb1c,g2sh2c).

Suppose Alice knows x=logg1h1=logg2h2, then she can choose a random value r and computes c=Hash(g1,h1, g2,h2,g1r,g2r) and s=r−ex mod q. Therefore c=Hash(g1,h1,g2,h2,g1sh1c,g2sh2c).

DLEQ2(g1,h1,g2,h2,u,v,w) is a triple (c,s1,s2) used to prove that ulogg1h1vlogg2h2=w for g1,h1,g2,h2,u,v,w ∈ Gq, where c=Hash(g1,h1,g2,h2,u,v,w,g1s1h1c,g2s2h2c,us1vs2wc).

Suppose Alice knows x=logg1h1 and y=logg2h2, she can choose random values r1 and r2, and then computes c=Hash(g1,h1,g2,h2,u,v,w,g1r1,g2r2,ur1vr2), s1=r1−cx mod q, and s2=r2−cy mod q. Therefore c=Hash(g1,h1,g2,h2,u,v,w,g1s1h1c,g2s2h2c,us1vs2wc).

FIG. 6 is an example method 600 showing the operation of an example distributed single sign-on protocol in which no user profile information is sent to a service provider. Block 610 typically indicates a user U, such as user 110 of FIG. 1, sending to a service provider S, such as service provider 140 of FIG. 1, a request to access a service. Once the request is received, method 600 typically continues at block 620.
Block 620 typically indicates the service provider S, responsive to the request, returning a set of values to the user U. In this example, the set of values includes the unique identifier SID of the service provider S, a nonce nS generated by the service provider S, the value grS calculated by the service provider S based on a random number rS, 1<rS<q−1, selected by the service provider, and a list of at least t authentication servers {Adj, 1≦j≦t}. The t authentication servers used in the protocol are any t operational authentication servers in set A, and are typically selected based on workload, bandwidth, processing power, reliability, and/or the like. Further, it is possible to send requests to more than t authentication servers. In this case, the first t partial tokens received from the authentication servers are typically used to compute an authentication token as described in connection with block 660. Once the set of values is returned to the user U, then method 600 typically continues at block 630.
Block 630 typically indicates the user U selecting a random number rU, 1<rU<q−1 and calculating grU. This term may be used in generating a session key for use between the user U and the service provider S after successful completion of the distributed single sign-on protocol. Further, block 630 typically indicates performing the actions indicated by blocks 640 and 650 for each j where 1≦j≦t and where t is the minimum number of secret key shares and/or user profile shares needed to reconstruct the secret key or user profile.
Block 640 typically indicates the user U sending a set of values to each authentication server Adj. In this example, the set of values includes the unique identifier UID of the user U, the unique identifier SID of the service provider S, the nonce nS generated by the service provider S, and the a pair of values including the value grS calculated by the service provider S and the value grU calculated by the user U. Once the set of values has been sent, method 600 typically continues at block 650.
Block 650 typically indicates each authentication server Adj, responsive to the sending of block 640, sending the indicated set of values to the user U. In this example, DLEQ is generally used to verify if authentication server Adj sent a correct partial authentication token Tdj. Once the set of values sent by each authentication server Adj have been received by the user U, method 600 typically continues at block 660.
Block 660 typically indicates the user U computing an authentication token hKs=R(Tdk,1≦j≦t) from the t received partial authentication tokens Tdj. Once the authentication token has been computed, the user U typically sends the user ID, UID, the calculated hKS and optionally grU to the server S. Then method 600 typically continues at block 670.
Block 670 typically indicates the service provider S verifying the authentication token hKS by calculating kS=1(UID, SID, nS, └grS,grU┘) and then using the secret key KS known only to itself to check if hSKS=hKS holds, where hKS is received from the user U. If the equation holds, then user U is granted access to the requested service. Otherwise access is denied. Once access is granted, if a secure communication channel between the user U and the service provider S is desired then, in this example, the value grUrS is used as a session key for the secure communication channel. Such a session key may be generated based on Diffie-Hellman key agreement. At this point, method 600 is typically complete.
FIG. 7 is an example method 700 showing the operation of an example distributed single sign-on protocol in which user profile information is sent to a service provider. Method 700 is essentially the same as method 600 but further includes securely providing a user profile to the service provider S. Block 710 typically indicates a user U, such as user 110 of FIG. 1, sending to a service provider S, such as service provider 140 of FIG. 1, a request to access a service. Once the request is received, method 700 typically continues at block 720.
Block 720 typically indicates the service provider S, responsive to the request, returning a set of values to the user U. In this example, the set of values includes the unique identifier SID of the service provider S, a nonce nS generated by the service provider S, the value grS calculated by the service provider S based on a random number rS, 1<rS<q−1, selected by the service provider, and a list of t authentication servers {Adj,1≦j≦t}. Once the set of values is returned to the user U, then method 700 typically continues at block 730.
Block 730 typically indicates the user U selecting a random number rU, 1<rU<q−1 and calculating grU. This term may be used in generating a session key for use between the user U and the service provider S after successful completion of the distributed single sign-on protocol. Further, block 730 typically indicates performing the actions indicated by blocks 740 and 750 for each j where 1≦j≦t and where t is the minimum number of secret key shares and/or user profile shares needed to reconstruct the secret key or user profile.
Block 740 typically indicates the user U sending a set of values to each authentication server Adj. In this example, the set of values includes the unique identifier UID of the user U, the unique identifier SID of the service provider S, the nonce nS generated by the service provider S, and the a pair of values including the value grS calculated by the service provider S and the value grU calculated by the user U. Once the set of values has been sent, method 700 typically continues at block 750.
Block 750 typically indicates each authentication server Adj, responsive to the sending of block 740, sending the indicated set of values to the user U. In this example, DLEQ and DLEQ2 are generally used to prevent active attacks launched by compromised authentication servers. DLEQ is generally used to verify if authentication server Adj sent a correct partial authentication token Tdj. DLEQ2 is generally used to verify if authentication server Adj sent a correct partial profile token Tdj′. Once the set of values sent by each authentication server Adj have been received by the user U, method 700 typically continues at block 760.
Block 760 typically indicates the user U computing an authentication token hKS=R(Tdj, 1≦j≦t) from the t received partial authentication tokens Tdj. Further, block 760 typically indicates the user U computing a user profile mapping Pf encrypted with the service provider S secret key KS, h′KSPf=R(Tdj′, 1≦j≦t). Once the authentication token hKS and encrypted user profile mapping h′KSPf have been computed, the user sends them as well as UID and optionally grU to the service provider S. Method 700 then typically continues at block 770.
Block 770 typically indicates the service provider S calculating hS=1(UID,SID,nS,└grS,grU┘) and h′S=2(UID,SID,nS,└grS,grU┘) and then uses the secret key KS known only to itself to check if hSKS=hKS holds and extracts the user profile mapping Pf=h′KSPf/h′SKS, where hKS and h′KSPf are received from the user U. If the equation holds, then user U access to the requested service is granted. Otherwise access is denied. At this point, method 700 is typically complete.
FIG. 8 is a block diagram showing an example method 800 for updating shares of secrets, such as secret key shares and user profile shares, without affecting the underlying secrets. In general, DSSO system secrets such as secret keys and user profiles are protected by splitting them into shares that are distributed among a set of authentication servers. But given a sufficient amount of time, attackers may eventually compromise a large enough number of the shares to deduce a secret. To thwart such an attack, secret share in a DSSO system may be updated periodically using a proactive share updating method, such as method 800. In this example, in order for an attacker to compromise the DSSO system, the attacker would have to compromise a sufficient number of secret shares in order to deduce a secret before such shares are updated. Implementing proactive share updating can make such compromising very difficult.
With respect to updating secret key shares KSi, block 810 typically indicates each authentication server Ai generating a random polynomial fi,update(x) of order t−1 with random coefficients and with a constant of 0:

fi,update(x)=αt,1x+ . . . +αi,t−1xt−1,

Once the random polynomial is generated, method 800 typically continues at block 820.
With respect to updating secret key shares KSi, block 820 typically indicates authentication server Ai calculating updating values Ki,j=fi,update(xj), 1≦j≦n. Once the updating values have been calculated, method 800 typically continues at block 830.
With respect to updating secret key shares KSi, block 830 typically indicates authentication server Ai distributing the updating values Ki,j to all other authentication servers in set A. Further, the authentication server Ai typically broadcasts the values gαt,1, . . . , gαi,t−1 to all the other authentication servers in set A. Once the distributing and broadcasting are complete, method 800 typically continues at block 840.
With respect to updating secret key shares KSi, block 840 typically indicates authentication server Ai receiving updating values Kj,i from each of the other authentication servers in set A, and verifying whether gKj,i=(gαj,1)xj . . . (gαj,t−1)xjt−1 or not, where 1≦j≦n. If the equation holds, the new shares are added to the original share KSi, resulting in the new updated share:




  
    K
    S
    
      ′
      ⁢
      
        
      
      ⁢
      i
    
  
  =
  
    
      K
      S
      i
    
    +
    
      
        ∑
        
          j
          =
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        n
      
      ⁢
      
        K
        
          j
          ,
          i
        
      
    
  




Accordingly, the corresponding new secret key share polynomial fnew(x) is the summation of the original polynomial f(x) and all the randomly generated polynomials fi,update(x), such that KSri is the secret key share generated from fnew(x). Thus the secret key share KSi at each authentication server Ai in set A is updated without changing the secret key KS.
With respect to updating user profile shares PUi, block 810 typically indicates each authentication server Ai generating a random polynomial wi,update(x) of order t−1 with random coefficients and with a constant of 0:

wi,update(x)=βi,1x+ . . . +βi,t−1xt−1.

Once the random polynomial is generated, method 800 typically continues at block 820.
With respect to updating user profile shares PUi, block 820 typically indicates authentication server a calculating updating values Wi,j=wi,update(xj), 1≦j≦n. Once the updating values have been calculated, method 800 typically continues at block 830.
With respect to updating user profile shares PUi, block 830 typically indicates authentication server Ai distributing the updating values Wi,j to all other authentication servers in set A. Further, the authentication server Ai typically broadcasts the values gβi,1, . . . , gβi,t−1 to all the other authentication servers in set A. Once the distributing and broadcasting are complete, method 800 typically continues at block 840.
With respect to updating user profile shares PUi, block 840 typically indicates authentication server Ai receiving updating values Wj,i from each of the other authentication servers in set A, and verifying whether gWj,i=(gβj,1)xj . . . (gβj,t−1)xjt−1 or not, where 1≦j≦n. If the equation holds, the new shares are added to the original share PUi, resulting in the new updated share:




  
    P
    U
    
      ′
      ⁢
      
        
      
      ⁢
      i
    
  
  =
  
    
      P
      U
      i
    
    +
    
      
        ∑
        
          j
          =
          1
        
        n
      
      ⁢
      
        W
        
          j
          ,
          i
        
      
    
  




Accordingly, the corresponding new user profile share polynomial wnew(x) is equal to original polynomial w(x)+Σj=1n wi,update(x). Each authentication server Ai then uses the new share PUri and the stored Pf,Γ to update its user profile share P′f,Γi=P′f,ΓiU. Thus the user profile share PUi at each authentication server Ai in set A is updated without changing the user profile Pf.
FIG. 9 is a block diagram showing an example computing environment 900 in which the technologies described herein may be implemented. A suitable computing environment may be implemented with numerous general purpose or special purpose systems. Examples of well known systems may include, but are not limited to, cell phones, personal digital assistants (“PDA”), personal computers (“PC”), hand-held or laptop devices, microprocessor-based systems, multiprocessor systems, servers, workstations, consumer electronic devices, set-top boxes, and the like.
Computing environment 900 typically includes a general-purpose computing system in the form of a computing device 901 coupled to various components, such as peripheral devices 902, 903, 904 and the like. System 900 may couple to various other components, such as input devices 903, including voice recognition, touch pads, buttons, keyboards and/or pointing devices, such as a mouse or trackball, via one or more input/output (“I/O”) interfaces 912. The components of computing device 901 may include one or more processors (including central processing units (“CPU”), graphics processing units (“GPU”), microprocessors (“μP”), and the like) 907, system memory 909, and a system bus 908 that typically couples the various components. Processor 907 typically processes or executes various computer-executable instructions to control the operation of computing device 901 and to communicate with other electronic and/or computing devices, systems or environment (not shown) via various communications connections such as a network connection 914 or the like. System bus 908 represents any number of several types of bus structures, including a memory bus or memory controller, a peripheral bus, a serial bus, an accelerated graphics port, a processor or local bus using any of a variety of bus architectures, and the like.
System memory 909 may include computer readable media in the form of volatile memory, such as random access memory (“RAM”), and/or non-volatile memory, such as read only memory (“ROM”) or flash memory (“FLASH”). A basic input/output system (“BIOS”) may be stored in non-volatile or the like. System memory 909 typically stores data, computer-executable instructions and/or program modules comprising computer-executable instructions that are immediately accessible to and/or presently operated on by one or more of the processors 907.
Mass storage devices 904 and 910 may be coupled to computing device 901 or incorporated into computing device 901 via coupling to the system bus. Such mass storage devices 904 and 910 may include non-volatile RAM, a magnetic disk drive which reads from and/or writes to a removable, non-volatile magnetic disk (e.g., a “floppy disk”) 905, and/or an optical disk drive that reads from and/or writes to a non-volatile optical disk such as a CD ROM, DVD ROM 906. Alternatively, a mass storage device, such as hard disk 910, may include non-removable storage medium. Other mass storage devices may include memory cards, memory sticks, tape storage devices, and the like.
Any number of computer programs, files, data structures, and the like may be stored in mass storage 910, other storage devices 904, 905, 906 and system memory 909 (typically limited by available space) including, by way of example and not limitation, operating systems, application programs, data files, directory structures, computer-executable instructions, and the like.
Output components or devices, such as display device 902, may be coupled to computing device 901, typically via an interface such as a display adapter 911. Output device 902 may be a liquid crystal display (“LCD”). Other example output devices may include printers, audio outputs, voice outputs, cathode ray tube (“CRT”) displays, tactile devices or other sensory output mechanisms, or the like. Output devices may enable computing device 901 to interact with human operators or other machines, systems, computing environments, or the like. A user may interface with computing environment 900 via any number of different I/O devices 903 such as a touch pad, buttons, keyboard, mouse, joystick, game pad, data port, and the like. These and other I/O devices may be coupled to processor 907 via I/O interfaces 912 which may be coupled to system bus 908, and/or may be coupled by other interfaces and bus structures, such as a parallel port, game port, universal serial bus (“USB”), fire wire, infrared (“IR”) port, and the like.
Computing device 901 may operate in a networked environment via communications connections to one or more remote computing devices through one or more cellular networks, wireless networks, local area networks (“LAN”), wide area networks (“WAN”), storage area networks (“SAN”), the Internet, radio links, optical links and the like. Computing device 901 may be coupled to a network via network adapter 913 or the like, or, alternatively, via a modem, digital subscriber line (“DSL”) link, integrated services digital network (“ISDN”) link, Internet link, wireless link, or the like.
Communications connection 914, such as a network connection, typically provides a coupling to communications media, such as a network. Communications media typically provide computer-readable and computer-executable instructions, data structures, files, program modules and other data using a modulated data signal, such as a carrier wave or other transport mechanism. The term “modulated data signal” typically means a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, communications media may include wired media, such as a wired network or direct-wired connection or the like, and wireless media, such as acoustic, radio frequency, infrared, or other wireless communications mechanisms.
Power source 990, such as a battery or a power supply, typically provides power for portions or all of computing environment 900. In the case of the computing environment 900 being a mobile device or portable device or the like, power source 990 may be a battery. Alternatively, in the case computing environment 900 is a desktop computer or server or the like, power source 990 may be a power supply designed to connect to an alternating current (“AC”) source, such as via a wall outlet.
Some mobile devices may not include many of the components described in connection with FIG. 9. For example, an electronic badge may be comprised of a coil of wire along with a simple processing unit 907 or the like, the coil configured to act as power source 990 when in proximity to a card reader device or the like. Such a coil may also be configure to act as an antenna coupled to the processing unit 907 or the like, the coil antenna capable of providing a form of communication between the electronic badge and the card reader device. Such communication may not involve networking, but may alternatively be general or special purpose communications via telemetry, point-to-point, RF, IR, audio, or other means. An electronic card may not include display 902, I/O device 903, or many of the other components described in connection with FIG. 9. Other mobile devices that may not include many of the components described in connection with FIG. 9, by way of example and not limitation, include electronic bracelets, electronic tags, implantable devices, and the like.
Those skilled in the art will realize that storage devices utilized to provide computer-readable and computer-executable instructions and data can be distributed over a network. For example, a remote computer or storage device may store computer-readable and computer-executable instructions in the form of software applications and data. A local computer may access the remote computer or storage device via the network and download part or all of a software application or data and may execute any computer-executable instructions. Alternatively, the local computer may download pieces of the software or data as needed, or distributively process the software by executing some of the instructions at the local computer and some at remote computers and/or devices.
Those skilled in the art will also realize that, by utilizing conventional techniques, all or portions of the software's computer-executable instructions may be carried out by a dedicated electronic circuit such as a digital signal processor (“DSP”), programmable logic array (“PLA”), discrete circuits, and the like. The term “electronic apparatus” may include computing devices or consumer electronic devices comprising any software, firmware or the like, or electronic devices or circuits comprising no software, firmware or the like.
The term “firmware” typically refers to executable instructions, code, data, applications, programs, or the like maintained in an electronic device such as a ROM. The term “software” generally refers to executable instructions, code, data, applications, programs, or the like maintained in or on any form of computer-readable media. The term “computer-readable media” typically refers to system memory, storage devices and their associated media, and the like.
In view of the many possible embodiments to which the principles of the present invention and the forgoing examples may be applied, it should be recognized that the examples described herein are meant to be illustrative only and should not be taken as limiting the scope of the present invention. Therefore, the invention as described herein contemplates all such embodiments as may come within the scope of the following claims and any equivalents thereto.

## Claims

1. A distributed single sign-on system comprising a plurality of n authentication servers associated with a service provider operable to provide a service to a user, wherein a secret key KS associated with the service provider is split into n distinct secret key shares, each distinct secret key share KSi associated with authentication server Ai of the plurality of n authentication servers where 1<i≦n, and wherein each distinct secret key share KSi is sent to its associated authentication server Ai along with a service provider identifier SID, and wherein each authentication server Ai stores the distinct secret key share KSi in association with the service provider identifier SID, and wherein the splitting of the secret key KS is based on a random polynomial f(x) of order t−1, where 1<t≦n, the random polynomial f(x) having random coefficients and a constant wherein the constant is set to KS, and where any t secret key shares of the secret key KS can be used to reconstruct the secret key KS, and wherein the random polynomial f(x)=KS+a1x+ . . . +at−1xt-1 mod q where the random coefficients {ai ∈ Zq}, and where q is a large prime number that divides the Euler totient function of a large prime p, and where Zq represents integers from 0 to q−1, and where KSi=f(xi) for a set of n distinctive values {xi ∈ Zq\{0}}.

2. The system of claim 1 wherein each authentication server Ai verifies the distinct secret key share KSi before storing it.

3. The system of claim 1 wherein a user profile mapping Pf associated with the user is split into n distinct user profile shares, each distinct user profile share Pf,Γi associated with authentication server Ai of the plurality of n authentication servers, and wherein each distinct user profile share Pf,Γi is sent to its associated authentication server Ai along with the identifier of the user, UID, and wherein each authentication server Ai verifies the distinct user profile share Pf,Γi and stores the distinct use profile share Pf,Γi in association with the user identifier UID.

4. The system of claim 3 wherein the splitting of the user profile mapping Pf is further based on a secret number ΓU and a random polynomial w(x) of order t−1, where 1≦t≦n, the random polynomial w(x) having random coefficients and a constant wherein the constant is set to ΓU, and where any t user profile shares of the user profile Pf can be used to reconstruct the user profile Pf.

5. The system of claim 4 wherein w(x)=ΓU+b1x+ . . . +bt−1xt−1 mod q where the random coefficients {bi ∈ Zq}, q is a large prime number that divides the Euler totient function of a large prime p, and where Zq represents integers from 0 to q−1, where PUi=w(xi) for a set of n distinctive values {xi ∈ Zq\{0}}, and where Pf,Γ=(Pf)ΓU−1 and Pf,Γi=Pf,ΓPUi.

6. The system of claim 1 wherein Pf is an encryption key used to encrypt a user profile associated with the user with a symmetric encryption, and the encrypted profile is sent to each authentication server Ai of the plurality of n authentication servers, and to the service provider during authentication service.

7. The system of claim 1 wherein each authentication server Ai of the plurality of n authentication servers receives a user identifier UID and an authentication password KUi, both associated with the user.

8. The system of claim 7 wherein each authentication password KUi is generated from a user password and the unique identifier associated with the authentication server.

9. The system of claim 8 wherein each authentication password KUi is generated with a hash function Hash( ): KUi=Hash(UID, Password, AIDi, Nsalt) where Password is a user-generated password, and where AIDi is a unique identifier for the i-th authentication server Ai, and where Nsalt is a random number.

10. The system of claim 9 wherein each authentication server Ai stores authentication password KUi in associated with user identifier UID.

11. The system of claim 1 wherein the service provider, responsive to a request from the user, directs the user to a list of at least t authentication severs {Adj, 1≦j≦t} of the plurality of n authentication servers, where 1≦t≦n, for authentication service.

12. The system of claim 11 wherein the service provider receives an authentication token from the user, the authentication token computed based on a set of t partial tokens, each partial token Tdj of the set received from a corresponding one of the t authentication severs Adj, and wherein the user is granted access to the service if the authentication token is verified by the service provider.

13. The system of claim 12 wherein the authentication token is encrypted with a secret key associated with the service provider, and wherein the encrypted authentication token is computed from a set of partial authentication tokens, each partial authentication token Tdj in the set provided by the corresponding one of the t authentication severs Adj.

14. The system of claim 12 wherein the correctness of each partial token Tdj received from a corresponding authentication server Adj is verified with a non-interactive zero-knowledge proof.

15. The system of claim 12 wherein the service provider receives a user profile associated with the user wherein the user profile is encrypted with a secret key associated with the service provider, and wherein the encrypted user profile is computed from a set of partial profile tokens, each partial profile token T′dj in the set provided by the corresponding one of the t authentication severs Adj.

16. The system of claim 15 wherein the correctness of each partial profile token T′dj received from a corresponding authentication server Adj is verified with a non-interactive zero-knowledge proof.

17. A method for updating an original share of a secret, the method performed by each authentication server Ai of a plurality of n authentication servers, where 1<i≦n, the method comprising:
generating a random polynomial fi,update(x) of order t−1 with a constant of 0 where 1<t≦n;
computing an updating value Si,j=fi,update(xj), where 1<j≦n, corresponding to each authentication server Aj;
distributing each update value Si,j to the corresponding authentication server Aj; and
updating the original share by adding the updating values received from the n authentication servers to the original share wherein the original share at each authentication server Ai is updated without changing the related secret.

18. A method of splitting a secret number Pf into a plurality of n shares Pf,Si, 1<i≦n, the method comprising:
selecting a secret number S, 1<S<q−1, where q is a large prime number that divides the Euler totient function of a large prime p;
calculating S−1 mod q and Pf, S=(Pf)S−1 mod p;
generating a random polynomial f(x) of order t−1 with random coefficients and with a constant S, where 1<t≦n; and
computing the plurality of n shares wherein each share Pf, Si, 1<i≦n, is calculated by first computing vi=f(xi) for a set of n distinctive values {xi ∈ Zq\{0}}, where Zq represents integers from 0 to q−1, and then computing Pif,s=(Pf,s)Vi, 1<i≦n, wherein any t shares from the set of n shares Pif, S, 1<i≦n can be used to reconstruct the secret number Pf.