# Minimum Disclosure Routing for network virtualization

**ABSTRACT** Although virtual collocation of Service Providers (SPs) on top of Infrastructure Providers (InPs) via network virtualization brings various benefits, we posit that operational confidentiality has not been considered in this network model. We extend and apply the Secure Multiparty Computation (SMC) protocol to solving Minimum Disclosure Routing (MDR), that is, enabling an SP to route packets without disclosing routing information to InPs. Our study reveals that MDR can be achieved securely with marginal latency overhead with regard to the convergence time in well-engineered routing algorithms. Our study sheds light on the path for network virtualization to be used to resolve the challenges for ISPs of today.

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**ABSTRACT:**Network virtualization is a key technology that is necessary to support diverse protocol suites in the future Internet. A virtualized network uses a single physical infrastructure to support multiple logical networks. Each logical network can provide its users with a custom set of protocols and functionalities. Much research work has focused on developing infrastructure components that can provide some level of logical isolation between virtual networks. However, these systems often assume a somewhat cooperative environment where all network infrastructure providers, virtual network operators, and users collaborate. As this technology matures and becomes more widely deployed, it is also important to consider the effects of and possible defenses against malicious operators and users. In this paper, we explore these security issues in network virtualization. In particular, we systematically discuss the relationship between all entities and potential attacks to illustrate the importance of considering security issues in the design and implementation of virtualized networks. We also present several ideas on how to proceed toward the goal of secure network virtualization in the future Internet.01/2012; - [Show abstract] [Hide abstract]

**ABSTRACT:**Although the virtual collocation of service providers (SPs) on top of infrastructure providers (InPs) via network virtualization brings various benefits, we posit that operational confidentiality has not been considered in this network model. We extend and apply the Secure Multiparty Computation (SMC) protocol to solving Minimum Disclosure Routing (MDR), namely, enabling an SP to route packets without disclosing routing information to InPs. We implement the proposed MDR protocol and evaluate its performance via experiments by comparing it against the prediction based on our analytical performance model. Our study reveals that MDR can be securely achieved with marginal latency overhead with regard to the convergence time in well-engineered nonsecure routing algorithms. Our study sheds light on the path for network virtualization to be used to resolve the challenges for the ISPs of today.IEEE/ACM Transactions on Networking 12/2013; 21(6):1839-1851. · 2.01 Impact Factor -
##### Conference Paper: Secure resource provisioning across multiple domains

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**ABSTRACT:**Network resource provisioning is an important technique for infrastructure providers (infra-providers) because it enables them to utilize their facilities with high efficiency. However, to fully satisfy user requests it is probably necessary to use facilities across multiple domains, for which the conventional resource provisioning methods are unsuitable for the multiple domains because they require unrevealed information from infra-providers. The competitive relationships among infra-providers make it difficult for them to reveal their information to the infra-providers. In this paper, we propose a framework and method for resource provisioning across multiple domains that uses infra-providers' confidential information without exposing it to other infra-providers. To preserve the confidentiality of the infra-providers' information, we propose a cooperative framework using multiparty computation (MPC). However, although MPC provides confidentiality it also brings about nearly intractable computational overhead. Therefore, we pick out values that are locally commutable in each domain and essential for resource provisioning. By using MPC only for these values, our proposed method achieves both tractable MPC overhead and good quality provisioning while preserving information secrecy. Evaluation results show that the computational overhead is tractable and that the average utility fee is at least on the same level as that of the conventional methods.Integrated Network Management (IM 2013), 2013 IFIP/IEEE International Symposium on; 01/2013

Page 1

Minimum Disclosure Routing

for Network Virtualization

Masaki FukushimaTeruyuki Hasegawa

KDDI R&D Laboratories Inc.

Email: {fukusima,teru,hasegawa}@kddilabs.jp

Toru Hasegawa

Akihiro Nakao

The University of Tokyo

Email: nakao@iii.u-tokyo.ac.jp

Abstract—Although virtual collocation of Service Providers

(SPs) on top of Infrastructure Providers (InPs) via network

virtualization brings various benefits, we posit that operational

confidentiality has not been considered in this network model. We

extend and apply the Secure Multiparty Computation (SMC)

protocol to solving Minimum Disclosure Routing (MDR), that

is, enabling an SP to route packets without disclosing routing

information to InPs. Our study reveals that MDR can be achieved

securely with marginal latency overhead with regard to the

convergence time in well-engineered routing algorithms. Our

study sheds light on the path for network virtualization to be

used to resolve the challenges for ISPs of today.

I. INTRODUCTION

As multiple access technologies to the Internet become

available to users, such as ADSL, FTTH and 3G/4G wireless,

Internet Service Providers (ISPs) are facing a mixture of

challenges that may seem harder than ever to fulfill concur-

rently, such as (1) extending footprint to cover large user-base

and multiple access means per user, (2) reducing operational

cost, (3) improving network availability, and (4) maintaining

operational confidentiality.

An emerging concept of network virtualization (NV) re-

cently proposed in various projects [1]–[3] is expected to

help ISPs achieve some of the goals, especially (1)-(3), at the

same time. For example, virtual collocation [4], [5] separates

Infrastructure Providers (InPs) that provide multiple isolated

slices of physical resources and Service Providers (SPs) that

utilize slices to operate virtual networks on, in order for the

SPs to cost-effectively extend their network footprint on top of

multiple InPs without investing on physical infrastructure and

to improve network availability by splicing multiple paths [6].

However, the last bullet (4) mentioned above, operational

confidentiality, may be left unresolved even with such a

new concept of NV to the rescue for achieving the diverse

mixture of goals of ISPs. We observe that an ISP often strives

to keep its competitors away from its operational practices

developed to survive business tussle. It is common for the

followers of market-leaders in various businesses to analyze

their strategies/operations and to employ them to catch up [7],

[8]. Free-riding on other ISPs’ operational expertise turns out

to be quite effective since ISPs often cultivate the market in

similar geographical regions [9], [10]. In the German wireless

telecommunication market, followers have taken such a “herd-

ing strategy” to bring severe price-cutting competition and the

profit has plunged by 50% in five years [11]. In the light of

these observations, one must note that NV in fact may have

negative impact on confidentiality of operational information

of SPs, since virtual collocation [4], [5] implies that an InP

runs its own SP service on its top as well as on the other

(competing) InPs that have access to the operational details

of the SP on top of them. For example, virtual collocation

may allow two competing InPs such as AT&T and Verizon to

extend the footprint of their own SP services over the resources

of each other, which, however, endangers the operational

confidentiality of both SPs. Therefore, if NV is to be employed

to satisfy all the goals (1)-(4) of ISPs mentioned previously,

the challenge is to achieve secure network operations of SPs

without disclosing much information to the underlying InPs.

In this paper, taking distributed routing in SP’s virtual

networks as an example, we focus on Minimum Disclosure

Routing (MDR), where an SP overlaid on top of multiple

InPs minimizes disclosure of its routing information of the

virtual network, such as topology and link/path cost, to the

underlying InPs, while the SP’s virtual routers collectively and

securely perform distributed routing computation1. We show

that the MDR problem can be solved through the extension to

Secure Multiparty Computation (SMC) [14], where multiple

parties cooperatively compute a function from each party’s

confidential input. Our feasibility study reveals that the pro-

posed method is supposed to achieve secure routing without

degrading convergence time. Accordingly, we conclude that

our proposed method together with NV fulfills all the contra-

dicting goals of ISPs concurrently.

The rest of the paper is organized as follows. Section II

defines the problem and Section III proposes the solution.

Section IV evaluates the proposal and Section V discusses

the important issues. Section VI introduces the related work.

And finally Section VII briefly concludes.

II. PROBLEM

A. A Walk-through Scenario

We consider the network virtualization shown in Figure 1

where a service provider (SP) is operating a slice (i.e., a

virtual network) on top of four infrastructure providers (InPs)

Ie,If,Ig, and Ih. For the sake of discussion, we introduce a

term subslice to denote a part of a slice on top of each InP,

1Note that disclosure of link and path cost leads to disclosure of further

information such as link bandwidth [12], [13].

This paper was presented as part of the 14th IEEE Global Internet Symposium (GI) 2011 at IEEE INFOCOM 2011

978-1-4244-9920-5/11/$26.00 ©2011 IEEE875

Page 2

Subslice e

src

Subslice f

f2

Subslice g

Subslice h

SPh’s slice

dst

e1

e2

g1

g2

h2

h1

Physical linkPhysical node

Virtual intra-subslice link

Virtual inter-subslice link

Virtual internal router

Virtual border router

End node (customer)

Path from src to dst

InPs’ physical networks

InP Ie

InP If

InP Ig

InP Ih

f1

Fig. 1.

four InPs)

An example virtualized network environment (an SP operating over

in other words, a set of virtual routers and virtual links each

InP is hosting. For example, in Figure 1, the subslice e is

a part of the SP’s slice on top of InP Ie. Virtual routers on

the borders of the subslices are interconnected at two peering

locations (e1,f1,g1) and (f2,g2,h2), as is often the case with

the Internet of today [9], [15].

Suppose in this example that the SP is actually operated by

InP Ihthat is a business competitor to the rest of InPs, Ie, If,

and Ig. The SP (SPh) purchases virtual routers and virtual

links from these three InPs, builds a slice running an arbitrary

networking protocol, and provides end-to-end services to its

customers src and dst.

Suppose SPh is willing to implement the shortest-path

routing, that is, to route a packet from src in the subslice

e to dst in the subslice h through the path with the smallest

hop count. For the sake of simplifying routing, we set the

hop-count between routers within a peering location such as

e1,f1,g1to zero since they are typically collocated [9], [15].

For example, the shortest path from src to dst is 7 hops (7

virtual intra-subslice links) via e2,e1 through the subslice f

and via h2,h1.

Now, SPh faces a fundamental problem that its virtual

routers must calculate the shortest path while disclosing only

the encrypted or fragmented topology information that cannot

be reconstructed into something meaningful to the other InPs,

e.g., how e1finds that this packet should exit from e to f rather

than to g without obtaining raw hop-counts of virtual links

in the other subslices f,g,h. Unless SPh could not assure

the confidentiality of its operational information, it would not

utilize virtualized network resources from its competitors.

B. Minimum Disclosure Routing (MDR)

As shown in Section II-A, an SP may encounter MDR

problem, where each virtual router needs to obtain its next hop

information without disclosing any such confidential routing

information to its underlying InPs.

MDR is formulated as the problem of distributed compu-

tation that (1) takes local topology information as an input

from each virtual router, which is a set of distances (e.g., hop-

counts, link-weights, etc.) of the virtual links to its neigh-

bors, (2) exchanges only the encrypted or fragmented routing

information among virtual routers as intermediate results of

computation, which is computed from the local topology

information, (3) gives next-hop information as an output to

each virtual router.

As a result, an InP hosting a subslice can obtain only

the local topology information and next hop information of

the subslice it is hosting. It cannot obtain local topology

information and next hop information of the other subslices

and any routing information.

C. Threat Model

Any solution to a security problem needs clear definition of

the threat model to assume. Thus, for MDR, we assume that

an InP be a curious-but-honest adversary in security jargon,

i.e., an adversary that may passively collect information but

will not actively attack the system.

We assume that an InP can observe any information (includ-

ing software, data and protocol messages) stored at any virtual

router it is hosting. This is because, technically, an InP has

access to any information stored in registers, memory, storage

on its top. However, we assume the InP will not maliciously

add, modify or remove any such information since such active

attacks can be traced by the SP. Besides, we assume that two

or more InPs may not collude to expose the SP’s confidential

routing information.

The threat model defined above implies that none of the

existing routing algorithms such as RIP and OSPF can achieve

MDR, because they require the virtual routers to send/re-

ceive confidential routing information (e.g., the distance to

a destination) between different subslices and thus disclose it

to underlying InPs. Most importantly, even if an SP na¨ ıvely

encrypts confidential routing information, the SP needs to store

the encryption key on top of InPs’ memory and storage in

order for a virtual router to decrypt the encrypted information.

Therefore, the InP also has access to the key and can decrypt

the encrypted information.

III. PROPOSED SOLUTION

Our approach to achieving MDR is to extend the generic

SMC by defining a new primitive to transfer a secret in

addition to the standard primitives so that our extended SMC

may be applied to a distributed routing problem such as MDR.

A. Secure Multiparty Computation (SMC)

SMC is defined as cooperative computation of a function

where multiple parties provide inputs and cooperatively cal-

culate outputs of the function, while keeping each party’s input

and output invisible from the other parties. SMC requires that

any intermediate results of the computation must not be dis-

closed to each party, since they might contain the information

that may infer the other party’s input and output. Although the

requirement of SMC appears infeasible to satisfy, surprisingly,

there exist several generic SMC protocols [14], [16], [17] if

876

Page 3

every pair of the parties has a communication channel between

them (i.e., if the parties have full-mesh connectivity.)

In the generic SMC protocol [17], each party first protects

its own input by using the secret sharing scheme [18]; a

scheme to encode a secret input into multiple shares and

distribute the shares among the parties. Any single party

cannot recover the secret unless a certain subset of the other

parties disclose their shares to this single party for decoding.

Then, they compute the function while all the intermediate

computation results are also shared among them, which re-

quires exchanging messages between every pair of parties.

Finally, they recover the final output of the function.

B. Overview of Solution

From a viewpoint of SMC, MDR is an SMC problem that

multiple “virtual routers” (hereafter referred to as “routers”)

need to compute a function that takes local topology infor-

mation as an input from each router and gives next hop

information as an output to each router. However, the generic

SMC protocol cannot be applied to MDR due to a chicken-

or-egg problem—the generic SMC protocol requires full-mesh

connectivity between the routers, while routing is a problem

to logically establish such full-mesh connectivity.

Also, MDR can be viewed as a distributed routing problem,

which can be often divided into the local router problems.

Exercising this insight, we consider decomposing MDR into

local router computations, each of which is performed in a

set of fully-connected border routers located within the same

peering location, namely, defined as inter-subslice clique (or

simply referred to as clique). By definition, the border routers

in such a clique can perform the generic full-mesh version

of SMC protocol to solve the local problems. Furthermore,

since each border router in a clique is from a different InP,

running SMC among the border routers in the clique ensures

none of the underlying InPs may obtain the inputs (i.e., routing

information) from the other InPs.

In a nutshell, we solve MDR by running a distributed rout-

ing algorithm in a logical topology called clique-level topology

shown in Figure 2. Formally, a clique-level topology is a

multigraph of cliques, where a pair of cliques is connected by

clique-level link(s) if it is connected by intra-subslice path(s).

Each clique-level link between a pair of cliques represents the

shortest intra-subslice path between two routers, each at the

different clique. Also, the topology includes stubs (i.e., end

nodes) and clique-stub links connecting these stubs to cliques.

Each clique-stub link represents the shortest intra-subslice path

connecting a stub to a border router in the same subslice.

C. Primitive Operations in Extended SMC

In order to run a distributed routing algorithm in the clique-

level topology, we extend the SMC protocol in two-fold and

define four primitives for a clique of routers to invoke.

First, we identify the following three primitives for solving

local problems in a clique consisting of L parties (i.e., L border

routers). In the following, [x] = ([x]1,...,[x]L) denotes L

3

4

2

dst

Clique-level link

Clique-stub link

Inter-subslice clique

End node

e1

f1

g1

h2

f2

g2

2

Clique c1

Clique c2

link kf

link kg

(1) [2] = SHARE(2)

(2) [3] = SHARE(3) (3) TRANSFER(kf, [2])

(4) [5] = COMPUTE(+, [3], [2])

(5) [kf] = COMPUTE(<, [5], [6])

(6) kf= RECOVER([kf])

src

Fig. 2.

operations (1) to (6) are described in Section III-D

The clique-level topology of the slice shown in Figure 1. The

shares of a secret x (e.g., a distance value), generated by the

secret sharing scheme [18].

• [x] = SHARE(x) is for sharing a secret x among the

clique. It takes the secret x as an input from one of the

L parties, and gives the shares [x] = ([x]1,...,[x]L) of

the secret x as outputs to the L parties. Each share [x]?

is held by a different party.

• [y] = COMPUTE(F,[x]) is for computing a secret

y = F(x) by the generic SMC protocol [17] from a

publicly known function F and another secret x shared

among the clique. It takes the shares [x] of the secret

x as inputs from the L parties, and gives other shares

[y] of the computed secret y as outputs to the L parties.

Each party learns nothing regarding the secrets x, y and

intermediate computation results.

• x = RECOVER([x]) is for recovering a secret x shared

among the clique. It takes the shares [x] of the secret x

as inputs from the L parties, and gives the secret x as an

output to the L parties.

Second, we design another primitive to transfer a secret

shared among a clique to its neighboring clique in the clique-

level topology.

• TRANSFER(link,[x]) is for transferring a secret x

shared among this clique to a neighboring clique via link.

It takes the shares [x] of the secret x as inputs from the

L parties in this clique, and gives other shares of the

same secret x as outputs to the parties in the neighboring

clique.

D. Walk-through Scenario Revisited

We revisit the same example in Section II-A to sketch our

idea to solve MDR (i.e., how the border router e1obtains next

hop information) by using Figure 2 and the primitives defined

in Section III-C.

First, as shown in Figure 2 (1), the border router h2shares

the secret distance 2 of the clique-stub link to dst by invoking

SHARE among the clique c2. This distance 2 should be

invisible from the other subslices e,f,g because it includes

the distances of links in the subslice h. Also, in Figure 2 (2),

f1shares the secret distance 3 of the link kfamong the clique

c1.

Then, in Figure 2 (3), these secret distances are flooded

in the clique-level topology by advertising them between the

877

Page 4

neighboring cliques. For instance, the clique c2 advertises

the secret distance 2 originated from h2 to the neighboring

clique c1by invoking TRANSFER to kf. During this flooding

process, the secret distances of links along the flooding path

are added to the secret distance. For instance, in Figure 2

(4), the clique c1 adds the secret distance 3 of kf to the

secret distance 2 advertised via kf by invoking COMPUTE

and obtains an accumulated secret distance 5 from the clique

c1 to dst via kf. Likewise, the clique c1 obtains a secret

distance 6 from the clique c1 to dst via kg (not shown in

Figure 2).

Finally, in Figure 2 (5), the clique c1is ready to compare

two secret distances, 5 and 6, advertised via kfand kgrespec-

tively by invoking COMPUTE, and in Figure 2 (6), obtain a

secret next hop information kf. By invoking RECOVER, the

border routers in the clique c1(including e1) find that kf is

the link to their next hop for dst.

E. Formal Solution

We describe our solution to the shortest path MDR in a

generic clique-level topology consisting of N cliques and M

destinations. This problem is addressed by a protocol that runs

a distance vector routing algorithm between cliques, while

each secret distance is invisible from underlying InPs by our

primitives as follows.

A clique has K clique-level links and S (S ≤ M) clique-

stub links. We consider constructing a clique-level routing

table for a given clique, r = (r1,...,rM), where rmtakes the

link ID k ∈ {0,...,K} of the link to the next hop clique for

each destination m ∈ {1,...,M}. Link ID k ∈ {1,...,K} is

mapped to each of K clique-level links and k = 0 is reserved

for S clique-stub links, where rm= 0 indicates that the pack-

ets for the destination m should be forwarded from this clique

to the direct clique-stub link (i.e., the shortest intra-subslice

path) to m. Each of its clique-level link k ∈ {1,...,K} has

length dk, and its clique-stub link to each destination m has

length em. (em= ∞ if there is no such clique-stub link to

m.)

First, as an input to the protocol, the clique shares its local

topology information d = (d1,...,dK) and e = (e1,...,eM)

by invoking [d] = SHARE(d) and [e] = SHARE(e). The

shares [D1] of its own distance vector D1= (D1

is initialized to [e], where D1

to each destination m at the beginning of the step 1.

Then, at each step t (1 ≤ t), the clique transfers Dt

to its neighbors via each clique-level link k = 1,...,K

by invoking TRANSFER(k,[Dt]). In turn, via each link k,

this clique receives the shares [Dt

vector Dt

shortest distance from this neighbor connected via link k to

each destination m at the beginning of the step t. Using these

shares [Dt

the shares of its new distance vector defined as a function

1,...,D1

M)

mis the current shortest distance

k] of a neighbor’s distance

k,M), where Dt

k= (Dt

k,1,...,Dt

k,mis the current

1],...,[Dt

K] of distance vectors, this clique obtains

Dt+1

=

=

UpdateDistance(d,e,Dt

(min0≤k≤KCt

1,...,Dt

K)

km|m = 1,...,M),

(1)

MIN

ADD

ADD

1,1

t

D

,1

t

K

D

1d

K

d

1e

1

1

t

D

?

…

…

…

…

…

K wires

MIN

ADD

ADD

1,

t

M

D

,

t

K M

D

M

e

1

t

M

D

?

…

…

…

…

…

…

K + 1 wires

M wires

for destination 1

for destination M

Fig. 3.

defined in Eq. (1)

Block-level (not gate-level) circuit representation of UpdateDistance

where

Ct

km=

{

em,

dk+Dt

k=0,

k?=0,

km,

by invoking [Dt+1] = COMPUTE(UpdateDistance, [d], [e],

[Dt

Finally, this protocol converges at a step tmax (i.e., the

diameter of the network, which is estimated as at most 10 in

a Tier-1 network [19]). The border routers in the clique obtain

their routing table as an output by computing a function

1],...,[Dt

K]).

r

=

=

NextHop(d,e,Dtmax

(argmin0≤k≤KCtmax

]) and recovering r = RECOVER([r]).

1

,...,Dtmax

??m = 1,...,M),

K

)

km

(2)

by invoking [r] = COMPUTE(NextHop, [d], [e], [Dtmax

..., [Dtmax

K

1

],

IV. FEASIBILITY STUDY

To verify feasibility of the proposed solution described in

Section III-E, we examine extra latency incurred by SMC

protocol is comparable with respect to the convergence time

in typical routing algorithms. At every step of the solution,

each clique of routers invokes COMPUTE on UpdateDistance

implemented by the generic SMC protocol [17]. The SMC

protocol requires each router to exchange messages with every

other router in its clique and to perform computation on the

received messages, thus, incurs extra latency for both compu-

tation and communication compared to non-secure versions of

routing protocols.

The latency of each UpdateDistance function, Tupdate, is

Tupdate= Tcomm+ Tcomp

(3)

where Tcommand Tcompare latencies for communication and

computation, respectively.

Figure 3 shows logic circuit for the function UpdateDis-

tance. Although a function in SMC is represented in a logic

circuit of AND, OR, and NOT gates, each gate involves

communications among routers unlike the usual logic circuits.

Thus, Tcommdepends on the size (the total number of gates)

and the depth (the number of gates computed in sequence due

to their dependency) of the circuit, and is formulated as

Tcomm= size · s/B + depth · P

(4)

878

Page 5

0

20

40

60

80

100

120

0 2000

The number M of routing table entries

40006000 8000 10000

K = 12, B = 1 Gbps

K = 4, B = 1 Gbps

K = 12, B = 10 Gbps

K = 4, B = 10 Gbps

Tupdate(msec)

Fig. 4.Latency of an invocation of COMPUTE on UpdateDistance

where s is the message size, B and P are the bandwidth

and one-way propagation delay, respectively, of peering links

connecting border routers in a clique. Appendix A shows

size = 74MK and depth = 10 + 9log(K + 1) hold for

each UpdateDistance.

For each of these gates in the circuit, each router performs

a set of computations on small integer operands. Since, as

shown in Figure 3, the circuit in question can be decomposed

per each destination, we can leverage parallel computation as

follows. Tcompcan be multiplicatively reduced as follows,

Tcomp= size · Tgate/nparallel

(5)

where Tgateis the time required for computation per gate and

nparallelis the degree of parallelism.

We evaluate the latency Tupdatederived from the equation

(3) with typical SP’s network configurations. Figure 4 shows

Tupdate as functions of the number of routing table entries,

M. As the SMC protocol is performed by an inter-subslice

clique (i.e., peering routers collocated together within a single

city area [9], [15]), and thus P is set to 1 millisecond. Since

such short peering links have large bandwidth, B is set to 1

Gbps and 10 Gbps. The degree K depends on the topology

of SP’s slice. According to actual measurement results [20],

we set K = 12 (average degree of backbone routers) and

K = 4 (average degree of POPs). The message size s needs

to be 3 bits, since the secret sharing scheme [18] encodes

one bit of secret into shares of size roughly logL bits and

we suppose L = 6 as the number of tier-1 InPs that the SP

operates on. According to [21], a recent commodity 1.35 GHz

GPGPU can perform computation for each gate (5 additions,

4 multiplications and one modulo2) in 57 clocks, which is

Tgate= 42 nanoseconds on each core, and since it has 240

cores, nparallel= 240. Memory bandwidth is not considered

since it is much larger than network bottleneck.

From Figure 4, we observe that the latency overhead Tupdate

is sub-hundred milliseconds for a large routing table with up

to 10k entries. As a result, the proposed solution will converge

within a second because it requires as many number of

invocations of UpdateDistance as the diameter of the network,

2Computation for each gate is rather simple because the SMC protocol un-

der our consideration is an information-theoretic scheme, not a cryptographic

scheme.

which is estimated as at most 10 in a Tier-1 network with 471

routers [19]. Since the convergence time of well-engineered

OSPF is in the order of sub-seconds [22], we conclude that

the convergence time in the proposed solution is comparable to

that in typical routing algorithms, thus, the proposed solution

is secure, yet, no worse than the existing routing algorithms

in terms of convergence time.

V. DISCUSSION

A. Correctness of MDR

For the sake of brevity, instead of providing the formal

proof of the correctness of MDR calculation, this section

discusses an intuitive sketch of the proof. Our approach can

be viewed as running a secure version of the Bellman-Ford

algorithm in a network of the cliques of routers. Information

on such a clique can never be reverse-engineered by any single

InP, since inputs/outputs of each clique is securely separated

via SHARE/RECOVER, the local computation is conducted

securely via COMPUTE, and the communication between

neighboring cliques is secured via TRANSFER. Correctness

and security of COMPUTE, SHARE and RECOVER are

provided in SMC [14] and the correctness of routing is

attributed to that of the standard Bellman-Ford algorithm [23].

B. Security of MDR

Any solution to a security problem needs thorough analysis

of the security level it provides. We suppose that semi-honest

InPs try to reverse engineer the SP’s routing by mounting

two types of attacks on the proposed solution. First, adver-

saries may attempt to decode confidential information from

its shares stored on top of semi-honest InPs. Obviously, this

attack is impossible because the secret sharing scheme [18]

used in the solution is information-theoretically secure under

our assumption that there is no collusion between two or

more InPs. Second, side channel attack may be launched that

exploits information such as timings of computation/message

transmission and message size. In the proposed solution, all

the primitive invocation sequence and timing are fixed and

computational time and message size are constant. In other

words, timing and message size of our protocol only depend

on the size of the network (M and tmax), which are constant

thus not confidential. As a result, the proposed solution has

no side channel that leaks values of confidential inputs (d and

e) to a semi-honest InP.

C. OSPF

Although our method can be naturally applied to RIP, its

application to OSPF is not so straightforward. In fact, our

primitives are generic enough to be applied to any distributed

algorithm, but should it be naively applied, it is suboptimal,

since the SMC for Dijkstra’s algorithm is costly. Alternatively,

since OSPF area border routers exchange distance vectors

but not link state information, our solution can be applied

to the inter-area distance vector routing in OSPF. However,

this approach suffers from the same performance problem as

discussed in [24]. Applicability of our method to OSPF is left

for our future work.

879

Page 6

VI. RELATED WORK

Security issues in network virtualization have just begun

attracting attentions. Keller et al. [25] have identified the prob-

lem of accountability in hosted virtual networks. In contrast,

our work addresses confidentiality and is complementary to

the accountability and discusses fundamental security require-

ments in virtualized environments.

A few proposals exist for confidentiality of topology in-

formation in conventional inter-domain networking [26], [27],

where several operators need to cooperatively provide end-to-

end paths. These studies have not adopted any sophisticated

computation techniques like SMC and simply hide the infor-

mation not necessary for the computation or disclose some of

confidential information required for the computation.

A large body of work in SMC studies distributed compu-

tation without disclosing each party’s confidential information

[14], [16], [17]. Unfortunately, the generic SMC protocols

including [16], [17] and specific SMC protocols (e.g., privacy-

preserving shortest path [28] and inter-domain routing between

ASes [29]) are not applicable to distributed routing since they

assume every pair of the parties has a communication channel

between them, while distributed routing is to establish such

logical channels. We break down the problem into smaller lo-

cal SMC problems that require only the local communications.

To the best of our knowledge, our work is the first to extend

and apply the SMC protocol to distributed routing.

VII. CONCLUSION

We posit that operational confidentiality is crucial for en-

abling virtual collocation of SPs on top of InPs via network

virtualization (NV) for the real business scenarios. We focus

on Minimum Disclosure Routing (MDR) to enable an SP

to route packets without disclosing routing information to

InPs and propose that the extension to the generic Secure

Multiparty Computation (SMC) achieves MDR securely. Our

study reveals that the proposal is feasible since the extra

latency overhead incurred in the convergence time in our

secure routing protocol is within sub-seconds in large Tier-

1 ISP networks and is comparable to the convergence time in

well-engineered intra-domain routing algorithms. Our solution

presented in this paper sheds light on the path for network

virtualization to be used to resolve all the challenges for ISPs

of today, (1) footprint, (2) cost, (3) availability, and especially

(4) operational confidentiality, concurrently.

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APPENDIX

The size and the depth of the UpdateDistance circuit is

calculated as follows. Each wire in the circuit carries a distance

value at most 16 (as in RIP) and thus encoded into five bits.

Each ADD block (a five-bit adder) is a sequence of five one-bit

full adders (each with size 5 and depth 2), and thus has size 25

and depth 10. Since we have M · K ADD blocks in parallel,

the upper half of the circuit has size 25MK and depth 10.

Each MIN block (a minimum selector with K + 1 inputs) is

a log(K + 1)-deep binary tree of K minimum selectors with

two inputs (each with size 49 and depth 9), and has size 49K

and depth 9log(K + 1). Because we have M MIN blocks in

parallel, the lower half of the circuit has size 49MK and depth

9log(K+1). In total, the entire circuit of UpdateDistance has

size = 25MK + 49MK and depth = 10 + 9log(K + 1).

880

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