Transcript Anonymous Communication -

Efficient Self-Healing Group Key Distribution
with Revocation Capability
by Donggang Liu, Peng Ning, Kun Sun
Presented by Haihui Huang
([email protected])
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Outline
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Introduction
Group key distribution overview
Self-healing key distribution
Revocation capability
Novel personal key distribution
Contribution and conclusion
Future work
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Introduction
• Common way to ensure communication
security: encrypt and authenticate messages
• Challenge:
– how to distribute keys to valid nodes
• Challenges in ensuring communication
security for mobile wireless ad hoc networks
over unreliable channels
– Volatile membership
– Disruption of communication by adversary
– Resource constraints
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Group Key Distribution Techniques
• Group controller
– Can’t scale to large groups
• Iolus
– subgroup hierarchy
• Logical Key Hierarchy(LKH) or Key Graph
– Keys are organized into a tree hierarchy
• Self-healing key distribution
• Stateless key distribution
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Self-healing Key Distribution
• Users are capable of recovering lost group
keys on their own
• No need to request additional transmissions
from the group manager
– Lower network traffic
– Decrease the load on the group manager
• To recover the key via self-healing
– A user must be a member both before and after the
session in which a particular key is sent
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Revocation Capability
• The ability to revoke users and thus prevent
them from learning new keys
• t-revocation capability
– Possible to prevent at most t users at a time from
learning new session key
– With the revocation polynomial g(x) constructed as
g(x)=(x-r1)(x-r2)…(x-rw)
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Personal Key Share Distribution-Scheme 1
• t-revocation capability
• To distribute keys to selected group members so that each
member shares a distinct personal key with the group manage
• But the other(revoked) group members and adversary cannot
get any information of the keys
• Choose a random t-degree polynomial f(x) from Fq[x] and
select f(i) to be the personal key share for each member
• Group manager broadcasts a single polynomial w(x) so that
– Valid group member Ui can recover f(i) from w(x) and
personal secret Si
– Revoked group member Ui’ will NOT be able to recover
f(i’)
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Personal Key Share Distribution-Scheme 1(cont)
• Construct w(x) with the help of a revocation polynomial g(x)
and a masking polynomial h(x) by computing
w(x)=g(x)*f(x)+h(x)
• g(x) is constructed in such a way that
– For valid member Ui, g(i) <> 0
– For revoked member Ui’, g(i’)==0
• Choose a random t-degree polynomial f(x) from Fq[x] and
select f(i) to be the personal key share for each member
• Group manager broadcasts a single polynomial w(x) so that
– Valid group member Ui can recover f(i) from w(x) and personal secret
Si : f(i) = ( w(i) - h(i) ) / g(i)
– Revoked group member Ui’ will NOT be able to recover f(i’) as
g(i’)==0
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How to achieve self-healing
• Use secret sharing
– Based on polynomial interpolation
– Bind the ability of users to recover from packet loss to the
user’s membership status
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How to achieve self-healing(2)
• Split group session key Kj into two t-degree
polynomials, pj(x) and qj(x) such that
Kj=pj(x)+qj(x)
• In session j1: broadcast polynomials
{p1(x),…,pj1(x),qj1(x),…, qj(x) ,…qj2(x),…, qm(x)}
• In session j2(j2>j1): broadcast polynomials
{p1(x),…,pj1(x), …, pj(x),…,pj2(x),qj2(x),…,qm(x)}
• For any session j(j1<j<j2), we can recover
Kj=pj(x)+qj(x)
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Personal Key Share Distribution- Scheme 2
• Self-healing key distribution with t-revocation
capability
• In the jth session key distribution, given a set of
revoked member Ids, Rj={r1,r2,…,rwj), |Rj|=wj<t
• Group manager broadcasts message
Bj= {Rj}
∪{Pj,i(x) = gj(x)pi(x) + hj,i(x)}i=1,...,j
∪{Qj,i(x) = gj(x)qi(x) + hj,i+1(x)}i=j,…m
where gj(x) = (x − r1)(x − r2)...(x − rwj ).
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Reducing Storage Requirement
• In Scheme 2, the storage overhead in each
group member is O(m2logq).
– m: total sessions
– logq: session key size
• Use only ONE masking polynomial for each
pi(x),qi(x)
• Reduce the storage requirement in each
member from O(m2logq) to O(mlogq) in
Scheme 3
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Personal Key Share Distribution- Scheme 3
• Improved self-healing key distribution with trevocation capability
• In the jth session key distribution, given a set of
revoked member Ids, Rj={r1,r2,…,rwj), |Rj|=wj<t
• Group manager broadcasts message
Bj= {Rj}
∪{Pi(x) = gj(x)pi(x) + hi(x)}i=1,...,j
∪{Qj,i(x) = qi(x) + fi(x)}i=j,…m
where gj(x) = (x − r1)(x − r2)...(x − rwj ).
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Personal Key Share Distribution- Scheme 4
• Trading off self-healing capability for less
broadcast size
• Introduce a “sliding window” of l sessions
– only redundant information for the sessions that
fall into this window is broadcasted
– Can NOT ensure the same self-healing property as
in previous schemes
– Reduce storage overhead to (2m+2l-1)logq
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Personal Key Share Distribution- Scheme 5
• Aimed at situations where they are relatively
long term but infrequent communication
failures
• Introduce a “sliding window” of (l-1)d sessions
– Assume each group member can receive at least d
consecutive broadcast key distribution messages
– Selectively include the same amount of redundant
information from a large “window” of session(i.e.
2(l-1)d+1) in each key distribution message
– storage overhead : (2m+2(l-1)d+1)logq
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Conclusion
• Presented several group key distribution
schemes for very large and dynamic groups
over reliable channels
• Developed several efficient unconditionally
secure and self-healing group key distribution
schemes that significantly improved over the
previous approaches
• Developed 2 techniques that allow trade-offs
between broadcast message size and
recoverabilities of lost session keys
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Future work
• Develop a model that characterizes failures in
large and highly mobile wireless networks
• Further investigate the performance of the
proposed schemes in this model
• Seek more efficient ways to perform the initial
key distribution for the proposed schemes
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Questions?
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