The Information-Theoretic Approach to
Security/Privacy
Eirik Rosnes
Simula@UiB, N-5020 Bergen, Norway
Cyber Symposium
May 23, 2017
Information theory
Case study: Distributed storage systems (DSSs)
Outline
1. Information theory
2. Case study: Distributed storage systems (DSSs)
IT and Security
|
E. Rosnes
1 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Introduction
• When we talk about security/privacy, people usually think about
cryptographic tools.
• An alternative approach is based on information theory which provides
unconditional secrecy.
• This talk is about the information-theoretic approach.
IT and Security
|
E. Rosnes
2 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Introduction
• When we talk about security/privacy, people usually think about
cryptographic tools.
• An alternative approach is based on information theory which provides
unconditional secrecy.
• This talk is about the information-theoretic approach.
IT and Security
|
E. Rosnes
2 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Introduction
• When we talk about security/privacy, people usually think about
cryptographic tools.
• An alternative approach is based on information theory which provides
unconditional secrecy.
• This talk is about the information-theoretic approach.
IT and Security
|
E. Rosnes
2 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Information theory (Shannon 1948)
Alice
Bob
Message M
Alice’s
Encoder
An
Noisy communication
channel
P ( b|a )
Bn
Bob’s
decoder
Estimate MB
What is the maximum communication rate?
IT and Security
|
E. Rosnes
3 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Information theory (Shannon 1948)
Alice
Bob
Message M
Alice’s
Encoder
An
Noisy communication
channel
P ( b|a )
Bn
Bob’s
decoder
Estimate MB
What is the maximum communication rate?
IT and Security
|
E. Rosnes
3 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Wiretap channel model
Alice
Eve’s
decoder
Estimate ME
Eve
Bob
En
Message M
Alice’s
Encoder
A
n
Communication
channel
P ( b,e|a )
Bn
Bob’s
decoder
Estimate MB
What is the maximum communication rate such that Eve learns nothing about
the message?
Assumption: Eve has a worse channel.
IT and Security
|
E. Rosnes
4 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Wiretap channel model
Alice
Eve’s
decoder
Estimate ME
Eve
Bob
En
Message M
Alice’s
Encoder
A
n
Communication
channel
P ( b,e|a )
Bn
Bob’s
decoder
Estimate MB
What is the maximum communication rate such that Eve learns nothing about
the message?
Assumption: Eve has a worse channel.
IT and Security
|
E. Rosnes
4 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Wiretap channel model
Alice
Eve’s
decoder
Estimate ME
Eve
Bob
En
Message M
Alice’s
Encoder
A
n
Communication
channel
P ( b,e|a )
Bn
Bob’s
decoder
Estimate MB
What is the maximum communication rate such that Eve learns nothing about
the message?
Assumption: Eve has a worse channel.
IT and Security
|
E. Rosnes
4 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Covert communication
Alice
Willie
Transmission
status T
Bob
Message M
Willie’s
observation
Alice’s
Encoder
Estimate TW
Wn
A
n
Communication
channel
P ( w,b|a )
Bn
Bob’s
decoder
Estimate MB
What is the maximum communication rate such that Willie will not detect
whether communication takes place or not?
Assumption: Willie has a worse channel.
IT and Security
|
E. Rosnes
5 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Covert communication
Alice
Willie
Transmission
status T
Bob
Message M
Willie’s
observation
Alice’s
Encoder
Estimate TW
Wn
A
n
Communication
channel
P ( w,b|a )
Bn
Bob’s
decoder
Estimate MB
What is the maximum communication rate such that Willie will not detect
whether communication takes place or not?
Assumption: Willie has a worse channel.
IT and Security
|
E. Rosnes
5 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Covert communication
Alice
Willie
Transmission
status T
Bob
Message M
Willie’s
observation
Alice’s
Encoder
Estimate TW
Wn
A
n
Communication
channel
P ( w,b|a )
Bn
Bob’s
decoder
Estimate MB
What is the maximum communication rate such that Willie will not detect
whether communication takes place or not?
Assumption: Willie has a worse channel.
IT and Security
|
E. Rosnes
5 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Case study: Distributed storage systems
IT and Security
|
E. Rosnes
6 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Case study: Distributed storage systems
• The amount of digital data generated grows 40% per year.
IT and Security
|
E. Rosnes
6 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Case study: Distributed storage systems
• The amount of digital data generated grows 40% per year.
• 40 ZB (1 ZB= 1021 bytes) of data will be generated yearly by 2020.
IT and Security
|
E. Rosnes
6 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Case study: Distributed storage systems
• The amount of digital data generated grows 40% per year.
• 40 ZB (1 ZB= 1021 bytes) of data will be generated yearly by 2020.
(1.8 ZB was generated in 2011.)
IT and Security
|
E. Rosnes
6 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Case study: Distributed storage systems
• The amount of digital data generated grows 40% per year.
• 40 ZB (1 ZB= 1021 bytes) of data will be generated yearly by 2020.
(1.8 ZB was generated in 2011.)
Need to store, process, and deliver massive amounts of data.
IT and Security
|
E. Rosnes
6 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Case study: Distributed storage systems
• The amount of digital data generated grows 40% per year.
• 40 ZB (1 ZB= 1021 bytes) of data will be generated yearly by 2020.
(1.8 ZB was generated in 2011.)
Need to store, process, and deliver massive amounts of data.
• Inexpensively
IT and Security
|
E. Rosnes
6 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Case study: Distributed storage systems
• The amount of digital data generated grows 40% per year.
• 40 ZB (1 ZB= 1021 bytes) of data will be generated yearly by 2020.
(1.8 ZB was generated in 2011.)
Need to store, process, and deliver massive amounts of data.
• Inexpensively
• Reliably
IT and Security
|
E. Rosnes
6 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Case study: Distributed storage systems
• The amount of digital data generated grows 40% per year.
• 40 ZB (1 ZB= 1021 bytes) of data will be generated yearly by 2020.
(1.8 ZB was generated in 2011.)
Need to store, process, and deliver massive amounts of data.
• Inexpensively
• Reliably
IT and Security
|
E. Rosnes
6 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Motivation
4
·10
Exabytes (1018 bytes)
4
3
2
1
0
2005
2009
2013
2020
Year
IT and Security
|
E. Rosnes
7 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Motivation
4
·10
Exabytes (1018 bytes)
4
3
2
1
0
2005
2009
2013
2020
Year
IT and Security
|
E. Rosnes
7 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Data storage in the old times
In the old times...
• Single pieces of very reliable hardware
IT and Security
|
E. Rosnes
8 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Data storage in the old times
In the old times...
• Single pieces of very reliable hardware → very expensive!
IT and Security
|
E. Rosnes
8 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
Distributed storage
• Data is stored across multiple interconnected inexpensive storage units in a
distributed fashion.
IT and Security
|
E. Rosnes
9 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
Distributed storage
• Data is stored across multiple interconnected inexpensive storage units in a
distributed fashion.
• Individual storage units (storage nodes) are unreliable, but reliability is
provided globally.
IT and Security
|
E. Rosnes
9 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
• Individual storage nodes are prone to failures → need to provide resilience
to node failures (fault tolerance).
IT and Security
|
E. Rosnes
10 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
• Individual storage nodes are prone to failures → need to provide resilience
to node failures (fault tolerance).
IT and Security
|
E. Rosnes
10 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
• Individual storage nodes are prone to failures → need to provide resilience
to node failures (fault tolerance).
IT and Security
|
E. Rosnes
10 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
• Individual storage nodes are prone to failures → need to provide resilience
to node failures (fault tolerance).
IT and Security
|
E. Rosnes
10 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
• Individual storage nodes are prone to failures → need to provide resilience
to node failures (fault tolerance).
IT and Security
|
E. Rosnes
10 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
• Individual storage nodes are prone to failures → need to provide resilience
to node failures (fault tolerance).
IT and Security
|
E. Rosnes
10 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
• Individual storage nodes are prone to failures → need to provide resilience
to node failures (fault tolerance).
• Basic approach: Replication.
IT and Security
|
E. Rosnes
10 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
• Individual storage nodes are prone to failures → need to provide resilience
to node failures (fault tolerance).
• Basic approach: Replication.
IT and Security
|
E. Rosnes
10 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
• Individual storage nodes are prone to failures → need to provide resilience
to node failures (fault tolerance).
• Basic approach: Replication.
IT and Security
|
E. Rosnes
10 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
• Individual storage nodes are prone to failures → need to provide resilience
to node failures (fault tolerance).
• Basic approach: Replication.
IT and Security
|
E. Rosnes
10 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
• Individual storage nodes are prone to failures → need to provide resilience
to node failures (fault tolerance).
• Basic approach: Replication.
IT and Security
|
E. Rosnes
10 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
• Individual storage nodes are prone to failures → need to provide resilience
to node failures (fault tolerance).
• Basic approach: Replication.
• Data is stored in a distributed fashion across three storage nodes.
IT and Security
|
E. Rosnes
10 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
• Individual storage nodes are prone to failures → need to provide resilience
to node failures (fault tolerance).
• Basic approach: Replication.
• Data is stored in a distributed fashion across three storage nodes.
• Individual nodes are unreliable, but the system provides reliability globally.
IT and Security
|
E. Rosnes
10 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Replication
Replication: Replicate the data n times
• Simple, but...
IT and Security
|
E. Rosnes
11 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Replication
Replication: Replicate the data n times
• Simple, but... high storage overhead
IT and Security
|
E. Rosnes
11 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Replication
Replication: Replicate the data n times
• Simple, but... high storage overhead
IT and Security
|
E. Rosnes
11 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Replication
Replication: Replicate the data n times
• Simple, but... high storage overhead
IT and Security
|
E. Rosnes
11 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Replication
Replication: Replicate the data n times
• Simple, but... high storage overhead
IT and Security
|
E. Rosnes
11 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Replication
Replication: Replicate the data n times
• Simple, but... high storage overhead → very costly in terms of hardware,
real-state, maintenance (cooling)...
IT and Security
|
E. Rosnes
11 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Replication
Replication: Replicate the data n times
• Simple, but... high storage overhead → very costly in terms of hardware,
real-state, maintenance (cooling)...
• Need to reduce the storage overhead!
IT and Security
|
E. Rosnes
11 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Replication
Replication: Replicate the data n times
• Simple, but... high storage overhead → very costly in terms of hardware,
real-state, maintenance (cooling)...
• Need to reduce the storage overhead!
Can we do better?
IT and Security
|
E. Rosnes
11 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage using erasure correcting codes
Example: (9, 7) maximum distance separable (MDS) code. t = 2
IT and Security
|
E. Rosnes
12 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage using erasure correcting codes
Example: (9, 7) maximum distance separable (MDS) code. t = 2
• A piece of data is divided into k = 7 symbols,
IT and Security
|
E. Rosnes
12 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage using erasure correcting codes
Example: (9, 7) maximum distance separable (MDS) code. t = 2
• A piece of data is divided into k = 7 symbols, and encoded into n = 9
symbols. (We add n − k = 2 symbols of redundancy.)
IT and Security
|
E. Rosnes
12 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage using erasure correcting codes
Example: (9, 7) maximum distance separable (MDS) code. t = 2
• A piece of data is divided into k = 7 symbols, and encoded into n = 9
symbols. (We add n − k = 2 symbols of redundancy.)
• 7 nodes store the plain data,
IT and Security
|
E. Rosnes
12 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage using erasure correcting codes
Example: (9, 7) maximum distance separable (MDS) code. t = 2
• A piece of data is divided into k = 7 symbols, and encoded into n = 9
symbols. (We add n − k = 2 symbols of redundancy.)
• 7 nodes store the plain data, 2 nodes store redundancy.
IT and Security
|
E. Rosnes
12 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage using erasure correcting codes
Example: (9, 7) maximum distance separable (MDS) code. t = 2
• A piece of data is divided into k = 7 symbols, and encoded into n = 9
symbols. (We add n − k = 2 symbols of redundancy.)
• 7 nodes store the plain data, 2 nodes store redundancy.
• The data can be retrieved from any subset of 7 storage nodes.
IT and Security
|
E. Rosnes
12 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage using erasure correcting codes
Example: (9, 7) maximum distance separable (MDS) code. t = 2
• A piece of data is divided into k = 7 symbols, and encoded into n = 9
symbols. (We add n − k = 2 symbols of redundancy.)
• 7 nodes store the plain data, 2 nodes store redundancy.
• The data can be retrieved from any subset of 7 storage nodes.
IT and Security
|
E. Rosnes
12 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage using erasure correcting codes
Example: (9, 7) maximum distance separable (MDS) code. t = 2
• A piece of data is divided into k = 7 symbols, and encoded into n = 9
symbols. (We add n − k = 2 symbols of redundancy.)
• 7 nodes store the plain data, 2 nodes store redundancy.
• The data can be retrieved from any subset of 7 storage nodes.
IT and Security
|
E. Rosnes
12 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage using erasure correcting codes
Example: (9, 7) maximum distance separable (MDS) code. t = 2
• A piece of data is divided into k = 7 symbols, and encoded into n = 9
symbols. (We add n − k = 2 symbols of redundancy.)
• 7 nodes store the plain data, 2 nodes store redundancy.
• The data can be retrieved from any subset of 7 storage nodes.
• Storage overhead n/k = 1.28 (n/k = 3 for 3-replication).
IT and Security
|
E. Rosnes
12 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
Distributed storage systems come in many flavors:
IT and Security
|
E. Rosnes
13 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
Distributed storage systems come in many flavors:
• Data centers,
IT and Security
|
E. Rosnes
.
13 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
Distributed storage systems come in many flavors:
• Data centers, cloud storage networks,
IT and Security
|
E. Rosnes
.
13 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
Distributed storage systems come in many flavors:
• Data centers, cloud storage networks, and P2P storage/backup systems.
IT and Security
|
E. Rosnes
13 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
Distributed storage systems come in many flavors:
• Data centers, cloud storage networks, and P2P storage/backup systems.
• Google File System, Facebook’s Hadoop distributed file system, and
Microsoft’s Windows Azure cloud system.
IT and Security
|
E. Rosnes
13 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Distributed storage
γBS
F
µ
Mλ
hα
α
γD2D
α
α
α
µ
Distributed storage systems come in many flavors:
• Data centers, cloud storage networks, and P2P storage/backup systems.
• Google File System, Facebook’s Hadoop distributed file system, and
Microsoft’s Windows Azure cloud system.
• Wireless distributed storage for content delivery.
IT and Security
|
E. Rosnes
13 / 16
Information theory
Case study: Distributed storage systems (DSSs)
What about security?
Types
Two ways to look at it:
• Security against passive attacks.
• Security against active attacks.
Solution
• Cryptographic approach:
Easy to implement.
Complex key management.
• Information-theoretic approach.
IT and Security
|
E. Rosnes
14 / 16
Information theory
Case study: Distributed storage systems (DSSs)
What about security?
Types
Two ways to look at it:
• Security against passive attacks.
• Security against active attacks.
Solution
• Cryptographic approach:
Easy to implement.
Complex key management.
• Information-theoretic approach.
IT and Security
|
E. Rosnes
14 / 16
Information theory
Case study: Distributed storage systems (DSSs)
What about security?
Types
Two ways to look at it:
• Security against passive attacks.
• Security against active attacks.
Solution
• Cryptographic approach:
Easy to implement.
Complex key management.
• Information-theoretic approach.
IT and Security
|
E. Rosnes
14 / 16
Information theory
Case study: Distributed storage systems (DSSs)
What about security?
Types
Two ways to look at it:
• Security against passive attacks.
• Security against active attacks.
Solution
• Cryptographic approach:
Easy to implement.
Complex key management.
• Information-theoretic approach.
IT and Security
|
E. Rosnes
14 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Security against passive attacks: An intuition
Objective (strong secrecy)
To achieve I (m; e) = 0.
The main principle is to append random data to the file. This achieves security
at the expense of a higher storage overhead!!!
IT and Security
|
E. Rosnes
15 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Security against passive attacks: An intuition
m1
m2
m1 + m2
m1 + 2m2
Objective (strong secrecy)
To achieve I (m; e) = 0.
The main principle is to append random data to the file. This achieves security
at the expense of a higher storage overhead!!!
IT and Security
|
E. Rosnes
15 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Security against passive attacks: An intuition
m1 + r
r
m1 + 2r
m1 + 3r
Objective (strong secrecy)
To achieve I (m; e) = 0.
The main principle is to append random data to the file. This achieves security
at the expense of a higher storage overhead!!!
IT and Security
|
E. Rosnes
15 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Security against passive attacks: An intuition
m1 + r
r
m1 + 2r
m1 + 3r
Objective (strong secrecy)
To achieve I (m; e) = 0.
The main principle is to append random data to the file. This achieves security
at the expense of a higher storage overhead!!!
IT and Security
|
E. Rosnes
15 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Security against passive attacks: An intuition
m1 + r
r
m1 + 2r
m1 + 3r
Objective (strong secrecy)
To achieve I (m; e) = 0.
The main principle is to append random data to the file. This achieves security
at the expense of a higher storage overhead!!!
IT and Security
|
E. Rosnes
15 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Security against passive attacks: An intuition
m1 + r
r
m1 + 2r
m1 + 3r
Objective (strong secrecy)
To achieve I (m; e) = 0.
The main principle is to append random data to the file. This achieves security
at the expense of a higher storage overhead!!!
IT and Security
|
E. Rosnes
15 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Security against passive attacks: An intuition
m1 + r
r
m1 + 2r
m1 + 3r
Objective (strong secrecy)
To achieve I (m; e) = 0.
The main principle is to append random data to the file. This achieves security
at the expense of a higher storage overhead!!!
IT and Security
|
E. Rosnes
15 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Private information retrieval
• In data storage applications, besides resilience against disk failures and
data protection against illegitimate users, the privacy of the data retrieval
query may also be of concern.
• For instance, one may be interested in designing a storage system in which
a file can be downloaded without revealing any information of which file is
actually downloaded to the servers storing it.
The fundamental question is how much it costs in terms of download.
IT and Security
|
E. Rosnes
16 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Private information retrieval
• In data storage applications, besides resilience against disk failures and
data protection against illegitimate users, the privacy of the data retrieval
query may also be of concern.
• For instance, one may be interested in designing a storage system in which
a file can be downloaded without revealing any information of which file is
actually downloaded to the servers storing it.
The fundamental question is how much it costs in terms of download.
IT and Security
|
E. Rosnes
16 / 16
Information theory
Case study: Distributed storage systems (DSSs)
Private information retrieval
• In data storage applications, besides resilience against disk failures and
data protection against illegitimate users, the privacy of the data retrieval
query may also be of concern.
• For instance, one may be interested in designing a storage system in which
a file can be downloaded without revealing any information of which file is
actually downloaded to the servers storing it.
The fundamental question is how much it costs in terms of download.
IT and Security
|
E. Rosnes
16 / 16