### Thesis Defense Presentation

```Russell Martin
August 9th, 2013
Contents
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Introduction to CPABE
Bilinear Pairings
Group Selection
Key Management
Key Insulated CPABE
Conclusion & Future Work
Need for Attribute Based Encryption
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Private Key Cryptosystems
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Identity Based Encryption
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AES
Single key for all users
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Users given unique keys
Good for signatures, not so much encryption
Attribute Based Encryption
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“Fuzzy” IBE
Decryption controlled by matching “d of k” attributes
CPABE
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ABE schemes are single level of control
Fine grain access control
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KPABE
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Monotonic access trees
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Access tree in user’s key, list of attributes in ciphertext
Users encrypting files have limited control of who decrypts
CPABE
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Access tree in ciphertext, list of attributes in user’s key
Users encrypting have strong control
Access Tree
CPABE
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Five functions
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Setup
Key Generation
Encryption
Decryption
Delegation
Bilinear Pairings
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Decisional Diffie-Hellman is easy, Computational
Diffie-Hellman is hard
Bilinear Pairings
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Inputs most commonly elements of a specific elliptic
curve
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Restricted to r-torsion points of the curve
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r*P=O
Computed by the Weil or Tate pairing, using Miller’s
algorithm
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Computation of tangent/vertical/lines between one or two points on the
curve
Setup
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Selection of bilinear group, generators, and
exponentiations
Key Generation
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Generate a key for the user who possesses the list of
attributes, S
Encryption
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Encrypt the message M with the access policy τ
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Y = Set of all leaf nodes in tree
Decryption
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Recursive decryption starting at top of tree
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If leaf node, decrypt node:
Decryption
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If non-leaf node, polynomial interpolation from child
node results
Decryption
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Assuming access tree satisfied, interpolation at root
occured
Group Selection
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CPABE uses
, a=1
No justification for the usage or performance of this
curve
Can we do better with performance? Size? Security?
Embedding Degree
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Directly related to size and security of groups of the
bilinear pairing
Minimum value k such that
, r = number of
points on elliptic curve
Ratio of size of input group to output group
Larger embedding degree believed to be higher
security
Curve Types
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Ben Lynn’s Pairing Based Cryptography Library
Labeled as type A through G
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Type B and C not implemented in library
Types A, B, C are symmetric (supersingular)
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Same group for both input elements of pairing
Types D - G are ordinary
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Generated by the complex multiplication equation
Curve Types
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Type A - k=2, 512 bit inputs, 1024 bit outputs
Type D (MNT Curves) - k=6, 159 bit inputs, 954 bit
outputs
Type E - k=1, 1020 bit inputs, 1020 bit outputs
Type F (Barreto-Naehrig) - k=12, 158 bit inputs, 1896
bit outputs
Type G - k=10, 149 bit inputs, 1490 bit outputs
Performance
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Tested key generation, encryption, and decryption
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Encryption and Decryption were over horizontal and vertical access policies
1 to 100 attributes in each policy
CHARM - Python library for cryptography
prototyping
 Overhead over C implementation for CPABE
mostly in serialization & parsing
Horizontal vs Vertical Access Policy
Performance - Key Generation
Performance - Horizontal Encryption
Performance - Vertical Encryption
Performance - Horizontal Decryption
Performance - Vertical Decryption
Performance
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Operation Breakdown:
Performance
Operations per function:
 Key Generation - Multiplications and
exponentiations , 1:2 ratio
 Encryption - Multiplications and exponentiations,
3:1 ratio
 Decryption - All operations, focused in output
group
 Pairings take up majority of CPU time
Size
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Key
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Ciphertext
Performance Summary
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Type F - Fastest encryption & key gen, slowest
decryption
Minor differences in horizontal vs. vertical access
policies
Type G performance is not recommended
Type D is close to type E, but both slower than type
A
Type F has the smallest keys, type D has the smallest
ciphertexts
Focus on optimizations to pairing operation
Pairings Outside of Elliptic Curves
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RSA is possible, by using exponentiation as the
pairing function
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Still requires normal comparable security sizes - EC vs RSA
Hyperelliptic curves
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Higher embedding degree is not worth additional complexity
Vector of integers
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Again, restricted to integer sizes (RSA)
Key Management
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CPABE wants to not use trusted servers
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Revocation & renewal difficult
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No access control outside of ciphertext
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Want immediate revocation of full keys
Minimize overhead in renewal
Focus on full key revocation, not attribute
Key Management Possibilities
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Key expiration date
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Adds many more attributes due to numeric attributes and timestamps
Proxy Key
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Additional pairings, and still direct communication with proxy server
User Blacklist
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Requires to be done by user encrypting files
Hierarchical Access Roles
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Large overhead, need to control number of unique values
Key Insulated ABE
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Temporary keys based on a time period
Revocation is not immediate
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Must wait until end of time period
Pseudorandom function with identity as seed
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Get next value for the next time period
Users given helper key
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Updates current key to valid key for next value
Key Insulated CPABE
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Replace random r value in users’ keys with a
pseudorandom value k
Setup - same as CPABE, except with definition of
pseudorandom and hash functions
Key Generation:
Key Insulated CPABE
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Helper Update:
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Additional value here due to gα and β private
User Update:
Key Insulated CPABE
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Encryption:
Key Insulated CPABE
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Decryption:
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Interpolation - no change
Final Decryption:
Performance
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No changes to number of operations during pairings
Additional multiplications and hashings to handle T()
in encryption/key generation
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Equivalent of an additional attribute in key generation
User needs to perform multiplication for each
attribute during update
Size
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3 values, all in the input group
Largest in type A pairing - 1536 bits
Security
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Security of revocation directly linked to security of
pseudorandom function
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If users can compute k values, they can generate any keys
Outside of this, same security claims as CPABE
No need to hide details of T() function
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Needed for encryption
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How to handle previous time periods
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Users keep old keys - large storage overhead
Force rencryption of files after number of time periods?
How to handle new users
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Would not have previous keys, no access to previous files
Application depedent
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Broadcast schemes work well for this
Conclusion
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Type F curves provide fastest key generation and
encryption for CPABE
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Limited in decryption due to large output groups
Type A curves provide best decryption times
Key Insulated CPABE allows non-immediate
revocation at low overhead
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Security same as CPABE
Issues with storage of multiple keys
Future Work
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Other pairing libraries (MIRACL)
Optimizations to operations
Comparison of KICPABE to other broadcast
revocation schemes
Security of KICPABE under other modified CPABE
models
```