Bounded WaitFree Byzantine Storage With Information Theoretic Security

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Bounded Wait-Free Byzantine StorageWith
Information Theoretic Security

• Amitanand S. Aiyer, UT-Austin
• Prof. Lorenzo Alvisi, UT-Austin
• Prof. Rida A. Bazzi, ASU

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Byzantine Storage

• Nodes
• Storage System

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Byzantine Storage

• Nodes
• Storage System
• Tolerate faults
• up to f

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Byzantine Storage

• Atomic Semantics
• Wait-Free
• Asynchronous n/w
• No server-server communication

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State of the Art
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State of the Art
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State of the Art
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State of the Art
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State of the Art
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State of the Art
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State of the Art
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State of the Art
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State of the Art
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State of the Art
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State of the Art
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State of the Art
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Information Theoretic Security
against Byzantine Readers

• Existing approaches
• Use PKI
• Based on unproven assumptions
• May not hold
• Use Secret Sharing
• Informational theoretic security

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Outline

• Single writer protocol
• Bounded, atomic and wait-free
• Benign writer and readers
• Tolerate Byzantine readers
• Without cryptography
• Need private channels to the writer
• Can support multiple writers
• using standard techniques

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Outline

• Single writer protocol
• Bounded, atomic and wait-free
• Benign writer and readers
• Tolerate Byzantine readers
• Without cryptography
• Need private channels to the writer
• Can support multiple writers
• using standard techniques

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Model

• One writer
• servers
• may be Byzantine
• A finite set of readers

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Model

• Channels between Servers and Clients
• Asynchronous
• Reliable
• Authenticated
• No server-server communication
• Readers/Writer may crash
• are not malicious.

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Basic Write Protocol
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Basic Write Protocol
Byzantine Disk Paxos Optimal Resilience with
Byzantine Shared Memory Abraham et al. Dist
Comp. Nov 2006
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Basic Write Protocol
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Basic Write Protocol
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Basic Write Protocol
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Basic Write Protocol
Wait-Freedom
Boundness?
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Concurrent Reader Detection
x x in ( f 1 ) different

Bounded Wait-Free f-resilient Atomic Byzantine
Data Storage Systems for an Unbounded Number of
Clients. Bazzi Ding DISC 2006
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Concurrent Reader Detection
x x in ( f 1 ) different

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Write Protocol
Detect Concurrent Readers
Wait-Freedom
Boundness
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Write Protocol
Detect Concurrent Readers
Wait-Freedom
Boundness
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Write Protocol
Detect Concurrent Readers
Wait-Freedom
Boundness
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Write Protocol
Detect Concurrent Readers
Wait-Freedom
Boundness
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Read protocol

• Write-Read atomicity
• written by writer
• ( f 1 ) matching responses
• not older than the latest completed write
• Timestamp ( 2f 1 ) smallest timestamp
• servers not in sync with writer
• f servers may be malicious
• Read-Read atomicity
• Reader does a write back

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Read protocol
Register
Collect Values
Write Back
Write Back
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Read protocol
Register
Collect Values
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Read protocol
Register
Collect Values
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Read protocol
Register
Collect Values
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Read protocol
Register
Collect Values
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Read protocol
Register
Collect Values
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Read protocol
Register
Collect Values
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Read protocol
Register
Collect Values
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Read protocol
Register
Collect Values
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Read protocol
Register
Collect Values
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Read protocol
Register
Collect Values
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Read protocol
Register
Collect Values
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Read protocol
Register
Collect Values
Minimal Byzantine Storage Martin et al. DISC2002
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Read protocol
Register
Collect Values
Minimal Byzantine Storage Martin et al. DISC2002
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Read protocol
Register
Collect Values
Minimal Byzantine Storage Martin et al. DISC2002
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Read protocol
Register
Collect Values
Minimal Byzantine Storage Martin et al. DISC2002
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Read protocol
Register
Collect Values
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Read protocol
Register
Collect Values
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Read protocol
Register
Collect Values
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Read protocol
Register
Collect Values
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Read protocol
Register
Collect Values
Write Back
Write Back
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Read protocol
Register
Collect Values
Write Back
Write Back
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Protocol Guarantees

• Atomic Semantics
• Wait-Free
• Bounded
• Size
• Number

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Read protocol
Register
Collect Values
Write Back
Write Back
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Read protocol
Register
Collect Values
Write Back
Write Back
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Outline

• Single writer protocol
• Bounded, atomic and wait-free
• Benign writer and readers
• Tolerate Byzantine readers
• Without cryptography
• Need private channels to the writer
• Can support multiple writers
• using standard techniques

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Outline

• Single writer protocol
• Bounded, atomic and wait-free
• Benign writer and readers
• Tolerate Byzantine readers
• Without cryptography
• Need private channels to the writer
• Can support multiple writers
• using standard techniques

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Byzantine Readers

• Byzantine Readers
• Write back a wrong value
• Not wait for enough ACKs
• Options
• No write back
• Require proofs for write back

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Byzantine Readers

• Byzantine Readers
• Write back a wrong value
• Not wait for enough ACKs
• Options
• No write back
• Require proofs for write back

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Byzantine Readers

• Byzantine Readers
• Write back a wrong value
• Not wait for enough ACKs
• Options
• No write back
• Require proofs for write back

Efficient replication of large data objects Fan
Lynch DISC 2003
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Write back Proofs

• Option 1 PKI
• Collect signatures
• Based on computational hardness of factoring etc.
• Unproven assumptions
• Option 2 Secret Sharing
• Information theoretic security

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Write back Proofs

• Option 1 PKI
• Collect signatures
• Based on computational hardness of factoring etc.
• Unproven assumptions
• Option 2 Secret Sharing
• Information theoretic security

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Proof Structure

• Show that servers responded with a particular
  message M
• Secret Sharing
• with threshold
• reconstruction iff shares are received

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Write back proofs

• To accept a WB-1 message
• Show that servers responded with
  
• To accept a WB-2 message
• Show that servers
  responded to the WB-1 message

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Proofs using Secret Sharing

• Generate and share a random secret
• Using Tompa Wools secret sharing scheme
• shares required to reconstruct
• Servers reveal share only on sending
• Reconstruct the secret
• iff received t shares
• iff received t messages

How to share a secret with cheaters Tompa Wool
J. Crypto 88
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New Write protocol

• Generate Two Secrets
• For WB-1, reconstructed by ( f 1 shares
• For WB-2, reconstructed by ( n f shares
• Send this along with the values
• Before starting the actual write

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New Write Protocol
Phase 1
Phase 2
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New Write Protocol
Phase 0
Phase 1
Phase 2
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New Write Protocol
Private Channel
Phase 0
Phase 1
Phase 2
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New Read Protocol

• Collect shares1 along with the values
• proof for WB-1
• Similarly collect shares2 with the Ack for WB-1
• proof for WB-2
• Retry until succeed

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Read Protocol
Register
Collect Values
Write Back Vals
Write Back TS
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Read Protocol
Register
Collect Values
Write Back Vals
Write Back TS
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New Read Protocol
Register
Collect Values
Write Back Vals
Write Back TS
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New Read Protocol
Register
Collect Values
Write Back Vals
Write Back TS
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New Read Protocol
Register
Collect Values
Write Back Vals
Write Back TS
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New Read Protocol
Register
Collect Values
Write Back Vals
Write Back TS
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New Read Protocol
Register
Collect Values
Write Back Vals
Write Back TS
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New Read Protocol
Register
Collect Values
Write Back Vals
Write Back TS
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New Read Protocol
Register
Collect Values
Write Back Vals
Write Back TS
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New Read Protocol
Register
Collect Values
Write Back Vals
Write Back TS
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Outline

• Single writer protocol
• Bounded, atomic and wait-free
• Benign writer and readers
• Tolerate Byzantine readers
• Without cryptography
• Need private channels to the writer
• Can support multiple writers
• using standard techniques

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Outline

• Single writer protocol
• Bounded, atomic and wait-free
• Benign writer and readers
• Tolerate Byzantine readers
• Without cryptography
• Need private channels to the writer
• Can support multiple writers
• using standard techniques

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Conclusion

• Atomic and wait-free register
• Bounded
• Optimal replicas
• Tolerate Byzantine readers
• Information Theoretically

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