Receiver Anonymity via Incomparable Public Keys Brent R. Waters, Edward W. Felten, and Amit Sahai Department of Computer Science Princeton University

Receiver Anonymity via Incomparable Public Keys

Brent R. Waters, Edward W. Felten, and Amit Sahai

Department of Computer Science

Princeton University

Receiver Anonymity

Alice can give Bob information that he can use to send messages to Alice, while keeping her true identity secret from Bob.

Bulletin Board

alt.anonymous.messages

Anonymous ID

“Where are good Hang Gliding spots?”

Send to: alt.anonymous.messages

Bob

Alice

Receiver Anonymity

• Anonymous Identity– Information allowing a sender to send messages to

an anonymous receiver

– May contain routing and encryption information

• Requirements– Receiver is anonymous even to the sender

– Anonymous Identity can be used several times

– Communication is secret (encrypted)

– Messages are received efficiently

A Common Method

Bulletin Board


Alice

Alice anonymously receives encrypted message from both Bob and Charlie by reading a newsgroup.

Anonymous ID 1



Encrypt with: a45cd79e

Anonymous ID 2

“What Biology conferences are interesting?”



Bob

Charlie

The Encryption Key is Part of the Identity

Bulletin Board


Alice

Bob and Charlie collude and discover that they are encrypting with the same public key and thus are sending messages to the same person.

Anonymous ID 1




Anonymous ID 2




Bob

Charlie

The Encryption Key is Part of the Identity

Bulletin Board


Alice

Bob and Charlie then aggregate what they each know about the Anonymous Receiver and are able to compromise her anonymity.

Anonymous ID 1




Anonymous ID 2




Bob

Charlie

Hang Gliding + Biology => Alice

Using an Independent Public Key per Sender

Bulletin Board


Alice

Alice creates a separate public/private key pair for each sender. Upon receiving a message on the newsgroup Alice tries all her private keys until one matches or she has tried them all.

a45cd79e

207c5edb

Bob

Charlie

Keys to Try

48b33c03

ae668f53

Using an Independent Public Key per Sender

Bulletin Board


Alice

Alice creates a separate public/private key pair for each sender. Upon receiving a message on the newsgroup Alice tries all her private keys until one matches or she has tried them all.

a45cd79e

207c5edb

Bob

Charlie

Keys to Try

48b33c03 43bca289

ae668f53

40b2f68c

2fce8473

075ca5ef

b9034d40

86cf1943

56734ba5

207defb1

70f4ba54

04d2a93c

398bac49

e3c8f522

b593f399

46cce276

Incomparable Public Keys

• Receiver generates a single secret key• Receiver generates several Incomparable Public

Keys (one for each Anonymous Identity)• Receiver use the secret key to decrypt any

message encrypted with any of the public keys• Holders of Incomparable Public Keys cannot tell

if any two keys are related (correspond to the same private key)

Using an Incomparable Public Keys to Receive Messages Efficiently

Bulletin Board


Alice

Alice creates a one secret key and distributes a different Incomparable Public Key to each sender.

a45cd79e

207c5edb

Bob

Charlie

Keys to Try

59b39c03

207defb1

70f4ba54

04d2a93c

398bac49

e3c8f522

b593f399

46cce276

Key Generation

• Based on ElGamal encryption– All users share a global (strong) prime p

– Operations are performed in group of Quadratic Residues of Zp

• Secret Key Generation: – Choose an ElGamal secret key a

• Generate a new Incomparable Public Key:– Pick random generator, g, of the group

– Public key is (g,ga)

*

Security Intuition

• Cannot distinguish equivalent keys (g,ga), (h,ha) from non-equivalent ones (g,ga), (h,hb)– Assuming Decisional Diffie-Hellman is hard

Security Intuition


• However, this is not enough if the receiver might respond to a message

Security Intuition



Bob

Charlie(h,ha)

(g,ga)

Security Intuition

• Cannot distinguish equivalent keys (g,ga), (h,ha) from non-equivalent ones (g,ga), (h,hb) – Assuming Decisional Diffie-Hellman is hard


Bob

Charlie(h,ha)

(g,ga)

Pair-wise multiply

Security Intuition

• Cannot distinguish equivalent keys (g,ga), (h,ha) from non-equivalent ones (g,ga), (h,hb) – Assuming Decisional Diffie-Hellman is hard


Bob

Charlie(h,ha)

(g,ga)

Pair-wise multiply

(gh,(gh)a)

Alice can decrypt messages encrypted with this new key.

Solution

• Record keys that were validly created

• The ciphertext will contain a “proof” about which key was used for encryption

• The private key holder can alternatively distribute each Incomparable Public Keys with its MAC

Encryption

C = (gr,garK)

– (g,ga) is an Incomparable Public Key

Encryption

C = (gr,garK), H(r), EK(r,(g,ga), plaintext)

– (g,ga) is an Incomparable Public Key

– H is a secure hash function

– K is a random symmetric key

– r is a random exponent

Decryption

C = (gr,garK), H(r), EK(r,(g,ga), plaintext)

• Use secret key a to decrypt the ElGamal encrypted ciphertext and learn the symmetric key K

Decryption

C = (gr,garK), H(r), (r,(g,ga), plaintext)


• Use K to decrypt the symmetrically encrypted ciphertext

Decryption




• Check that the public key inside the envelope has been distributed

Decryption





• Check that the claimed public key was used– Hash r and check it against claimed hash of r

Decryption





• Check that the claimed public key was used– Hash r and check it against claimed hash of r– Raise the public key to the r to check that it was

used in the ElGamal encryption

Decryption





• Check that the claimed public key was used– Hash r and check it against claimed hash of r– Raise the public key to the r to check that it was

used in the ElGamal encryption• If all test pass accept the plaintext

Security

• Provably secure in the Random Oracle Model assuming DDH is hard

• We have another construction based only on general assumptions

• We can apply similar techniques to a CCA secure

cryptosystem such as Cramer-Shoup

Efficiency

• Efficiency is comparable to standard ElGamal

• One exponentiation for encryption

• Two exponentiations for decryption and verification of a message

Comparison with Alternative Methods

Several Independent Public Keys

- Running time increases linearly with number of potential senders

Several Independent Symmetric Keys

+ Encryption and decryption operations are faster

- Running time increases linearly with number of potential senders

- No secrecy of past messages if sender’s key is captured

- Key must be distributed securely

Comparison with Alternative Methods (cont.)

Message Markers

Sender puts a random tag on each message that identifies him and which key to use

Tag Key

5d234 98b2e6

3891c 7ac023

Comparison with Alternative Methods (cont.)

Message Markers

Sender puts a random tag on each message that identifies him and which key to use

+ Potentially quick way for the receiver to identify her messages and discard messages destined for others

- Cannot reuse a mark

- Therefore both sender and receiver must update expected next mark – leads to problems if messages are lost

Tag Key

5d234 98b2e6

3891c 7ac023

Applications

• Use in anonymous communication between users– Users already employ newsgroups such as

alt.anonymous.messages to send PGP encrypted messages to anonymous receivers

• Protection of anonymity in case of device compromise– Receiver distributes a set of sensor nodes that he

does not want to be traced back to him

– Initially trusts the devices, but they could be captured or otherwise compromised

Embedding Incomparable Public Keys in Security Protocols

Use with other schemes to enhance anonymity and efficiency

• We adapted SKEME key exchange protocol to incorporate Incomparable Public Keys– Allows for establishment of efficient session key

while maintaining anonymity guarantees • Peer-to Peer systems

– P5 allows tradeoff anonymity and efficiency• By making all public keys Incomparable we can

enhance anonymity while still giving user a tradeoff option

Implementation

• Implemented Incomparable Public Keys by extending GnuPG (PGP) 1.2.0

• Available at http://www.cs.princeton.edu/~bwaters/research/

GnuPG (PGP) Background

• Users post encrypted messages to newsgroups to attempt receiver anonymity

• Software for automatically retrieving messages from newsgroups– Jack B. Nymble

– Private Idaho

Implementation: Benefit

• Receivers can give have one private key to decrypt messages sent from any one of many Incomparable Public keys

• Interface is similar to original GnuPG interface

• Only a few changes needed to be made existing code (ElGamal encryption already exists in GnuPG)

Related Work

• Bellare et al. (2001) – Introduce notion of Key-Privacy

– If Key-Privacy is maintained an adversary cannot match ciphertexts with the public keys used to create them

– The authors do not consider anonymity from senders

• Pfitzmann and Waidner (1986)– Use of multicast address for receiver anonymity

– Discuss implicit vs. explicit “marks”

Related Work (cont.)

• Chaum (1981)– Mix-nets for sender anonymity

– Reply addresses usable only once

– Other work follows this line

Conclusion

• The contents of public keys are important in protecting the receiver’s anonymity from the sender

• Incomparable Public Keys provide a secure and efficient way of accomplishing receiver anonymity

• Incomparable Public Keys are useful in practice with Key Exchange and P2P systems

Documents

Receiver Anonymity via Incomparable Public Keys Brent R. Waters, Edward W. Felten, and Amit Sahai Department of Computer Science Princeton University