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Enhancing Online Privacy: Anonymity Mechanisms and Adversaries in Cryptography

This article explores the forms of anonymity in early social contexts and modern computer-based systems. It delves into anonymity mechanisms such as cryptography, steganography, and traffic analysis prevention, along with the adversaries in the field. The text covers symmetric and public-key cryptography, Chaum's untraceable mail concept, and cascading mixes to ensure sender, recipient, and message anonymity.

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Enhancing Online Privacy: Anonymity Mechanisms and Adversaries in Cryptography

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  1. Anonymity - Beginnings • Early (pre-computer) uses for social reasons (ability to act more freely, have work accepted without prejudice, etc.) • Traffic analysis an issue prior to computers (e.g., Bodyguard of Lies) • Computer TAP solvable with cryptography • With public-key cryptography, theoretical possibility for anonymity and pseudonymity

  2. Forms of Anonymity • Traffic Analysis Prevention • Sender, Recipient, Message Anonymity • Voter Anonymity • Pseudonymity • Revokable anonymity • Data anonymity

  3. Anonymity Mechanisms • Cryptography • Steganography • Traffic Analysis Prevention (TAP) • Mixes, crowds • Data sanitization/scrubbing • k-anonymity

  4. Adversaries • Global vs. Restricted • All links vs. some links • All network nodes vs. some or no nodes • Passive vs. Active • Passive – listen only • Active – remove, modify, replay, or inject new messages • Cryptography Assumptions • All unencrypted contents are observable • All encrypted contents are not, without key

  5. Symmetric Key Cryptography • One key, Kab, associated with entities A and B • Same key used for encryption and decryption: C=E(M,Kab), M=D(C,Kab)=D(E(M,Kab)Kab) • For message M, ciphertext C = {M}K • Anyone with Kab can form ciphertext • Anyone with Kab can decrypt C • For message M, MIC or MAC uses hash fcn • If only A and B have Kab, then MAC • If group key, then MIC • Depending on E, may require crypto hash fcn

  6. Public Key Cryptography • Two keys, K and K-1, associated with entity A • K is public key, K-1 is private key • Keys are inverses: {{M}K}K-1 = {{M}K-1}K = M • For message M, ciphertext C = {M}K • Anyone can send A ciphertext using K • Only A has K-1 so only A can decrypt C • For message M, signature S = {M}K-1 • Anyone can verify M,S using K • Only A can sign with K-1

  7. Details we omit • Limit on size of M, based on size of K in PKC • Need to format M to avoid attacks on PKC • Use confounder to foil guessed ptxt attacks • Typical use of one-way hash H to distill large M to reasonable size for signing • Typical use of PKC to distribute symmetric key for actual encryption/decryption of larger messages • See http://www.rsa.com/rsalabs/ for standards

  8. Chaum – Untraceable Mail • Wish to receive email anonymously, but • Be able to link new messages with past ones • Respond to the sender • Do not trust single authority (e.g., Paypal) • Underlying message delivery system is untrusted • Global active adversary

  9. Chaum Mix 1 • Mix is like a special type of router/gateway • It has its own public key pair, K1 and K1-1 • Recipient A also has public key pair, Ka and Ka-1 • Sender B prepends random confounder Ra to message M, encrypts for A: Ca = {Ra|M}Ka • B then prepends confounder for mix to C and encrypts for mix: C1 = {R1|A|Ca}K1 • B sends C1 to mix, which later send Ca to A

  10. Chaum Mix 2 • Mix simply decrypts and strips confounder from message to A • Incoming message and outgoing message do not appear related • Use padding to ensure same length (some technical details here) • Gather a batch of messages from different sources before sending them out in permuted order

  11. Chaum Mix • As long as messages are not repeated, adversary can't link an incoming message with an outgoing one (anonymous within the batch) • Mix can discard duplicate messages • B can insert different confounder in repeats • B can use timestamps – repeats look different • Mix signs message batchs, sends receipt to senders • This allows B to prove to A if a message was not forwarded

  12. Cascading Mixes 1 • If one mix is good, lots of mixes are better! • B prepares M for A by selecting sequence of mixes, 1, 2, 3, … , n. • Message for A is prepared for Mix 1 • Message for Mix 1 is prepared for Mix 2 • … Message for Mix n-1 is prepared for Mix n • Layered message is sent to Mix n • Each mix removes its confounder, obtains address of next mix (or A), and forwards when batch is sent in permuted order

  13. Cascading Mixes 2 • Mix in cascade that fails to forward a message can be detected as before (the preceding mix gets the signed receipt) • Any mix in cascade that is not compromised can provide unlinkability • This gets us anonymous message delivery, but does not allow return messages

  14. Return Addresses 1 • B generates a public key Kb for the message • B seals its true address and another key K using the mix's key K1: RetAddr = ({K,B}K1, Kb) • A encrypts reply M and confounder R0 with message key Kb and sends to mix along with return address: Reply = {K,B}K1, {R0|M}Kb • Mix decrypts address and key, uses key K to re-encrypt reply: {{R0|M}Kb}K and send to B

  15. Return Addresses 2 • B must generate new return address keys for each message (K and Kb) so there are no duplicates • Mix must remove duplicates if found • Symmetric cryptography may be used for both K and Kb here (but not for mix key!) • How? • Cascade can return messages by building the return address in reverse order, then peeling off layers as the reply is forwarded (and encrypted) along the return path

  16. Return Addresses 3 • For cascaded mixes, must build return address for the whole path • Receiver uses built-up return address and return key to send reply • Each mix on return path unwraps its portion of return address, re-encrypts, and forwards to next address • Sender had all the keys (it built the return address) so it can decrypt reply

  17. Mix Generics • Mix must make input messages unlinkable with output messages • Messages must all be same length • Messages must all be encrypted so as to appear random • Can't hide source/destination addresses along a single hop in path, but must hide sender and receiver, as well as distance along path • Mix must randomize order of output • Mix may have any number of triggers

  18. Mix Triggers • Timed mix • Mix gathers messages for period T, then sends • Threshold mix • Mix gathers N messages, then sends • Hybrid mix • Mix sends when N messages or period T reached • Pool mix • Mix keeps pool of messages of size P, when pool reaches size N+P, N randomly chosen messages are sent • Continuous mix • Mix attaches random delay D from some distribution to each msg M, sends M when delay is reached

  19. Mix Padding • In addition to padding messages to some constant length (and segmenting longer messages), mix may introduce dummy messages into traffic • Dummy messages especially useful in timed mixes (may not have many messages to send) • Strong resistance from network guys • Research question: how much does this form of padding help, and what is the relationship between increase in anonymity and cost of padding?

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