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Anonymous Communication

Anonymous Communication. CSE 548 Lecture Prepared and presented by Vinayak Kandiah 10/08/07. Content Organization. Introduction to Anonymous Communication Introduction Anonymity using a Mix and Mix Networks Mix Network Classification Onion Routing Attacks on Mix Networks Split Mix

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Anonymous Communication

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  1. Anonymous Communication CSE 548 Lecture Prepared and presented by Vinayak Kandiah 10/08/07

  2. Content Organization • Introduction to Anonymous Communication • Introduction • Anonymity using a Mix and Mix Networks • Mix Network Classification • Onion Routing • Attacks on Mix Networks • Split Mix • Merge Mix • Using Split and Merge in Same Network. • C-Mix (a network coding type anonymous scheme) • Performance Evaluation • Conclusion CSE 548 - Advanced Computer/Network Security

  3. Introduction • Message secrecy achieved by cryptography. • Identities of communicating users and path info need to be hidden. • Wireless environment - identity associated with location. • Anonymity of a node is the state of not being identifiable within a given set of nodes [1]. • Different types of anonymity: • Source anonymity. • Destination anonymity. • Path anonymity. CSE 548 - Advanced Computer/Network Security

  4. Anonymity using a Mix • “Mix” technique proposed by Chaum in 1981 [2]. • A single node called “Mix” re-orders and changes message appearances. • Uses some cryptographic operations. • Initially suggested as an anonymous re-mailer. • Obvious drawbacks – single point of failure, bottleneck, centralized secrets. CSE 548 - Advanced Computer/Network Security

  5. Mix Networks • Chaum’s idea expanded to anonymous network communication. • Mix networks use multiple nodes which perform mixing operations. • Heavily uses cryptographic operations. • Various design choices available (also used as a basis for classification). CSE 548 - Advanced Computer/Network Security

  6. Mix Network Classification Classified based on four main criteria [3]: • Node Operation • Continuous Mix: • Messages associated with random delay values. • Node holds for specified delay before forwarding. • Works with constant traffic rates. • Block\Pool Mix: • Messages held at node till a flushing condition is satisfied. • Flushing condition can be timed, threshold or hybrid. • Pool Mix – Not all messages are flushed every time. • Works even with variable traffic rates. CSE 548 - Advanced Computer/Network Security

  7. Mix Network Classification • Networking Framework • Asynchronous Model: • Message transmissions not restricted by timing constraints. • Route length independence. • Usually chosen for large, vast networks (Internet). • Synchronous Model: • Distinct rounds of communication. • Senders transmit messages at start of a time period. • Path lengths need to (fairly) same. • In a round, users participate as either sender or receiver NOT both. CSE 548 - Advanced Computer/Network Security

  8. Mix Network Classification • Cryptographic Sequence • Decryption Network: • Sender encrypts message multiple times. • Path nodes decrypt before forwarding (to change appearance). • Re-encryption Network: • Sender encrypts once and attaches a trapdoor for intended receiver. • Path nodes try to solve trapdoor or re-encrypt and forward. • Normally used in wireless environments (MANET). CSE 548 - Advanced Computer/Network Security

  9. Mix Network Classification • Routing Strategy • Source Routing: • Sender decides the path to the receiver. • Each path node only knows the previous and next nodes. • Loose Source Routing: • Sender specifies partial path to the destination. • Trusted intermediate nodes determine the remainder of the path. • Useful when sender doesn't know entire topology. CSE 548 - Advanced Computer/Network Security

  10. Onion Routing • An implementation of mixes for low latency networks. • Onion routing uses: • Pool mixes. • Asynchronous framework. • Decryption. • Source Routing. • Three phases: Circuit initiation, data transfer and circuit destruction. • For circuit init., sender selects route and prepares a repeatedly encrypted message. • Order of public key encryption is reverse of path. CSE 548 - Advanced Computer/Network Security

  11. Onion Routing • Consider the sample network and path shown in the figure. • In this case, order of public key encryption is R2, M5, M2 and M1. • Before each encryption a header is added. • Each node prior to decryption obtains: {next, Kf, Kb, TTL, {payload}}MX Sample Network with path for Onion Routing. CSE 548 - Advanced Computer/Network Security

  12. Onion Routing • Each node knows previous and next hops, shared keys (Kf, Kb) and creates a VCI. • Receiver sends ACK on receiving the init onion. • Data Transfer: • Sender performs multiple symmetric encryptions using shared keys distributed. • Each node decrypts and forwards to corresponding VCI. • Message content and user identities are hidden. • Circuit destruction involves a KILL message to the path. CSE 548 - Advanced Computer/Network Security

  13. Attacks on Mix Networks • Several attacks to compromise anonymity of network. • Some attacks weaken anonymous schemes to be compromised by other attacks. • Different types of attacks based on certain properties. • Types of attacks are enumerated followed by selected examples. CSE 548 - Advanced Computer/Network Security

  14. Attacks on Mix Networks • Passive vs. Active • Passive Attacks • The adversary does not interfere with communication. • Merely observes the network and performs analysis. • Active Attacks • Adversary modifies, removes or introduces messages in the network. • Can be detected in some cases. • Internal vs. External • Internal Attacks • Attacks where the operations performed inside a mix node are known. • Node either compromised or colludes with other nodes. • External Attacks • Operations performed by mix node are not revealed. CSE 548 - Advanced Computer/Network Security

  15. Attacks on Mix Networks • Partial vs. Global • Partial Attacks • The adversary has access to only limited potion of the network. • Successful attack may however break anonymity of network nodes outside this area. • Global Attacks • Adversary is able to view and launch attack over the entire network. • Static vs. Adaptive • Static Attacks • The computational power and resources available to adversary are fixed. • Adaptive Attacks • Resources available to adversary increases as attacks progresses successfully. CSE 548 - Advanced Computer/Network Security

  16. Attacks on Mix Networks Traffic Analysis Attack • Passive attack, involves observation of messages and related data. • Correlation analysis on data to reveal peer relationships. • Various attack models for traffic analysis. • Special Attack model involving only end point observation [4] – Fundamental limits on Mix Technique. • Synchronous framework where attacker only observes links connected to end users. CSE 548 - Advanced Computer/Network Security

  17. Attacks on Mix Networks Traffic Analysis Attack • The attacker forms sender and receiver multisets for each round • Multiset is a generalization of a Set which can contain the same element multiple times. • Example: {S1,S2,S3}  <R1,R1,R4> • Attacker obtains a set of receiver multisets for each sender subset. • Two cases considered: • Closed Sender: all senders participate in all communication rounds • Open Sender: less than the total number of senders participate CSE 548 - Advanced Computer/Network Security

  18. Attacks on Mix Networks Traffic Analysis Attack • Peer relationships can be depicted as a bipartite graph. • The bipartite graph in turn can be characterized by a matrix. • Column headings are senders and row headings are receiver subsets. • Sum of weights of any column is 1. • Calculations performed based on multiset observationsto obtain each weight in the matrix. Bipartite graphs: Individual and combined peer relationships. CSE 548 - Advanced Computer/Network Security

  19. Attacks on Mix Networks Blending Attack • Attacker identifies a target message in the network and next mix node on its path. • Holds all messages from entering this node. • Attacker induces fake packets into this node. • All fake packets have a common next hop. • Now, the target message is mixed. • Only target message is forwarded to a different next hop. CSE 548 - Advanced Computer/Network Security

  20. Traffic Re-distribution • Change traffic patterns in terms of number and size of messages. • Split messages to increase and merge to decrease number of messages. • Message size manipulation depends on padding policy. • For split mix, messages padded to conform to actual message size. • For merge mix, variable padding is applied (message size is multiple of a basic block size). CSE 548 - Advanced Computer/Network Security

  21. Split Mix • Messages sent are split in the mix network. • Split messages follow different paths to the receiver. • Sender determines number of splits and splitting position in the network. • Sender prepares messages to be split in the network. • Only sender and splitting node knows details of splitting. • Originally proposed as Garlic Routing [5] to achieve better throughput and resilience. CSE 548 - Advanced Computer/Network Security

  22. Split Mix • Sender prepares message by using different keys for encryption. • Splitting node decrypts and forwards split messages to different nodes. Example of Split Mix and associated Garlic Message format. CSE 548 - Advanced Computer/Network Security

  23. Split Mix • Split mix can be used to defeat traffic analysis attacks. • Split mix can confuse the attacker from obtaining correct multisets. • Attacker will observe several potentially correct multisets. • When using these multiple multisets in closed and open sender calculations, errors and/or multiple solutions are obtained. CSE 548 - Advanced Computer/Network Security

  24. Split Mix • Split Mix does not work when each receiver gets a message from only one sender. • As shown in the figure, even if messages are split, the multiset can be correctly obtained as <r1,r2,r3>. CSE 548 - Advanced Computer/Network Security

  25. Split Mix • However, when receivers get messages from multiple senders, split mix (with padding) obscures the correct multiset. • As shown in the figure, possible multisets are <r1,r1,r3> and <r1,r3,r3>. CSE 548 - Advanced Computer/Network Security

  26. Split Mix • When forming a multiset, it is obvious that each distinct receiver must appear at least once. • Remaining slots in the multiset equals difference between number of senders and receivers. • Assume a given no. of receivers (ndr) and remaining slots (slotsrem). • Maximum no. of multisets (Maxrm) will be obtained when number of splits for each message is greater than remaining slots. CSE 548 - Advanced Computer/Network Security

  27. Merge Mix • Merge mixing is also based on traffic re-distribution. • Combines messages in the mix network. • Merging is per-hop instead of end-to-end (like in split mix) • Merging cannot be end-to-end because: • Senders do not share path info • Merging node cannot know destination of packets • Merging messages is a decision made by mix node and not sender. CSE 548 - Advanced Computer/Network Security

  28. Merge Mix • Links in an onion routing are TLS encrypted (using pair-wise keys). • To merge, mix node encrypts messages with same next hop with pair-wise shared key. • Figure shows examples of merge mix. • End to end merging can be obtained only two paths share a suffix. CSE 548 - Advanced Computer/Network Security

  29. Merge Mix • Merge mix uses variable padding as shown in figure. • Merge mix obtains higher overall unlinkability at a mix node. • (ni-1)/2 times better (max), where ni is no. of input messages. • max is the scenario where no. of output = ni-1 • It reaches a slightly lower level of per message unlinkability (for max). • 0.99 for ni > 20, where 1 is perfect unlinkability. CSE 548 - Advanced Computer/Network Security

  30. Using Split and Merge Mixes in the Same Network • Split and Merge mixes could be used together to mitigate blending attacks. • When the target message results in 2 messages at the output. • The increase may be due to splitting or due to separation of previously merged message. • Either way, attacker needs to track additional path. CSE 548 - Advanced Computer/Network Security

  31. Using Split and Merge Mixes in the Same Network • Split and merge mixes used concurrently could have varied results in traffic analysis. • Figure (a) shows a beneficial scenario where the multiset is wrongly observed as <r1,r1,r2,r3>. • Figure (b) shows a detrimental scenario where the split and mix cancel each other out. CSE 548 - Advanced Computer/Network Security

  32. C-Mix • A technique to improve the computational efficiency of anonymous routing. • Based on properties of polynomial interpolation. • The message is reconstructed in a distributed manner (similar to network coding). • However, objective is to improve computational efficiency rather than communication efficiency. CSE 548 - Advanced Computer/Network Security

  33. C-Mix • Polynomial Interpolation-Based Secret Sharing proposed by Shamir [6]. • A dealer picks a polynomial equation of degree k-1 of the following form: • The secret S to be shared is a0 which is the y intercept of the curve. • Now the dealer derives n points from the curve. CSE 548 - Advanced Computer/Network Security

  34. C-Mix • ‘k’ co-ordinates are needed to obtain the polynomial equation of degree ‘k-1’. • If a(x) = y, then ‘k’ points (x1, y1)…(xk, yk) can reconstruct polynomial by Lagrange Interpolation Formula. • All computation can be performed over a field Zp. Polynomial equation of degree 4 and a0 = 2. CSE 548 - Advanced Computer/Network Security

  35. C-Mix • A basic C-Mix scheme is described first to explain the working principles. • Then the basic C-Mix scheme is refined to be more anonymous and secure. Basic C-Mix: • For the circuit initiation phase, sender chooses a number K over the field Zp. • Sender constructs a polynomial with: • Degree = len (len is the no. of mix nodes in route). • a0 is K. • Values a1…alen are randomly chosen. CSE 548 - Advanced Computer/Network Security

  36. C-Mix • Sender also chooses ‘len+1’ points on the curve needed. • Sender calculates for values 1≤ j ≤ len+1. • In the initial circuit setup phase the sender prepares headers in the form of an onion message. • Each layer of the header will have a (bj, yj) pair in addition to other details. CSE 548 - Advanced Computer/Network Security

  37. C-Mix • Sender calculates b1.y1 and transmits the onion to the next hop. • This will continue till the receiver calculates blen+1.ylen+1. • a0 doesn’t mean anything in this circuit initiation phase. • But it can be seen that the receiver can reconstruct the secret a0. • This is possible if each node calculates bkyk and forwards it. CSE 548 - Advanced Computer/Network Security

  38. C-Mix • For data transmission, the sender finds a curve of degree len+1 that shares len+1 points with the init curve and passes through the msg. • The only new point on the curve will be the point which the sender held in the circuit initiation. • In this way, the b values can be recalculated using the new x-coordinate and the receiver can reconstruct the message. CSE 548 - Advanced Computer/Network Security

  39. C-Mix Example of Basic C-Mix • Assume the path sd  M1  M2  dn, where sd is the sender and dn is the destination. • Let sender chosen polynomial for circuit initiation be • Let 3 points on the curve be {(1, 27),(2,40), (3, 59)} • Sender also calculates the values binit(1) = 3; binit(2) = -3; binit(dn) = 1. • Sender distributes the triplets {(1,27,3),(2,40,-3),(3,59, 1)} using onion routing. CSE 548 - Advanced Computer/Network Security

  40. C-Mix • Now assume that the sender wishes to transmit 31 to the destination. • Sender chooses the following new curve which shares the 3 points from init and passes through (0,31). • Then new point (4,73) is found on the curve. CSE 548 - Advanced Computer/Network Security

  41. C-Mix • The sender now calculates its new bsn(1) value as -1 and the payload as (-1)(73)= -73. • M1 receives this, updates its b1(1) value as 3((4/4-1)) = 4 and calculates new payload as -73+(4)(27)= 35. • This procedure continues as shown in figure and receiver derives the message as 31. CSE 548 - Advanced Computer/Network Security

  42. C-Mix • The basic scheme has the following vulnerabilities • The sender picks a new point whose x-coordinate needs to be propagated to the nodes. • If the value is transmitted as plain text, the attacker can observe it and track paths. • If the same value is used every time, the sum added to the payload remains the same. • So it is necessary to ensure that nodes update their b values without being tracked. CSE 548 - Advanced Computer/Network Security

  43. C-Mix Globally determined x values • All nodes in the path keep track of the no. of messages sent through each VCI. • The sender uses this value and a global function to identify the new x-coordinate. • The path nodes can also determine this new value and update their b values. • An attacker cannot detect a circuit because all paths use the message count and the global function. • A maximum number of messages are allowed through a Virtual Circuit. • If the limit is reached, a new path is to be determined. CSE 548 - Advanced Computer/Network Security

  44. C-Mix Multiple points for each node • Consider a case where the attacker has observed the incoming and outgoing payloads at a node. • In the basic scheme, the attacker would be able to identify the nodes binit value (and calculate b values for forthcoming transmissions). • To mitigate this, each node receives multiple point triplets. • In this case, the degree of the curve used will be greater than the number of nodes. • The attacker on observing the incoming and outgoing packets can no longer obtain the secrets (because the number of points is hidden). CSE 548 - Advanced Computer/Network Security

  45. C-Mix Security Properties • The secrecy of the transmitted message is based on the properties of polynomial interpolation. • As the receiver also holds certain points on the curve, C-Mix is secure against these attacks: • Colluding attack where all path nodes share information. • Blending attack from sender to receiver. • Traffic analysis attack after the number of points at each node are revealed. CSE 548 - Advanced Computer/Network Security

  46. C-Mix Anonymity Properties • In case of a colluding attack • Path anonymity is maintained with at least one uncompromised node. • In a collusion by comparing global values, same anonymity as onion routing. • When a blending attack is carried out • The attacker needs to know the number of points at a node to identify the points. • Identifying the points in turn only lead to path information which is previously known. • Traffic Analysis Attack • Defeats simple schemes but is susceptible to long term traffic analysis like Hitting Set Attack. • Same level of anonymity as onion routing. CSE 548 - Advanced Computer/Network Security

  47. Performance Evaluation Benchmark for Evaluation • The computation overhead introduced by split mix and efficiency of using C-Mix is evaluated. • Encryption/Decryption times for AES 256 observed using C++ cryptographic functions. • Time for multiplication and addition over a finite field Zp calculated using Maple 9. CSE 548 - Advanced Computer/Network Security

  48. Performance Evaluation • Split Mix when used with padding introduces additional overhead into the network. • This is due to the additional data that needs to be decrypted in the network. • The various scenarios used for the computational overhead comparison is shown in the table. • Note that the case No Pad is the same as the time taken for onion routing. CSE 548 - Advanced Computer/Network Security

  49. Performance Evaluation • The computation time taken by C-Mix is compared to onion routing for data transmission. • Different cases with different number of points in the network is considered. • First case assumes the message sizes to be same as the finite field size. • C-Mix is faster for up to 40 points when message size <4096 bits. CSE 548 - Advanced Computer/Network Security

  50. Performance Evaluation • Comparison for a fixed 1024 bit field size with AES 256 and varying field sizes. • The number of points is fixed at 30. • When 1024 bit field is used, C-Mix is faster compared to AES 256 for all message sizes. CSE 548 - Advanced Computer/Network Security

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