Desensitize Intra-domain Information for Inter-domain Routing

Overview of I2BGP This section describes the model of I2BGP and how it exports the information from intra-domain without revealing data and finally makes the route decision. The principles of traditional BGP path selection do not include the consideration of intra-domain performance. This document introduces an additional attribute, Attr, for BGP to accomplish data carrying and spreading. According to the description of , each domain is a confidential system with complete independence and autonomy. BGP runs at border routers of each domain and specifies the next hop when forwarding across. In order to fetch messages from each domain, I2BGP proposes the DIT technique. It masks the intra-domain topology and abstracts each domain into a characteristic topology graph with its border routers exclusively. Because there are direct and indirect connections among all border routers (nodes) with in the same AS we abstract these connections as edges between nodes. After taking the information out of the domain, in order to prevent the information in the domain from being leaked, DIT proposes a random obfuscation technology to ensure data security, which can ensure that information in the domain can be obtained while imitating information security issues. Finally, we spread the retrieved information to other domains through the new field Attr, and obtain the optimal route by comparing the final value.

Homomorphic Encryption This document introduces homomorphic cryptography to export information without revealing data, and to ensure the validity of the final calculation results. Homomorphic Cryptography provide a potential solution to the contradiction of information exportation and privacy, it is a kind of cryptographic technique that performs arithmetic operations on the encrypted data and yields a result equivalent to the cyphertext result of some computation on the unencrypted original data. Its principle can be explained as follow: De(En(a) o En(b)) = a o+ b, where En() is the encryption operation, De() is the decryption operation, o and o+are correspond to the operations on the plaintext and cyphertext domains, respectively. When o+ represents addition, this encryption is an additive homomorphic encryption, and when o+ represents multiplication, this encryption is a multiplicative homomorphic encryption. The encryption function that satisfies both additive homomorphism and multiplicative homomorphism properties is called fully homomorphic encryption, and it alse can perform any times of additive and multiplicative operations Homomorphic encryption algorithms usually have high computational complexity. I2BGP select a algorithm which encrypt simple numbers and satisfy homomorphic additivity to avoid this problem.

DIT Overview In order to achieve the target, this document uses an abstract method to mask the intra-domain topology and reuses the exsiting fields of BGP header. During the route convergence process, cumulative calculations (e.g., addition, min() or max()) over multiple domains can inherently protect the privacy of all upstream domains data, i.e., mathematically speaking, on the basis of c = a + b, it could not infer the values of a and b when only c is known. This is one of the foundations for the privacy protection in DIT. However, the inherent data privacy protection brought by cumulative calculations is effective only after at least one such operation has already been conducted. In other words, the cumulative calculations can only achieve non-destination domain data protection. For example, as shown in the , for AS 3, the value of AS 1 or AS 2 cannot be inferred from the cumulative summation sent from AS 2. However, AS 2 is directly connected to the destination domain of the route (AS 1), the value of AS 1 is directly exposed to AS 2 due to the lack of protection from cumulative calculation. That is, for the destination domain of each route, information leakage risk still exists, which is caused by directly connected neighbor domains, we name it the Direct Connection issue. To solve Direct Connection issue, we propose a basic method named Random Number Confusion. In the path selection process, it is only necessary to select the optimal path by basic comparisons. Just like giving random offsets to all nodes in the coordinate system will not change the relative positions. Therefore, for target domain, DIT adds a random number to the intra-domain data when initially spreading the data to the adjacent domain. After arriving the traget damain, the intra-domain data will be taken out and will not affect the comparison of the final results. After fetching the data, to carry the above intra-domain data, we add a new filed, Attr, to the BGP packet header, although which is not strictly required because we can also reuse existing fields, provided the re-definition of the field function is approved. And the quantified value of the destination-based cumulative path performance is embedded into this field and diffused to neighbor domains with the route update message.

Inter-domain information security scenarios DIT does not constrain the intra-domain switching policy implemented by each domain. shows a typical process of inter-domain routing message diffusion, AS B runs a traditional routing protocol and AS C uses a central controller similar to an SDN controller. This document takes the number of hops as example. Suppose AS D updates the route of d0, then based on the intra-domain topology information, d1 sends this update message to AS B (b2) and AS C (c2), where the Attr value is 12 = s_d + 2. The router compares the Attr to decide whether to update the local RIB. When the received Attr is smaller than the local, the route entry will be updated, otherwise it will not change. In the intra-domain, AS B or AS C exchange update messages using the intra-domain protocol. AS C (c3) sends this update to AS B (b3), where the Attr value is the number of hops of the optimal path from c3 to c2 (c3 -> c1 -> c2) plus the Attr value received by c2 (21 = 3 + 6 + 12). For AS B (b3), the received Attr is greater than the local, so the local RIB is not updated. Similarly, the Attr sent to AS C is 14 = 2 + 12, which is smaller than local value, then updates the corresponding route entry. AS B (b1) and AS C (c1) send update message to AS A (a1). Then, AS A updates the optimal path for reaching d0 in AS D based on the two messages received from AS B and AS C, in which Attr is 19 and 17, respectively. Take the example from a1 to d0, for a1, it will choose c1 as next hop because the corresponding path has a smaller Attr value.

Diffusion example: diffusion of DIT update messages and RIB updates triggered by a new route AS B(b2) -------- b2---- New Attr = Attr:maintain | |----------------------------------| |------/---------------------------| | Des|Next-hop AS-path|Attr|Des-AS| | Des|Next-hop AS-path|Attr|Des-AS| |--------------|-------|----|------| |--------------|-------|----|------| | d0 | d1 | 1 | 12 | D | | d0 | d1 | 1 | 12 | D | |----------------------------------| |----------------------------------| |----------------------------------| |------\---------------------------| | (1)B| AS D(d1) -> AS C(c2) -------- c2---- New Attr = Attr:maintain | |----------------------------------| |------/---------------------------| | Des|Next-hop AS-path|Attr|Des-AS| | Des|Next-hop AS-path|Attr|Des-AS| |--------------|-------|----|------| |--------------|-------|----|------| | d0 | d1 | 1 | 12 | D | | d0 | d1 | 1 | 12 | D | |----------------------------------| |----------------------------------| |----------------------------------| |------\---------------------------| | (2)A| AS B(b3) -> AS C(c3) -------- c3---- New Attr > Attr:update | |----------------------------------| |------/---------------------------| | Des|Next-hop AS-path|Attr|Des-AS| | Des|Next-hop AS-path|Attr|Des-AS| |--------------|-------|----|------| |--------------|-------|----|------| | d0 | b2 | 3 | 14 | D | | d0 | c2->b3 | 2->3 22->17 D | |----------------------------------| |----------------------------------| |----------------------------------| |------\---------------------------| | (2)B| AS C(c3) -> AS B(b3) -------- b3----New Attr > Attr:maintain | |----------------------------------| |------/---------------------------| | Des|Next-hop AS-path|Attr|Des-AS| | Des|Next-hop AS-path|Attr|Des-AS| |--------------|-------|----|------| |--------------|-------|----|------| | d0 | c1 | 2 | 21 | D | | d0 | b2 | 2 | 14 | D | |----------------------------------| |----------------------------------| |----------------------------------| |----------------------------------| | (3)A| AS B(b1) -> AS A(a1) ---| | c1updated by intra-AS notification |----------------------------------| | |----------------------------------| | Des|Next-hop AS-path|Attr|Des-AS| | | Des|Next-hop AS-path|Attr|Des-AS| |--------------|-------|----|------| | |--------------|-------|----|------| | d0 | b2 | 3 | 19 | D | | | d0 | c2->c3 | 2->3 18->17 D | |----------------------------------| | |----------------------------------| |----------------------------------| | |------\---------------------------| | (3)B| AS C(c1) -> AS A(a1) |--|---- a1---- New Attr < Attr:update | |----------------------------------| |------/---------------------------| | Des|Next-hop AS-path|Attr|Des-AS| | Des|Next-hop AS-path|Attr|Des-AS| |--------------|-------|----|------| |--------------|-------|----|------| | d0 | c3 | 4 | 17 | D | | d0 | b1->c1 | 3->4 18->17 D | |------------------------------------ ------------------------------------ ]]>

Delta Trap While Random Number Confusion solves the destination direct connection issue, there is still a trap of information leakage. It can be drawed from a mathematical perspective. Suppose it is known that x1 + x2 = y1 and x1 + x2 + x3 = y2. Even if x1 and x2 are unknown, x3 can also be calculated by using the difference value(DRT) between y1 and y2, i.e., x3 = y2 - y1. As shown in the , the value of AS 3 can be obtained using the aforementioned difference value(DRT) method by A 4. To solve the problem, the document proposed Enhanced DIT.

Enhanced DIT Delta Trap (DRT) is triggered by one path which has one more hop (itself) than the other of same destination. From the perspective of connection topology, triangular structure is at risk of data leakage. Based on this, the document design a private number comparison algorithm leveraged by homomorphic encryption, which is capable of comparing paths in a triangle topology under guarantee of data security. The comparison result could guide the logical removal of non-shortest paths. It includes classic homomorphic encryption algorithm Paillier and a private number comparison algorithm. Paillier algorithm randomly selecting two large prime to generate key. Then it can process the corresponding value by encrypting and decrypting. Based on Paillier, the private number comparison which is used as an independent module of DIT to patch the leakage caused by Delta Trap(DRT). Private Number Comparison firstly detects the triangle structures from the network topology. Then it will compare paths, comparison and path selection would be accomplished by communicating with each other. As shown in , suppose A, B and C, each of which is responsible for local values, N_A, N_B, N_C , respectively. First, A sends encrypted N_A, En^A(N_A), to B and C. After receiving the message from A, B sends En^A(N_A) o En^A(N_B) to C, where o represents homomorphic addition calculation, which means En(x) o En(y) = En(x+y). After receiving the message from A and B, C sends En^A(N_A + N_B) o En^A(drt_C ) and En^A(N_A) o En^A(N_C + drt_C ) to A in the specifified order. After receiving the message from C, A decrypts and subtracts the two values, De^A (En^A(N_A + N_B + drt_C )) - De^A(En^A(N_A + N_C + drt_C )), and get the signed delta value DRT_C, which will be sent back to C. Finally, according to the value of DRT_C, C and A can determine the priority of the two paths, Path_(C->A) and Path_(C->B->A).

Comparison example: communication and computation process of homomorphic encryption-based private number comparison The specific process of diffusing is showed in . The received BGP message will trigger an UPDATE operation, after which A can then specify the downstream of subsequent transmission. For cases that the direct connection is the optimal path, as shown in the left figure, A directly diffuses the message and uses an identifier to notify the downstream C. For the cases that the direct connection, for example A to C, is not optimal. As shown in the right figure, then A will notify this update to the directly connected downstream node B instead of C, and then B will forward this update to C. Then for C, the path notified by B would be accepted as the optimal one.

Two types of diffusion constraint