Header Space Analysis Hauptseminar: Innovative Internettechnologien - PowerPoint PPT Presentation

Lehrstuhl Netzarchitekturen und Netzdienste Institut für Informatik Technische Universität München Formal Methods: Header Space Analysis Hauptseminar: Innovative Internettechnologien und Mobilkommunikation Benedikt Jaeger 23.5.2014

Content  Header in Messages  Composition of Messages  Different header  Header Space Analysis  Headerspace, Networkspace  Transfer functions  Reachability  Example IITM: Formal Methods: Header Space Analysis 2

Composition of Messages Header Payload  Header : information about the packet  Payload : actual Data IITM: Formal Methods: Header Space Analysis 3

Header  IPv4-Header Version IHL TOS Total Length Identification Flags Fragment Offset TTL Protocol Header Checksum Source Address Destination Address Options / Padding (optional)  IPv6-Header  MAC-Header  ARP Request / Reply  ICMP Echo Request / Reply, TTL Exceeded  TCP- / UDP-Header (Headercontent is from the script of „ Grundlagen: Rechnernetze und Verteilte Systeme “ in the SS 2013, TUM ) IITM: Formal Methods: Header Space Analysis 4

Header  IPv4-Header  IPv6-Header Version Traffic Class Flow Label Payload Length Next Header Hop Limit Source Address  MAC-Header Destination Address  ARP Request / Reply  ICMP Echo Request / Reply, TTL Exceeded  TCP- / UDP-Header (Headercontent is from the script of „ Grundlagen: Rechnernetze und Verteilte Systeme “ in the SS 2013, TUM) IITM: Formal Methods: Header Space Analysis 5

Header  IPv4-Header  IPv6-Header  MAC-Header Destination Hardware Address Destination Hardware Address Source Hardware Address Source Hardware Address Type  ARP Request / Reply  ICMP Echo Request / Reply, TTL Exceeded  TCP- / UDP-Header (Headercontent is from the script of „ Grundlagen: Rechnernetze und Verteilte Systeme “ in the SS 2013, TUM) IITM: Formal Methods: Header Space Analysis 6

Header  IPv4-Header  IPv6-Header  MAC-Header  ARP Request / Reply Hardware Type Protocol Type Hw Addr. Length P. Addr. Length Operation Sender Hardware Address Sender Hardware Address Sender Protocol Address Sender Protocol Address Target Hardware Address Target Hardware Address Target Protocol Address  ICMP Echo Request / Reply, TTL Exceeded  TCP- / UDP-Header (Headercontent is from the script of „ Grundlagen: Rechnernetze und Verteilte Systeme “ in the SS 2013, TUM) IITM: Formal Methods: Header Space Analysis 7

Header  IPv4-Header  IPv6-Header  MAC-Header  ARP Request / Reply  ICMP Echo Request / Reply, TTL Exceeded Type Code Checksum Identifier Sequence Number Data (optional)  TCP- / UDP-Header (Headercontent is from the script of „ Grundlagen: Rechnernetze und Verteilte Systeme “ in the SS 2013, TUM) IITM: Formal Methods: Header Space Analysis 8

Header  IPv4-Header  IPv6-Header  MAC-Header  ARP Request / Reply  ICMP Echo Request / Reply, TTL Exceeded  TCP- / UDP-Header Source Port Destination Port Sequence Number Acknowledgement Number Offset Reserved Window Checksum Urgent Pointer Options Source Port Destination Port Length Checksum (Headercontent is from the script of „ Grundlagen: Rechnernetze und Verteilte Systeme “ in the SS 2013, TUM) IITM: Formal Methods: Header Space Analysis 9

Header Space Analysis Represent reality in a model Reality Model Router, switch, NAT, firewall, … Middlebox (or simply switch) Packet Headerbits Position in Network Unique Ports IITM: Formal Methods: Header Space Analysis 10

Header Space Analysis 𝐼 ⊆ 0,1 𝑀  Headerspace  Point in Headerspace ℎ 00110010101010100101001010010010 𝑂 ⊆ 0,1 𝑀 × 0, … , 𝑄  Networkspace  Point in Networkspace (ℎ, 𝑞) 12 00110010101010100101001010010010 IITM: Formal Methods: Header Space Analysis 11

Header Space Analysis  Box Transfer Function 𝑈 ℎ, 𝑞 : ℎ, 𝑞 → ℎ 1 , 𝑞 1 , ℎ 2 , 𝑞 2 , … 𝐂𝐩𝐲 𝑼𝒔𝒃𝒐𝒕𝒈𝒇𝒔 𝑮𝒗𝒐𝒅𝒖𝒋𝒑𝒐 𝑼 𝑺 𝒊 𝒒 𝑼(𝒊, 𝒒) 𝑆 1 { ℎ, 𝑆 2 } 1001xxxx 𝑆 2 { ℎ, 𝑆 1 } 1011xxxx 𝑆 1 { ℎ, 𝑆 2 , ℎ, 𝑆 3 } 1111xxxx … … … IITM: Formal Methods: Header Space Analysis 12

Header Space Analysis  Box Transfer Function 𝑈 ℎ, 𝑞 : ℎ, 𝑞 → ℎ 1 , 𝑞 1 , ℎ 2 , 𝑞 2 , …  Transform Subspace 𝑇 to another Subspace 𝑇 ∗ 𝑼 𝟑 𝑼 𝟐 IITM: Formal Methods: Header Space Analysis 13

Header Space Analysis  Box Transfer Function 𝑈 ℎ, 𝑞 : ℎ, 𝑞 → ℎ 1 , 𝑞 1 , ℎ 2 , 𝑞 2 , …  Reversible: 𝑈 −1 −𝟐 𝑼 𝟑 −𝟐 𝑼 𝟐 IITM: Formal Methods: Header Space Analysis 14

Example: IPv4-Router  What must an IPv4-Router do?  Rewrite source and destination Mac: 𝑈 𝑛𝑏𝑑 ( ) 𝑈 𝑢𝑢𝑚 ( )  Decrement TTL: 𝑈 𝑑ℎ𝑙𝑡𝑣𝑛 ( )  Update checksum: 𝑈 𝑔𝑥𝑒  Forward packet : 𝑈 𝐽𝑄𝑤4 . = 𝑈 𝑔𝑥𝑒 𝑈 𝑑ℎ𝑙𝑡𝑣𝑛 𝑈 𝑢𝑢𝑚 𝑈 𝑛𝑏𝑑 . IITM: Formal Methods: Header Space Analysis 15

Example: IPv4-Router  Rewrite source and destination Mac: 𝑈 𝑛𝑏𝑑 ( ) ignored 𝑈 𝑢𝑢𝑚 ( )  Decrement TTL: ignored 𝑈 𝑑ℎ𝑙𝑡𝑣𝑛 ( )  Update checksum: ignored 𝑈 𝑔𝑥𝑒  Forward packet: 𝑈 𝐽𝑄𝑤4 . = 𝑈 𝑔𝑥𝑒 . IITM: Formal Methods: Header Space Analysis 16

Example: IPv4-Router ℎ, 𝑞 1 𝑗𝑔 𝑗𝑞_𝑒𝑡𝑢(ℎ) ∈ 𝑇 1 ℎ, 𝑞 2 𝑗𝑔 𝑗𝑞_𝑒𝑡𝑢(ℎ) ∈ 𝑇 2 𝑈 𝐽𝑄𝑤4 ℎ, 𝑞 = ℎ, 𝑞 3 𝑗𝑔 𝑗𝑞_𝑒𝑡𝑢(ℎ) ∈ 𝑇 3 𝑝𝑢ℎ𝑓𝑠𝑥𝑗𝑡𝑓 𝑻 𝟑 𝒒 𝟑 𝒒 𝟒 𝑻 𝟐 𝑻 𝟒 𝑺 𝑱𝑸𝒘𝟓 𝒒 𝟐 IITM: Formal Methods: Header Space Analysis 17

Header Space Analysis  Box Transfer Function 𝑈 ℎ, 𝑞 : ℎ, 𝑞 → ℎ 1 , 𝑞 1 , ℎ 2 , 𝑞 2 , …  Network Transfer Function Ψ( ) 𝑈 1 ℎ, 𝑞 𝑗𝑔 𝑞 ∈ 𝑡𝑥𝑗𝑢𝑑ℎ 1 Ψ ℎ, 𝑞 = … … 𝑈 𝑜 ℎ, 𝑞 𝑗𝑔 𝑞 ∈ 𝑡𝑥𝑗𝑢𝑑ℎ 𝑜  Topology Transfer Function Γ Γ ℎ, 𝑞 = (ℎ, 𝑞 ∗ ) 𝑗𝑔 𝑞 𝑑𝑝𝑜𝑜𝑓𝑑𝑢𝑓𝑒 𝑢𝑝 𝑞 ∗ {} 𝑗𝑔 𝑞 𝑗𝑡 𝑜𝑝𝑢 𝑑𝑝𝑜𝑜𝑓𝑑𝑢𝑓𝑒 IITM: Formal Methods: Header Space Analysis 18

Header Space Analysis  Multihop Packet Traversal Φ . = Ψ(Γ (.))  Position(s) of (h,p) after k steps: Φ 𝑙 (ℎ, 𝑞) = Ψ(Γ(… (Ψ Γ ℎ, 𝑞 … = ℎ 1 , 𝑞 1 , … IITM: Formal Methods: Header Space Analysis 19

Reachability  “Can Host A talk to Host B?“  Wildcard expression ∈ 0, 1, 𝑦 𝑀 E. g. 1001xxxx like 192.168.x.x  Send Wildcard header from A and check if it ever reaches B 𝒚𝒚𝒚𝒚𝒚𝒚𝒚𝒚 … 𝑩 𝑪 IITM: Formal Methods: Header Space Analysis 20

Reachability  Send Wildcard header from A and check if it ever reaches B 𝑏 → 𝑇 1 → … → 𝑇 𝑜−1 → 𝑇 𝑜 → 𝑐 𝑆 𝑏→𝑐 = {𝑈 𝑜 (Γ(𝑈 𝑜−1 … Γ 𝑈 1 ℎ, 𝑞 … } 𝑏→𝑐 𝑞𝑏𝑢ℎ𝑡 {𝟐𝟏𝟏𝟐𝟏𝒚𝟐𝟏, 𝟏𝟐𝟏𝟐𝟐𝒚𝟐𝟏} 𝒚𝒚𝒚𝒚𝒚𝒚𝒚𝒚 … 𝑩 𝑪 IITM: Formal Methods: Header Space Analysis 21

Reachability  Use 𝑈 −1 and Γ −1 = Γ to get the original header −1 (Γ 𝑈 −1 ℎ, 𝑐 … ) −1 (Γ(… (𝑈 ℎ 𝑏 = 𝑈 1 𝑜−1 𝑜 {𝟐𝟏𝟏𝟐𝟏𝒚𝟐𝟏, 𝟐𝟏𝟏𝟐𝟐𝒚𝟐𝟏} {𝟐𝟏𝟏𝟐𝟏𝒚𝟐𝟏, 𝟏𝟐𝟏𝟐𝟐𝒚𝟐𝟏} 𝒚𝒚𝒚𝒚𝒚𝒚𝒚𝒚 … 𝑩 𝑪 IITM: Formal Methods: Header Space Analysis 22

Complexity 𝑆 𝑏→𝑐 = {𝑈 𝑜 (Γ(𝑈 𝑜−1 … Γ 𝑈 1 ℎ, 𝑞 … } 𝑏→𝑐 𝑞𝑏𝑢ℎ𝑡  Worst Case:  Single box: 𝑃 𝑆 1 𝑆 2  𝑆 1 : Number of wildcard expressions  𝑆 2 : Number of rules of Transfer function  Overall network: 𝑃 𝑆 1 𝑆 2 … 𝑆 𝑜 = 𝑃 𝑆 𝑒  𝑒 ∶ Diameter of Network  𝑆 ∶ Maximum number of forwarding rules IITM: Formal Methods: Header Space Analysis 23

Complexity  But: Linear Fragmentation Assumption:  Not 𝑆 1 𝑆 2 only 𝑑𝑆 1 and 𝑑 ≪ 𝑆 2 𝑒 ∗ 𝑃 𝑆 2 = 𝑃(𝑒𝑆 2 )  𝑒 ∶ Diameter of Network  𝑆 ∶ Maximum number of forwarding rules IITM: Formal Methods: Header Space Analysis 24

Reachability Example  Which header can reach 𝑐 from 𝑏 ? 𝑪 𝒃 𝑩 𝑬 𝒄 𝑫 IITM: Formal Methods: Header Space Analysis 25

Reachability Example  2 different paths 𝑪 𝟏 𝑪 𝟐 𝑪 𝑬 𝟏 𝑩 𝟐 𝑬 𝟐 𝒃 𝑩 𝑬 𝒄 𝑩 𝟏 𝑩 𝟑 𝑬 𝟑 𝑫 𝑫 𝟏 𝑫 𝟐 IITM: Formal Methods: Header Space Analysis 26

Reachability Example 𝒊, 𝑩 𝟏 𝒋𝒈 𝒊 = 𝟐𝟏𝟏𝟐𝒚𝒚𝒚𝒚 𝒊, 𝑩 𝟐 𝒋𝒈 𝒊 = 𝟐𝟏𝟐𝟏𝒚𝒚𝒚𝒚 𝑼 𝑩 𝒊, 𝒒 = 𝒊, 𝑩 𝟑 𝒋𝒈 𝒊 = 𝟐𝟐𝟏𝟏𝒚𝒚𝒚𝒚 𝒚𝒚𝒚𝒚 𝒚𝒚𝒚𝒚 𝟐𝟏𝟐𝟏 𝒚𝒚𝒚𝒚 𝑪 𝟏 𝑪 𝟐 𝑪 𝑩 𝟐 𝑬 𝟏 𝑬 𝟐 𝒃 𝑩 𝑬 𝒄 𝑩 𝟏 IITM: Formal Methods: Header Space Analysis 27 𝑫 𝟏 𝑫 𝟐