Reverse lookup
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Generally speaking, a reverse lookup is the reverse of what is a typical query for a given context.
Reverse phone lookup
For instance, when someone says they need to look up a phone number, they usually mean that they know a person or business' name and want to find out what their phone number is. A reverse lookup, in this context, would then be to attempt to determine a name from a phone number that is already known. This has become a more common practice recently, as Google and some other search engines will now automatically reverse lookup many North American phone numbers if they are entered as search queries.
Reverse DNS lookup
In the context of the Internet Protocol and the Domain Name System, a reverse lookup is often referred to simply as reverse resolving, or more specifically reverse DNS lookups. Typically, DNS is used to determine what IP address is associated with a given hostname; so to reverse resolve a known IP address is to lookup what the associated hostname for it is.
Reverse DNS lookups for IPv4 addresses use the special domain in-addr.arpa. An IPv4 address is represented in the in-addr.arpa domain by a sequence of bytes in reverse order, represented as decimal numbers, separated by dots with the suffix .in-addr.arpa. For example, the reverse lookup domain name corresponding to the IPv4 address 1.2.3.4 is 4.3.2.1.in-addr.arpa. A host name for 1.2.3.4 can be obtained by issuing a DNS query for the PTR record for that special address 4.3.2.1.in-addr.arpa.
Reverse DNS lookups for IPv6 addresses use similarly the special domain ip6.arpa. An IPv6 address is represented as a name in the ip6.arpa domain by a sequence of nibbles in reverse order, represented as hexadecimal digits, separated by dots with the suffix .ip6.arpa. For example, the reverse lookup domain name corresponding to the IPv6 address 4321:0:1:2:3:4:567:89ab is b.a.9.8.7.6.5.0.4.0.0.0.3.0.0.0.2.0.0.0.1.0.0.0.0.0.0.0.1.2.3.4.ip6.arpa.