# Ephemeral Port Prediction

Published on 5 Apr 2020

When a TCP/IP client connects to a new remote host and port, it must select a local port to use for the connection. Usually, any free port will do, so most applications leave local port selection to the kernel. The kernel selects a port at random from the ephemeral port range. Except the selection isn’t really random. As it turns out, the selected port can be predicted in advance, revealing kernel state information.

## Simple client

First, let’s write a simple client to gather some real data. This client will create a UDP socket and connect it to a remote. As this is a UDP socket, no packets will be sent, but a local port will be selected for the connection.

// client.c: Simple socket client. Creates socket and prints local source port.

#include <stdio.h>      // printf
#include <stdlib.h>     // atoi
#include <unistd.h>     // close
#include <arpa/inet.h>  // ntohs
#include <sys/socket.h> // connect, socket

void sample() {
// Create socket
int sockfd;
if (sockfd = socket(PF_INET, SOCK_DGRAM, IPPROTO_UDP), -1 == sockfd) {
perror("socket");
}

// Connect to remote. This does NOT actually send a packet.
.sin_family = AF_INET,
.sin_port   = 0xbeef,     // arbitrary remote port
.sin_addr   = 0xbeefbeef  // arbitrary remote host
};
if (-1 == connect(sockfd, (const struct sockaddr *)&raddr, sizeof(raddr))) {
perror("connect");
}

// Display selected ephemeral port
perror("getsockname");
}
printf("local port: %i\n", ntohs(laddr.sin_port));

// Close socket
close(sockfd);
}

int main() {
for (int i = 0; i < 16; i++) {
sample();
}

return 0;
}

This program opens a socket 16 times back to back. We see that a unique, random looking source port is selected each time:

$gcc -std=c99 -o client client.c && ./client local port: 41039 local port: 46915 local port: 41778 local port: 39273 local port: 38680 local port: 37939 local port: 37757 local port: 45454 local port: 58115 local port: 42947 local port: 47022 local port: 45395 local port: 55042 local port: 52648 local port: 59649 local port: 58293  Each port is selected from the ephemeral port range (default is 32768 to 60999, inclusive), which on Linux can be obtained via: $ cat /proc/sys/net/ipv4/ip_local_port_range
32768	60999


And indeed, each port above is within this range. Now, let’s go deeper into understanding how these source ports were selected.

## Port Selection Algorithm

The precise mechanism through which ephemeral ports are selected isn’t standardized – every implementation, in theory, may do something different. On Linux, this happens within net/ipv4/udp.c in udp_lib_get_port(). This code is very mature now and hasn’t changed much in nearly 25 years.

The highlighted lines below select the ephemeral port (unless the port is already in use, but this is rare on all but the most loaded machines, so to keep things simple let’s ignore it for now).

/**
*  udp_lib_get_port  -  UDP/-Lite port lookup for IPv4 and IPv6
*
*  @sk:          socket struct in question
*  @snum:        port number to look up
*  @hash2_nulladdr: AF-dependent hash value in secondary hash chains,
*                   with NULL address
*/
int udp_lib_get_port(struct sock *sk, unsigned short snum,
{
struct udp_hslot *hslot, *hslot2;
struct udp_table *udptable = sk->sk_prot->h.udp_table;
int    error = 1;
struct net *net = sock_net(sk);

if (!snum) {
int low, high, remaining;
unsigned int rand;
unsigned short first, last;
DECLARE_BITMAP(bitmap, PORTS_PER_CHAIN);

inet_get_local_port_range(net, &low, &high);
remaining = (high - low) + 1;

rand = prandom_u32();
first = reciprocal_scale(rand, remaining) + low;


The first checked ephemeral port is first. If it is available, as is usually the case, it will be used. reciprocal_scale(x, y) takes a 32-bit unsigned integer x and linearly scales it to fit the interval [0, y). Thus, first is the 32-bit unsigned integer returned by prandom_u32(), linearly scaled to the interval [low, high].

As for the random number, it is produced by a “maximally equidistributed combined Tausworthe generator”, a combination of four simpler Tausworthe generators, more commonly known as linear feedback shift registers. The generator is implemented in lib/random32.c — here are the two most relevant functions:

/**
*	prandom_u32_state - seeded pseudo-random number generator.
*	@state: pointer to state structure holding seeded state.
*
*	This is used for pseudo-randomness with no outside seeding.
*	For more random results, use prandom_u32().
*/
u32 prandom_u32_state(struct rnd_state *state)
{
#define TAUSWORTHE(s, a, b, c, d) ((s & c) << d) ^ (((s << a) ^ s) >> b)
state->s1 = TAUSWORTHE(state->s1,  6U, 13U, 4294967294U, 18U);
state->s2 = TAUSWORTHE(state->s2,  2U, 27U, 4294967288U,  2U);
state->s3 = TAUSWORTHE(state->s3, 13U, 21U, 4294967280U,  7U);
state->s4 = TAUSWORTHE(state->s4,  3U, 12U, 4294967168U, 13U);

return (state->s1 ^ state->s2 ^ state->s3 ^ state->s4);
}
EXPORT_SYMBOL(prandom_u32_state);

/**
*	prandom_u32 - pseudo random number generator
*
*	A 32 bit pseudo-random number is generated using a fast
*	algorithm suitable for simulation. This algorithm is NOT
*	considered safe for cryptographic use.
*/
u32 prandom_u32(void)
{
struct rnd_state *state = &get_cpu_var(net_rand_state);
u32 res;

res = prandom_u32_state(state);
put_cpu_var(net_rand_state);

return res;
}
EXPORT_SYMBOL(prandom_u32);


The generator uses four 32-bit state variables (i.e. 128-bit seed) and has a period of $$2^{113}$$. Because the generator is maximally equidistributed, each 32-bit sample occurs as often as any other within the sequence, approximately $$2^{113} \cdot 2^{-32} = 2^{81}$$ times. Similarly, each sequence of two samples occurs approximately $$2^{113} \cdot \left( 2^{-32} \cdot 2^{-32} \right) = 2^{49}$$ times. More generally, each sequence of $$n$$ samples occurs approximately $$2^{113 - 32n}$$ times. Thus, with a sequence of only four samples, we should be able to uniquely determine the four state variables (i.e. the seed).

Because this is a linear generator, it can be precisely described by a generator matrix, $$\mathbf{G}$$, where the generator matrix can be multiplied by the current seed, $$\vec{x}$$, to yield one or more samples of output, depending on the number of rows in the generator matrix: $$\mathbf{G} \cdot \vec{x} = \vec{y}$$ If we can compute $$\mathbf{G}$$ and observe $$\vec{y}$$, we can then solve for $$\vec{x}$$ using Gaussian elimination. Once we know $$\vec{x},$$ we know where we are in the sequence — we can predict all future port choices.

### From Port Values To State Variables

Unfortunately, we cannot actually observe the state variables, at least not without modifying the kernel — we can only observe the selected port.

However, we know that the 32-bit output from prandom_u32() maps to the ephemeral port range via reciprical_scale():

// @file include/linux/kernel.h

/**
* reciprocal_scale - "scale" a value into range [0, ep_ro)
* @val: value
* @ep_ro: right open interval endpoint
*
* Perform a "reciprocal multiplication" in order to "scale" a value into
* range [0, @ep_ro), where the upper interval endpoint is right-open.
* This is useful, e.g. for accessing a index of an array containing
* @ep_ro elements, for example. Think of it as sort of modulus, only that
* the result isn't that of modulo. ;) Note that if initial input is a
* small value, then result will return 0.
*
* Return: a result based on @val in interval [0, @ep_ro).
*/
static inline u32 reciprocal_scale(u32 val, u32 ep_ro)
{
return (u32)(((u64) val * ep_ro) >> 32);
}


Say the ephemeral port range is the default — 32768 to 60999, inclusive. In this case, a prandom_u32 output of 0x00000000 would map to port 32768. 0x00025243 would also map to port 32768. But 0x00025244 would map to port 32769. This tells us something. If the observed source port is 32768, the upper 14 bits of the corresponding number output by prandom_u32 must be 0, as all 32-bit values that map to 32768 share the same 14 most significant bits — all zero.

It’s important to note that not all port values provide equal information. For instance, prandom_u32 values between 0x00025244 and 0x0004a486, inclusive, all map to port 32769, but here only the 13 most significant bits are shared – the 14th most significant bit could be a 0 or a 1.

In the worst case, 0x7FFFFFFF and 0x80000000 would both map to the same port, meaning observing that port value would not provide any meaningful information.

As long as we can gather 128-bits of information about sequential values from prandom_u32, we can infer its seed. Assuming the default port range, port values provide 12.843 bits of information, on average. Thus, with 10 observations, we expect to be able to infer the seed.

### Core Affinity

One more snag is that prandom_u32() uses get_cpu_var() and put_cpu_var() to get and set state variables, respectively. As the function names imply, each CPU maintains its own independent state — there’s no guarantee that two sequential samples are from the same CPU. However, in practice, processor affinity means the same CPU is used for multiple back-to-back calls to prandom_u32(). For instance, on a six core (12 due to hyper-threading) Intel i7-5820K, often hundreds of milliseconds, and occasionally multiple seconds, may elapse between core changes:

Furthermore, CPU changes do not appear to be random either. On the same Intel i7-5820K, the CPU used by the sampling process monotonically increases modulo the number of cores.

So in practice, if the generator is rapidly sampled in succession, there is a good possibility all samples will be from the same core.

Scheduling and CPU affinity are architecture specific. On a quad-core armv7, the sampling process was assigned to a core and never switched cores. It would be interesting to explore how CPU affinity differs in practice between architectures.

## Demo

Using the first ten sequential ports sampled earlier by our client, we can now compute the random number generator’s state.

# Ephemeral Port Prediction Tool

Enter ephemeral port range:

Enter 10 sequential ephemeral port samples

Linux kernel prandom_u32() seed (i.e. four 32-bit state variables in code above:

## Conclusions and Future Work

With less than a dozen TCP/IP connections, it is possible to determine the secret state of the random number generator of a remote client’s kernel.

This technique could, in theory, be used to establish peer-to-peer connectivity between peers behind symmetric NATs (for NATs which use this mechanism for port selection), thus saving on bandwidth cost.

It also raises potential security implications. In one scenario, while visiting a malicious website, a client could unwittingly execute JavaScript code that created 10 unique connections to a server. These connections could enable the server owner to learn the secret state of the random number generator of the client’s kernel. This generator serves as a common source of randomness for numerous languages (e.g. Python). This is an area that could use further exploration.

Finally, this work only considered the vanilla Linux kernel. It would be worthwhile to analyze how ephemeral ports are selected in other operating systems.