How can I generate a random bytea

Enhancing Jack Douglas's answer to avoid the need for PL/PgSQL looping and bytea concatenation, you can use:

CREATE OR REPLACE FUNCTION random_bytea(bytea_length integer)
RETURNS bytea AS $body$
    SELECT decode(string_agg(lpad(to_hex(width_bucket(random(), 0, 1, 256)-1),2,'0') ,''), 'hex')
    FROM generate_series(1, $1);
$body$
LANGUAGE 'sql'
VOLATILE
SET search_path = 'pg_catalog';

It's a simple SQL function that's cheaper to call than PL/PgSQL.

The difference in performance due to the changed aggregation method is immense for larger bytea values. Though the original function is actually up to 3x faster for sizes < 50 bytes, this one scales much better for larger values.

Or use a C extension function:

I've implemented a random bytea generator as a simple C extension function. It's in my scrapcode repository on GitHub. See the README there.

It nukes the performance of the above SQL version:

regress=# \a
regress=# \o /dev/null
regress=# \timing on
regress=# select random_bytea(2000000);
Time: 895.972 ms
regress=# drop function random_bytea(integer);
regress=# create extension random_bytea;
regress=# select random_bytea(2000000);
Time: 24.126 ms

I would like to be able to generate random bytea fields of arbitrary length

This function will do it, but 1Gb will take a long time because it does not scale linearly with output length:

create function random_bytea(p_length in integer) returns bytea language plpgsql as $$
declare
  o bytea := '';
begin 
  for i in 1..p_length loop
    o := o||decode(lpad(to_hex(width_bucket(random(), 0, 1, 256)-1),2,'0'), 'hex');
  end loop;
  return o;
end;$$;

output test:

select random_bytea(2);

/*
|random_bytea|
|:-----------|
|\xcf99      |
*/

select random_bytea(10);

/*
|random_bytea          |
|:---------------------|
|\x781b462c3158db229b3c|
*/

select length(random_bytea(100000))
     , clock_timestamp()-statement_timestamp() time_taken;

/*
|length|time_taken     |
|-----:|:--------------|
|100000|00:00:00.654008|
*/

_{dbfiddle here}

The pgcrypto extension has gen_random_bytes(count integer):

test=# create extension pgcrypto;
test=# select gen_random_bytes(16);
          gen_random_bytes
------------------------------------
 \xaeb98ae41489460c5292aafade4498ee
(1 row)

The create extension only needs to be done once.