Do any non-US ciphers exist? Plenty of ciphers come out of the USA from government research or selection competitions. AES and DES are examples.

Are there any public ciphers produced by other states, China or Iran for example? Do you really think they trust AES?

EDIT: List of ciphers from different nations:


USA: Skipjack
Japan: Camellia
Russia: GHOST
Korea: SEED
China: SMS4
Plenty of ciphers come out of the USA from government research or selection competitions. AES and DES are examples.


Indeed, the US is known from some crypto-related competitions that were/are open to anyone and they surely will do ample of government research related to cryptology, but you need to be sure that you differ between “they selected it” and “they created it”. There is a big difference! 
For example: what we now call AES was selected through an open competition by the USA, but the cipher design that became AES was not created by the USA.


  Are there any public ciphers produced by other states, China or Iran for example? Do you really think they trust AES?


Of course there are other countries and states that are known to be the origin of different ciphers, but listing them all would be a bit too broad. Instead, I’ll give you a quick heads-up:



Also, on page 3 of "The Design of Rijndael: AES – The Advanced Encryption Standard." by Joan Daemen and Vincent Rijmen (the creators of Rijndael – also known as AES), you can find a neat table that shows a list of the 15 AES candidates that were accepted for the first evaluation round, including their country of origin. 

For your convenience, here are those 15 candidates:


CAST-256
submitted by Entrust (company), from Canada
Crypton
submitted by Future Systems (company), from Republic of Korea
DEAL
submitted by Outerbridge, Knudsen (researchers), from USA &amp; Denmark
DFC
submitted by ENS-CNRS (researchers), from France
E2
submitted by NTT (company), from Japan
Frog
submitted by TecApro (company), from Costa Rica
HPC
submitted by Schroeppel (researcher), from USA
LOKI97
submitted by Brown et al. (researchers), from Australia
Magenta
submitted by Deutsche Telekom (company), from Germany
Mars
submitted by IBM (company), from USA
RC6
submitted by RSA (company), from USA
Rijndael
submitted by Daemen and Rijmen (researchers), from Belgium
SAFER+
submitted by Cylink (company), from USA
Serpent
submitted by Anderson, Biham, Knudsen (researchers), from United Kingdom &amp; Israel &amp; Denmark
TwoFish
submitted by Counterpane (company), from USA


From the 15 candidates that made it into the first evaluation round of the AES competition, only 5,5 originated in the USA. That’s a mere $36 \frac{2}{3}\%$ percent of US ciphers in their own cipher competition. 

Wrapping it up: 


AES is far from being a US government baby. Instead, cipher that won the AES competition (Rijndael) was born in the land of friendly people, “french” fries and tasty beer: Belgium!

Now, being a half-Belgian I may be a bit biased… but I honestly have a hard time trying to imagine why anyone would suspect a Belgian cipher design, just because it also happens to be used by the US government. Instead, that merely indicates that the cipher design is that good, that even the USA uses it to protect its valuable information and big parts of their national security.
A lot of ciphers were (and are) created outside of the USA. Yet, not all ciphers that are created are published; and if they are, they rarely gain attention due to missing publicity and/or popularity. That is one of many reasons why those competitions are interesting for cipher designers.

As said, listing all ciphers from all countries would be too broad, but the above list of “AES round 1 candidates” already shows Australia, Belgium, Canada, Costa Rica, Denmark, France, Germany, Israel, Japan, Republic of Korea, United Kingdom, and the USA. 

That should be ample to understand ciphers are not a US-only thing and that the US is not as dominant in crypto as you think. In the end, even AES is non-US. They adopted a Belgian cipher to their standards, but they didn’t create it. If you really want to suspect someone for having whatever kind of dominance in the field of symmetric crypto, I can’t stop you. But if you take a good look at the origins of individual ciphers, you’ll notice they come from all over the world… and currently, your main suspect would be Belgium  due to AES (aka Rijndael) and SHA-3 (aka Keccak).