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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:
As an Iranian Cryptology student in one of the most well-known Iranian Universities called Sharif University of Technology, I want to add this to the answers.
There doesn't seem to be any National Standard Cipher here in Iran. But It doesn't mean that there shouldn't be any classified cipher being used by the military or the revolutionary guards. As I am familiar with universities affiliated to Iranian military, there might not be the enough confidence for developing a reliable national cipher here.
I should mention that modern cryptology is relatively a new science in Iran and there are few researchers and scholars working on these topics here. Ciphers like AES, RSA and SHA-256 are quietly common among the scholars and are being used in industry now.
In recent couple of years the government and the military forces budgeted more for researches on information security related topics. One of the most famous conferences on information security and cryptography in Iran is named "ISCISC" the latest held was ISCISC13 the proceedings of english papers on this conference would be indexed on IEEE journal.
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:
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).
The answer is yes, non-US ciphers exist and are in fact very popular. Actually, some who are looking for alternatives, opt for non-NSA/NIST ciphers, for instance Salsa/ChaCha from DJB (who is US citizen). A lot of ciphers have been developed in EU and Japan. China definitely has developed ciphers for its own use, just like many other countries.
But long detailed response:
USA represent large amount the world market for high tech products and know-how, as well as representing significant chunk of high-tech jobs. In addition US has quite few of the best technical universities (all of the top 5). Already from this it would be easy to expect that a lot of research on all areas of high-tech to take place in USA. Including, of course cryptography.
People from USA have produced many of the most popular cryptographic algorithms. One good example is SHA-1/2 families, designed by NSA. Those are the widest used hash algorithms today.
It is expected that where USA has lead is the cryptographic know-how and analysis skills outside public information (i.e. what NSA knows but others don't). USA has many classified ciphers and other cryptographic algorithms in use which are not known outside the USA, for some see NSA Suite A Cryptography. The algorithms include at least: MEDLEY, SHILLELAGH, BATON, SAVILLE, WALBURN, JOSEKI-1 (according to that Wikipedia article). Non-suite A algorithms include e.g. SKIPJACK, FASTHASH, JUNIPER.
However, to be the latest NIST approved hash family, SHA-3 (Keccak) as well as AES cipher have been mostly done by european cryptographers. Most of their inventors are Belgian, with Italy involved in Keccak. It was USA (NIST) that held the competition. Thus, I would say that actually much of work inventing ciphers in academic world has moved elsewhere already. In fact, in many cases things are international co-operation, with people from US and abroad.
Where USA has been strong lately in cryptography is at least validating correctness of the implementation. All around the world, FIPS 140-2 validation is recognized as one of the most important validations cryptographic module may get, and fairly many governments used to see it as and endorsement.
The recent NSA spying speculations hit credibility of USA and NIST pretty badly.
This has caused people to start looking elsewhere and to distrust things invented in USA, especially ones invented by NSA, for instance, some of the currently deployed ECC curves. The alternatives include algorithms from US, but from parties not afflicted with NSA and NIST, like Dan J. Bernstein.
For algorithms invented elsewhere that US and not endorsed by NIST, you may want to look at ECRYPT. There you may find for instance, Camellia (Japan), Rabbit (Denmark).
Cryptographic algorithms in Iran and China? First it is important to acknowledge that cryptography is restricted in both of these countries. This means that for outsider, it is not easy to know very much. The research and know-how is more concentrated on government than e.g. on EU.
SMS4 cipher has been used in WAPI (Chinese Standard for Wireless LANs).
For information on Iran, see the answer by Habib, which covers that area very well.
Yes.
The Serpent Cipher was developed outside of America, and isn't maintained by an American group. It came in 2nd place during the AES competition. It has a higher safety factor than AES (Rijndael), but isn't as fast.
And there are stream ciphers being developed and validated by eSTREAM in Belgium. The Salsa20 stream cipher, by American cryptographer Daniel J. Bernstein, has been gaining a lot of traction.
