What is currently the most secure one-way encryption algorithm?

Warning: Since this post was written in 2010, GPUs have been widely deployed to brute-force password hashes. Moderately-priced GPUs can run ten billion MD5s per second. This means that even a completely-random 8-character alphanumeric password (62 possible characters) can be brute forced in 6 hours. SHA-1 is only slightly slower, it'd take one day. Your user's passwords are much weaker, and (even with salting) will fall at a rate of thousands of passwords per second. Hash functions are designed to be fast. You don't want this for passwords. Use scrypt, bcrypt, or PBKDF-2.

MD5 was found to be weak back in 1996, and should not be used anymore for cryptographic purposes. SHA-1 is a commonly used replacement, but has similar problems. The SHA-2 family of hash functions are the current replacement of SHA-1. The members of SHA-2 are individually referred to as SHA-224, SHA-256, SHA-384, and SHA-512.

At the moment, several hash functions are competing to become SHA-3, the next standardised cryptographic hashing algorithm. A winner will be chosen in 2012. None of these should be used yet!

For password hashing, you may also consider using something like bcrypt. It is designed to be slow enough to make large scale brute force attacks infeasible. You can tune the slowness yourself, so it can be made slower when computers are becoming faster.

Warning: bcrypt is based on an older two-way encryption algorithm, Blowfish, for which better alternatives exist today. I do not think that the cryptographic hashing properties of bcrypt are completely understood. Someone correct me if I'm wrong; I have never found a reliable source that discusses bcrypt's properties (other than its slowness) from a cryptographic perspective.

It may be somewhat reassuring that the risk of collisions matters less for password hashing than it does for public-key cryptography or digital signatures. Using MD5 today is a terrible idea for SSL, but not equally disastrous for password hashing. But if you have the choice, simply pick a stronger one.

Using a good hash function is not enough to secure your passwords. You should hash the passwords together with salts that are long and cryptographically random. You should also help your users pick stronger passwords or pass phrases if possible. Longer always is better.

Great question! This page is a good read. In particular, the author claims that MD5 is not appropriate for hashing passwords:

The problem is that MD5 is fast. So are its modern competitors, like SHA1 and SHA256. Speed is a design goal of a modern secure hash, because hashes are a building block of almost every cryptosystem, and usually get demand-executed on a per-packet or per-message basis. Speed is exactly what you don’t want in a password hash function.

The article then goes on to explain some alternatives, and recommends Bcrypt as the "correct choice" (his words, not mine).

Disclaimer: I have not tried Bcrypt at all. Consider this a friendly recommendation but not something I can back up with my own technical experience.

To increase password strength you should use a wider variety of symbols. If you have 8-10 characters in the password it becomes pretty hard to crack. Although making it longer will make it more secure, only if you use numeric/alphabetic/other characters.

SHA1 is another hashing (one way encryption) algorithm, it is slower, but is has a longer digest. (encoded messsage) (160 bit) where MD5 only has 128 bit.

Then SHA2 is even more secure, but it used less.

salting the password is always an extra level of defense

$salt = 'asfasdfasdf0a8sdflkjasdfapsdufp';
$hashed = md5( $userPassword . $salt );

Seeing that computers just keep getting faster and that mathematicians are still developing these algorithms

RSA encryption is secure in that it relies on a really big number being hard to factor. Eventually, computers will get fast enough to factor the number in a reasonable amount of time. To stay ahead of the curve, you use a bigger number.

However, for most web sites, the purpose of hashing passwords is to make it inconvenient for someone with access to the database to read the password, not to provide security. For that purpose, MD5 is fine1.

The implication here is that if a malicious user gains access to your entire database, they don't need the password. (The lock on the front door won't stop me from coming in the window.)

1 Just because MD5 is "broken" doesn't mean you can just reverse it whenever you want.

Besides being a cryptographically secure one-way function, a good hash function for password protection should be hard to brute force - i.e. slow by design. scrypt is one of the best in that area. From the homepage:

We estimate that on modern (2009) hardware, if 5 seconds are spent computing a derived key, the cost of a hardware brute-force attack against scrypt is roughly 4000 times greater than the cost of a similar attack against bcrypt (to find the same password), and 20000 times greater than a similar attack against PBKDF2.

That said, from commonly available hash functions, doing a few thousand of iterations of anything from the SHA family is pretty reasonable protection for non-critical passwords.

Also, always add a salt to make it impossible to share effort for brute forcing many hashes at a time.

NIST is currently running a contest to select a new hashing algorith, just as they did to select the AES encryption algorithm. So the answer to this question will likely be different in a couple of years.

You can look up the submissions and study them for yourself to see if there's one that you'd like to use.