There is no one single algorithm which is the best, cryptography provides many functions with many different assumptions about trust, key availability and safety, data requirement (confidentiality vs. authenticity), and so on.

In particular, some functions are:

-Public key cryptography for digital signing

-Public key cryptography for encryption (typically of keys used in symmetric algorithms).

-Key exchange (for users to exchange keys based on public key availability)

-Symmetric key cryptography (for two people sharing a key to encrypt data)

-Authentication of data

-Authenticated encryption (combining the last two) 

In each category there are best practices, standards, NIST recommendations, and software availability issues. So, choosing the "algorithm" does not have a meaning in absence of goals and systems requirements.

I agree with Moti, that your requirements will determine what the "best" security protocol might be.

In general, I think you can say that asymmetric key algorithms are the right solution if you cannot easily and securely deliver secret keys to the other party or parties. But they are computationally more complex, so ultimately not as fast.

With asymmetric key algorithms, the person wanting to receive encrypted and/or authenticated messages sends his public key(s) to the sender, or senders, in the open. The sender uses this person's public key to encrypt and/or authenticate his messages. One public key to authenticate, another to encrypt. The trick here is, only the recipient's private key can decipher the messages, and that private key is only ever stored in this recipient's own computer. That private key never goes beyond the owner's computer.

This link gives you a quick look at some of these asymmetric key algorithms:

http://www.encryptionanddecryption.com/algorithms/asymmetric_algorithms.html

Symmetric key algorithms require secret keys to be passed securely, because the same key is used to encrypt and to decrypt the message. These are the oldest of security algorithms, which were originally developed in ancient times. But they are also the most computationally efficient, so they are the fastest. One practical option is to use asymmetric key to distribute secret keys, then use symmetric for the "heavy lifting," so to speak.

Of the symmetric key algorithms, I think you'll find that AES is the one preferred by NIST, for the time being. Several others are actually no longer recommended, by NIST. And here is an equivalent quick look at symmetric algorithms:

http://www.encryptionanddecryption.com/algorithms/symmetric_algorithms.html

One category of symmetric key algorithm would be the symmetric key stream cipher, which is very efficient in terms of both speed and software footprint, but NIST doesn't seem to be too fond of these yet. I think that with an adequate pseudo-random number generator, one with long enough seed values, these should rival AES in "counter mode" without too much trouble.

This is a few years old now, but it is a really clear presentation on symmetric key stream ciphers.

http://csrc.nist.gov/groups/ST/CETA_2011/presentations/turan.pdf

Just to confuse you further, there are also other ways to protect big data:

Conference Paper Securing big data in the Cloud by protected mapping over mul...

I would also add the bio-dynamic algorithms that would  simulate the real life dynamics of possible cyber-attacks and respond with predictive capabilities to eliminate any future attacks.

Dear Hiba,

I have 6 years experience about information security systems. 

In my opinion, Information hiding techniques are more powerful than Cryptography algorithms. Based on my findings, Information security systems have two main branches, information hiding, and cryptography. In general, the cryptography scrambles plain-text into cypher-text which is reversible without data loss. The goal of cryptography is to prevent unauthorized access to information by scrambling them. On the other hand, information hiding is a powerful security technique which hides data and reduces computational cost. It conceals secret messages in cover media so that the secret messages are completely unnoticeable. The cryptography and information hiding are similar in a way that both are utilized to protect sensitive information.  However, imperceptibility Is the difference between them, i.e., information hiding concerns how to hide information unnoticeably. Generally, the information hiding can be further categorized into watermarking and steganography. 

In theory and in accordance with Shannon's theorem, OTP would offer perfect secrecy in the case of a genuine randomization source. The drawback of this simple cryptosystem is its practicability. In fact, there exists no panacea that fulfills the requirements of all use cases.

There is no one technique that can be used, and it all depends on what you are protecting and the constraints on the processing requirements (and regulations, of course).

Symmetric key encryption is almost always used for protecting data, and asymmeric encryption (RSA/Elliptic Curve/ElGamal) is used to protect the key or identify an entitiy.

For protecting the data, 128-bit/256-bit AES (symmetric block) and ChaCha (symmetric stream) are the two main methods used, and you should avoid moving away from these as they are the basis of many standards, and have been shown to be fast and secure. Google recommend ChaCha, just so that we can have an alterative to AES, if it is ever shown to be vulnerable in the future.

The industry is generally moving away from RSA as the key size is becoming rather long and it is CPU and memory intensive, so Elliptic Curve methods are often used for signing data (such as in Bitcoins, Tor and Signal) and for key negotiation.

Try to stick to well-defined standards, unless you need light-weight methods (such as for RFID tags) or quantum computing robust crypto.

Here's some links which explain the main methods:

http://asecuritysite.com/encryption/

http://asecuritysite.com/encryption/

AES with 256 bits is consider to be secure for some time. It is very well investigated algorithm. There is a new NIST competition (post quantum cryptography) and we will see which algorithm will be considered the best (https://csrc.nist.gov/projects/post-quantum-cryptography/round-1-submissions).