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What are the reasons why somebody would choose a symmetric system over an asymmetric system considering its disadvantage such as a key management and a key transmission?

Some people say a symmetric one is faster than an asymmetric one, but is this that significant?

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    $\begingroup$ "...a symmetric system over an asymmetric system considering its disadvantage such as a key management..." Both symmetric and asymmetric algorithms have keys that need management. $\endgroup$ – Future Security May 18 '18 at 1:42
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Speed

Some people say a symmetric one is faster than an asymmetric one, but is this that significant?

Yes. It is significant enough that most asymmetric systems are actually hybrid—they present an asymmetric external interface, but internally try to maximize their use of symmetric components.

Quantum resistance

The asymmetric primitives in common use (RSA, discrete logarithms, elliptic curves) are all potentially vulnerable to attacks if somebody manages to build a practical quantum computer. The symmetric primitives in common use are much more resilient to such attacks—it would possibly require going from 128-bit keys to a larger size, but that's it.

(See: post-quantum cryptography, for information on efforts to develop asymmetric primitives that will resist quantum computer attacks.)

Lack of need

Many applications just don't need asymmetric cryptography in the first place. Take, for example, storage encryption (as used, e.g., in modern smartphones) where the "sender" and "recipient" are in fact the same person but at different points in time. There is little or no need for asymmetric cryptography there, because any secret key, by definition, is held by both the sender and recipient.

Another example: encrypting a simple WiFi network (e.g., a home network) with a pre-shared key, where the key distribution problem is manageable. Entering a WiFi secret key manually into a handful of devices isn't a big logistical challenge.

Cost

Symmetric cryptography is much less hardware-demanding, which translates to more affordable costs. For example, two-factor authentication devices like RSA SecurID often use symmetric crypto simply because it's more affordable.

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  • $\begingroup$ Missing is that asymmetric encryption (RSA, EC) limits the data size to less than the key size and thus is unsuitable for encryption of data other than keys and very short data. $\endgroup$ – zaph May 18 '18 at 9:20

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