# Public Key vs. Secret Key Encryption

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* Definition: The purpose of a key in encryption systems is to ensure privacy by keeping information hidden from whom it is not intended. There are two types of encryption systems: secret-key* and

*public-key systems.*

*Encryption* is the transformation of data, the *plaintext,* into a form that is as close to impossible as possible to read, the *ciphetext,* without the appropriate knowledge (a key). Its purpose is to ensure privacy by keeping information hidden from anyone for whom it is not intended, even those who have access to the encrypted data, the *ciphetext*.

There are two types of encryption systems: *secret-key* and *public-key* systems (see Figure 1). In secret-key encryption, also referred to as symmetric cryptography, the same key is used for both encryption and decryption. The most popular secret-key cryptosystem in use today is the *Data Encryption Standard (DES,* see). In general, the security of a secret-key system depends on the strength of the algorithm and the length of the key. In a brute-force attack, an *N* bits long key, which implies 2 *N* possible keys, will take 2 *N* attempts for the hacker to find the correct key. That is, the longer the key is, the longer it will take for a certain computer to find the correct key among the 2 *N* possible keys. Besides the key, there is another factor to determine the interval of a successful brute force attack: the speed of each test which relies on the speed of the computer and the computational complexity of the encryption algorithm. Unfortunately in most cases, the longer the key is, the longer it takes to encrypt/decrypt the message, and the more one need to pay for it in terms of cost. To determine the length of a proper key for a certain application, one needs to look at several aspects: the intended security, the current and future computer power, and the speed of the state-of-the-art factoring algorithms. That is, you need a key long enough to be secure but short enough to be computationally feasible and low cost.

On the other hand, in a public-key system, each user has a *public key* and a *private key.* The public key maybe made public while the private key remains secret. Encryption is performed with the one key while decryption is done with the other. Today’s dominant public key encryption algorithms are factorization based. That is, the algorithms are based on the difficulty of factoring large numbers that are the product of two large prime numbers. One of the most popular public-key encryption algorithms, the *RSA public-key cryptosystem,* is a typical factorization based algorithm. To break such systems, one need to factor out the large number. Intuitively, the large the number is, the harder it is for a hacker to factor it.

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