# asymmetric cryptography (public key cryptography)

Asymmetric cryptography, also known as public-key cryptography, is a process that uses a pair of related keys -- one public key and one private key -- to encrypt and decrypt a message and protect it from unauthorized access or use. A public key is a cryptographic key that can be used by any person to encrypt a message so that it can only be deciphered by the intended recipient with their private key. A private key -- also known as a secret key -- is shared only with key's initiator.

When someone wants to send an encrypted message, they can pull the intended recipient's public key from a public directory and use it to encrypt the message before sending it. The recipient of the message can then decrypt the message using their related private key. On the other hand, if the sender encrypts the message using their private key, then the message can be decrypted only using that sender's public key, thus authenticating the sender. These encryption and decryption processes happen automatically; users do not need to physically lock and unlock the message.

Many protocols rely on asymmetric cryptography, including the transport layer security (TLS) and secure sockets layer (SSL) protocols, which make HTTPS possible. The encryption process is also used in software programs -- such as browsers -- that need to establish a secure connection over an insecure network like the Internet or need to validate a digital signature.

Increased data security is the primary benefit of asymmetric cryptography. It is the most secure encryption process because users are never required to reveal or share their private keys, thus decreasing the chances of a cybercriminal discovering a user's private key during transmission.

### How asymmetric cryptography works

Asymmetric encryption uses a mathematically related pair of keys for encryption and decryption: a public key and a private key. If the public key is used for encryption, then the related private key is used for decryption; if the private key is used for encryption, then the related public key is used for decryption.

The two participants in the asymmetric encryption workflow are the sender and the receiver; each has its own pair of public and private keys. First, the sender obtains the receiver's public key. Next, the plaintext -- or ordinary, readable text -- is encrypted by the sender using the receiver's public key; this creates ciphertext. The ciphertext is then sent to the receiver, who decrypts the ciphertext with their private key and returns it to legible plaintext.

Because of the one-way nature of the encryption function, one sender is unable to read the messages of another sender, even though each has the public key of the receiver.

### Uses of asymmetric cryptography

Asymmetric cryptography is typically used to authenticate data using digital signatures. A digital signature is a mathematical technique used to validate the authenticity and integrity of a message, software or digital document. It is the digital equivalent of a handwritten signature or stamped seal.

Based on asymmetric cryptography, digital signatures can provide assurances of evidence to the origin, identity and status of an electronic document, transaction or message, as well as acknowledge informed consent by the signer.

Asymmetric cryptography can also be applied to systems in which many users may need to encrypt and decrypt messages, including:

- Encrypted email - a public key can be used to encrypt a message and a private key can be used to decrypt it.
- The SSL/TSL cryptographic protocols - establishing encrypted links between websites and browsers also makes use of asymmetric encryption.
- Bitcoin and other cryptocurrencies rely on asymmetric cryptography as users have public keys that everyone can see and private keys that are kept secret. Bitcoin uses a cryptographic algorithm to ensure that only the legitimate owners can spend the funds.

In the case of the Bitcoin ledger, each unspent transaction output (UTXO) is typically associated with a public key. So if user X, who has an UTXO associated with his public key, wants to send the money to user Y, user X uses his private key to sign a transaction that spends the UTXO and creates a new UTXO that's associated with user Y's public key.

### Benefits and disadvantages of asymmetric cryptography

The benefits of asymmetric cryptography include:

- the key distribution problem is eliminated because there's no need for exchanging keys.
- security is increased as the private keys don't ever have to be transmitted or revealed to anyone.
- the use of digital signatures is enabled so that a recipient can verify that a message comes from a particular sender.
- it allows for non-repudiation so the sender can't deny sending a message.

Disadvantages include:

- it's a slow process compared to symmetric cryptography, so it's not appropriate for decrypting bulk messages.
- if an individual loses his private key, he can't decrypt the messages he receives.
- since the public keys aren't authenticated, no one really knows if a public key belongs to the person specified. Consequently, users must verify that their public keys belong to them.
- if a hacker identifies a person's private key, the attacker can read all of that individual's messages.

### Asymmetric vs. symmetric cryptography

The main difference between these two methods of encryption is that asymmetric encryption algorithms makes use of two different but related keys -- one key to encrypt the data and another key to decrypt it -- while symmetric encryption uses the same key to perform both the encryption and decryption functions.

Another difference between asymmetric and symmetric encryption is the length of the keys. In symmetric cryptography, the length of the keys -- which is randomly selected -- are typically set at 128-bits or 256-bits, depending on the level of security that's needed.

However, in asymmetric encryption, there must be a mathematical relationship between the public and private keys. Since hackers can potentially exploit this pattern to crack the encryption, asymmetric keys need to be much longer to offer the same level of security. The difference in the length of the keys is so pronounced that a 2048-bit asymmetric key and a 128-bit symmetric key provide just about an equivalent level of security.

Additionally, asymmetric encryption is slower than symmetric encryption, which has a faster execution speed.

### Examples of asymmetric cryptography

The RSA algorithm -- the most widely used asymmetric algorithm -- is embedded in the SSL/TSL protocols, which are used to provide communications security over a computer network. RSA derives its security from the computational difficulty of factoring large integers that are the product of two large prime numbers.

Multiplying two large primes is easy, but the difficulty of determining the original numbers from the product -- factoring -- forms the basis of public key cryptography security. The time it takes to factor the product of two sufficiently large primes is considered to be beyond the capabilities of most attackers, excluding nation-state actors who may have access to sufficient computing power. RSA keys are typically 1024- or 2048-bits long, but experts believe that 1024-bit keys could be broken in the near future, which is why government and industry are moving to a minimum key length of 2048-bits.

Elliptic Curve Cryptography (ECC) is gaining favor with many security experts as an alternative to RSA for implementing public key cryptography. ECC is a public key encryption technique based on elliptic curve theory that can create faster, smaller and more efficient cryptographic keys. ECC generates keys through the properties of the elliptic curve equation.

To break ECC, one must compute an elliptic curve discrete logarithm, and it turns out that this is a significantly more difficult problem than factoring. As a result, ECC key sizes can be significantly smaller than those required by RSA yet deliver equivalent security with lower computing power and battery resource usage making it more suitable for mobile applications than RSA.

### History of asymmetric cryptography

Whitfield Diffie and Martin Hellman, researchers at Stanford University, first publicly proposed asymmetric encryption in their 1977 paper, "New Directions in Cryptography." The concept had been independently and covertly proposed by James Ellis several years earlier, while he was working for the Government Communications Headquarters (GCHQ), the British intelligence and security organization. The asymmetric algorithm as outlined in the Diffie-Hellman paper uses numbers raised to specific powers to produce decryption keys. Diffie and Hellman had initially teamed up in 1974 to work on solving the problem of key distribution problem.

The RSA algorithm, which was based on the work of Diffie, was named after its three inventors -- Ronald Rivest, Adi Shamir and Leonard Adleman. They invented the RSA algorithm in 1977 and published it in *Communications of the ACM* in 1978.

Today, RSA is the standard asymmetric encryption algorithm and it's used in many areas, including TLS/SSL, SSH, digital signatures and PGP.

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