Introduction

Public-key cryptography (PKC), also known as asymmetric cryptography, is a framework that uses both a private and a public key, as opposed to the single key used in symmetric cryptography. The use of key pairs gives PKC a unique set of characteristics and capabilities that can be used to solve problems inherent in other cryptographic methods. This form of cryptography has become an important element of modern computer security, as well as an important component of the growing ecosystem of cryptocurrencies.

How does public key cryptography work?

In the PKC scheme, the public key is used by the sender to encrypt the information, and the private key is used by the receiver to decrypt it. Because the two keys are different from each other, the public key can be safely used without compromising the security of the private key. Each pair of asymmetric keys is unique, which ensures that a message encrypted using the public key can only be read by the person who has the corresponding private key.

Since asymmetric encryption algorithms generate key pairs that are mathematically related, their key lengths are much larger than those of symmetric cryptography. This large length, typically between 1024 and 2048 bits, makes it extremely difficult to calculate a private key from its public counterpart. One of the most common asymmetric encryption algorithms in use today is known as RSA.

In the RSA scheme, keys are generated using the modulus obtained by multiplying two numbers (often two large prime numbers). Simply put, the module generates two keys (one public that can be shared and one private that should be kept secret). The RSA algorithm was first described in 1977 by Rivest, Shamir, and Adleman (hence RSA) and remains a core component of public-key cryptography systems.

PKC as an encryption tool

Private-key cryptography solves one of the age-old problems of symmetric algorithms, namely the transmission of a key that is used for both encryption and decryption. Sending this key over an insecure connection could expose it to third parties, who could then read any messages encrypted with the shared key. Although there are cryptographic methods (such as the Diffie-Hellman-Merkle key exchange protocol) to solve this problem, they are still vulnerable to attack. Conversely, in private-key cryptography, the key used for encryption can be securely transmitted over any connection. As a result, asymmetric algorithms provide a higher level of protection than symmetric ones.

Creation of digital signatures

Another application of asymmetric cryptography algorithms is data authentication with digital signatures. Essentially, a digital signature is a hash created using the data in the message. When this message is sent, the signature can be verified by the recipient using the sender's public key. In this way, they can identify the source of the message and ensure that it has not been tampered with. In some cases, digital signatures and encryption are used together, meaning that the hash itself may be encrypted as part of the message. However, it should be noted that not all digital signature schemes use encryption methods.

Limitation

Although it can be used to improve computer security and provide message integrity checks, PKC has some limitations. Due to complex mathematical operations related to encryption and decryption, asymmetric algorithms can be quite slow when working with large volumes of data. This type of cryptography also depends on the assumption that the private key will always remain secret. If the private key is accidentally shared or disclosed, the security of all messages encrypted with the corresponding private key will be compromised. Users can also accidentally lose their private keys, and they will not be able to access the encrypted data.

Application of public key cryptography

This type of cryptography is used by many modern computer systems to ensure the security of confidential information. Emails, for example, can be encrypted using public-key cryptography techniques to preserve the confidentiality of their contents.

The Secure Sockets Layer (SSL) protocol, which enables secure connections to websites, also uses asymmetric cryptography. PKC systems have even been considered as a means of providing a secure electronic voting environment, potentially allowing voters to participate in elections from their home computers.

PKC also plays an important role in blockchain technology and cryptocurrencies. When setting up a new crypto wallet, a pair of keys (public and private) is generated. The wallet address is generated using a public key and can be securely shared with others. On the other hand, the private key is used to create digital signatures and verify transactions, so it should be kept secret.

Once a transaction has been verified by verifying the hash contained in the digital signature, that transaction can be added to the blockchain ledger. This digital signature verification system ensures that only the person who has the private key associated with the respective crypto wallet can move funds.

It should be noted that asymmetric cryptography used in cryptocurrency applications is different from that used for computer security purposes. For example, Bitcoin and Ethereum use a special algorithm to verify transactions known as "Elliptic Curve Digital Signature Algorithm (ECDSA)". ECDSA also creates digital signatures without using encryption. This means that the blockchain does not need encryption.

Results

Public key cryptography plays an important role in the security of today's digital systems, from computer security to the verification of cryptocurrency transactions. By using pairs of public and private keys, asymmetric cryptography algorithms solve the main security problems associated with symmetric ciphers. Although PKC has been in use for many years, new applications and applications are regularly being developed for it, especially in blockchain and cryptocurrency.