Imagine whispering a secret in a crowded room, but only the intended person can clearly hear you.
Public key cryptography makes this possible online using a unique two-key system: a public key that you share and a private key that you keep secret. With this system, anyone can send you encrypted messages using your public key (like whispering in the crowd), but only you can decrypt them using your private key (hearing the whisper clearly).
This blog will explore how public key cryptography works, its applications, and its crucial role in maintaining data security.
Key Takeaways
- Public key cryptography secures your online interactions using two special keys: a public key you can share and a private key you keep secret.
- Digital signatures play a crucial role in verifying the authenticity of a message in Public Key Cryptography.
- While powerful, public key cryptography can be computationally expensive and faces potential threats from quantum computing.
- Despite these limitations, public key cryptography remains a vital tool for safeguarding our digital world, with ongoing research focused on strengthening its resilience.
Understanding Cryptography

Cryptography, derived from the Greek words ‘Kryptos’ meaning hidden, and ‘graphein’ meaning to write, is the practice of securing communication from unauthorized access or modification. It involves transforming information to make it unreadable to anyone except the intended recipient.
Let’s break down some key terms:
- Encryption: The process of converting plaintext into ciphertext, making it unreadable to anyone except those possessing the key. Imagine whispering and scrambling your message with a pre-arranged code known only to you and the recipient.
- Decryption: The act of reversing encryption, transforming ciphertext back to plain text using the same secret key. Just like deciphering your whispered code to understand the message.
- Cipher: An algorithm for performing encryption and decryption. It determines how plaintext is transformed into ciphertext and vice versa.
- Key: A key is a piece of information used to control the operation of the cipher, ensuring that the encrypted message can only be decrypted by those with the correct key.
The history of cryptography dates back to ancient times. The Egyptians used hieroglyphics to hide the meaning of their writings. During World War II, the Germans used the Enigma machine to secure military communications. Today, we primarily rely on two main types of encryption:
Symmetric Encryption

Symmetric encryption is a method that uses a single secret key for both encryption and decryption, much like a padlock in which the same key opens and closes. This approach is simple and fast, but it poses challenges in securely sharing the key with multiple parties. Ensuring that the key remains secret and is not intercepted during exchange is a significant security concern.
Symmetric encryption is widely used in various applications due to its efficiency. Here are a few examples:
Data at Rest
Symmetric encryption is commonly used to protect data at rest, that is, data stored in databases, hard drives, or other storage mediums. It helps prevent unauthorized access to the data if the storage medium is lost or stolen. Examples include full-disk encryption (like BitLocker and FileVault) and database encryption.
Data in Transit
Symmetric encryption is often used for secure communication channels like virtual private networks (VPNs) or encrypted messaging apps. The data is scrambled while traveling between sender and receiver, making it unreadable to anyone intercepting it.
File and Disk Encryption
Symmetric encryption is used in file and disk encryption software to protect sensitive data. The same key is used to encrypt and decrypt the files or disks.
Wireless Security
Protocols like WPA2 use symmetric encryption to secure wireless networks. The same key is used to encrypt and decrypt the data packets sent over the network.
Asymmetric Encryption

Asymmetric encryption involves two keys: a public key and a private key. The public key is used for encrypting the data or message, while the private key is used for decrypting the encrypted data or message.
As the name suggests, the public key can be shared with anyone who wants to send you an encrypted message. However, the private key must be kept secret and known only to the person who wants to decrypt the message.
For example, Let's say Alice wants to send a secure message to Bob. Bob generates a pair of keys: a public key and a private key. He then shares his public key with Alice. Alice uses Bob's public key to encrypt her message before sending it to Bob.
Once Bob receives the encrypted message, he uses his private key to decrypt it and read its contents. This process ensures that only Bob can read the message, maintaining the confidentiality of their communication.
How Does Public Key Cryptography Work?

Public Key Cryptography changes secure communication by employing asymmetric encryption techniques, where two distinct keys are used: a public key, accessible to everyone, and a private key, kept confidential by the owner.
The public key functions as a universally usable lock, while the private key serves as the sole means of unlocking it. Thus, while any individual can secure information using the public key, only the owner of the corresponding private key can access the original content.
Public and Private Keys
The heart of public key cryptography lies in using a unique two-key system. They are:
- Public Key: This key is designed to be shared freely with anyone you want to communicate with securely. You can publish it on your website, include it in your email signature, or distribute it in any way that makes it easily accessible. They can use this lock (public key) to secure a message box for you, but they can't open it.
- Private Key: This key is the most crucial part and must be kept confidential at all times. It's like your personal key to the mailbox - only you possess it and use it to access the messages deposited with the public key. It should never be shared with anyone else to maintain the security of the system.
Key Generation and Distribution
The keys are generated together using special mathematical algorithms. The public key is made available to everyone, while the private key is kept secret. Let’s explain key generation and distribution from the perspective of cryptocurrency wallets.
When you create a cryptocurrency wallet, a unique pair of cryptographic keys is generated. This pair consists of a public key, which is your wallet address that others can see and send funds to, and a private key, which is confidential and used to sign transactions and access your funds.
The private key is often represented as a passphrase or a seed phrase, a series of randomly generated words. This seed phrase is crucial for the recovery of your wallet if you lose access to your device. It serves as the master key to your digital vault of cryptocurrencies. Therefore, it’s of utmost importance to keep this seed phrase secure and private.
On the other hand, the public key, or wallet address, is shared openly whenever you need to receive funds. It’s like your email address for cryptocurrencies. Anyone can send funds to this address, but only the person with the corresponding private key (or seed phrase) can access and spend those funds.
By relying on this key generation and distribution mechanism, cryptocurrencies enable secure and decentralized ownership of digital assets, ensuring that only the rightful owners with the corresponding private keys can access and control their funds.
Encryption and Decryption Process
The magic of public key cryptography unfolds through the encryption and decryption process:
Encryption with the Public Key
When someone wants to send you a secure message, they obtain your public key, which is openly available and can be freely distributed. This public key acts as an encryption tool, allowing anyone to encrypt data intended for you.
The sender then takes their plaintext message and runs it through a mathematical algorithm along with your public key. This process scrambles the original message into an unreadable form called ciphertext. The ciphertext appears as a random sequence of characters, making it impossible to decipher the original message without the corresponding private key.
Therefore, the strength of the encryption algorithm ensures that even with knowledge of the public key and the ciphertext, it is computationally infeasible to deduce the original plaintext message
Decryption with the Private Key
Once the ciphertext reaches you, the intended recipient, you can use your private key to decrypt and recover the original plaintext message. This private key is kept secret and known only to you, ensuring that no one else can decrypt messages intended for you.
Therefore, the decryption process involves running the ciphertext through a mathematical algorithm along with your private key. This algorithm is designed to reverse the encryption process, effectively unscrambling the ciphertext and revealing the original plaintext message.
Since the private key acts as the unique decryption key, it is capable of decoding ciphertext that was encrypted using the corresponding public key. However, without the correct private key, it is virtually impossible to recover the original message from the ciphertext, even with immense computational power.
In addition, the encryption and decryption processes are designed to work in tandem, ensuring that data encrypted with a specific public key can only be decrypted by the corresponding private key. This asymmetric approach eliminates the need for secure key exchange before communication, as the public key can be freely distributed without compromising the security of the private key.
Digital Signatures

Public key cryptography offers not only secure communication but also a powerful tool for message authentication - digital signatures. Digital signatures are like the electronic equivalent of a handwritten signature or a stamped seal, but they offer far more inherent security.
They provide a means for individuals and organizations to sign electronic documents, proving the origin, identity, and integrity of the sender.
How Digital Signatures Work
Digital signatures function like a sophisticated digital stamp of approval. Here's a breakdown of the process:
Signing a Message
When you want to digitally sign a message, you utilize your private key. This key acts like your personal signature stamp. You apply a mathematical algorithm (often involving hashing) to the message content along with your private key.
This creates a unique digital signature that is mathematically linked to both the message and your private key.
Verifying the Signature
Once you've signed the message, you can send it along with the digital signature to the recipient. The recipient, in turn, uses your publicly available key to verify the signature. This key acts like a verification tool specifically designed to work with your signatures.
The recipient applies the same mathematical algorithm (including hashing) to the message content they receive. They then compare the result with the digital signature you sent. If both match, it mathematically proves that the message originated from you and has not been tampered with in transit.
Importance of Message Authentication
Digital signatures play a crucial role in today's digital context, offering several key benefits:
- Authentication: They provide a verifiable way to confirm the sender's identity. By verifying the signature, the recipient can be assured that the message truly originated from you and not someone impersonating you.
- Non-Repudiation: Once a message is digitally signed, you cannot deny having sent it. The mathematical link between the message and your private key creates a tamper-proof record of your involvement.
- Data Integrity: Digital signatures also help ensure that the message content hasn't been altered during transmission. Any modification to the message would invalidate the signature, alerting the recipient of a potential tampering attempt.
Algorithms Used in Public Key Cryptography

Public key cryptography relies on various cryptographic algorithms to generate key pairs and perform encryption and decryption. While the underlying mathematics can be quite complex, here's a simplified explanation of some common public-key cryptography algorithms:
RSA (Rivest-Shamir-Adleman)
RSA, a widely used and well-established cryptographic algorithm, was invented in 1978 by Ron Rivest, Adi Shamir, and Leonard Adleman. It is based on the mathematical difficulty of factoring large prime numbers. RSA is commonly used to secure data encryption in email and other digital transactions over the Internet.
RSA also plays a crucial role in various secure communication protocols such as Secure Shell (SSH), Secure Sockets Layer/Transport Layer Security (SSL/TLS), Secure/Multipurpose Internet Mail Extensions (S/MIME), and OpenPGP. Many software applications, including email providers (Gmail, Outlook), web browsers (Edge, Chrome), VPNs (OpenVPN), and secure chat applications, utilize RSA encryption.
How RSA Works: Key Generation
RSA generates a public and private key pair using two large prime numbers. These prime numbers are kept secret. The algorithm performs complex mathematical operations to produce a public key (e, N) and a private key (d, N). The values e and d are mathematically linked to the prime numbers, but it is computationally infeasible to derive one from the other.
Encryption
To encrypt a message (M), the sender raises M to the power of the public exponent (e) modulo N (written as M^e mod N). This transforms the message into ciphertext (C).
Decryption
The recipient, using the private key (d, N), decrypts the ciphertext (C) by raising it to the power of the private exponent (d) modulo N (written as C^d mod N). This operation reverses the encryption process and recovers the original message (M).
Diffie-Hellman (Key Exchange)
Unlike RSA, which focuses on encryption and decryption, Diffie-Hellman is a key exchange protocol that allows two parties to securely establish a shared secret key over an insecure communication channel without transmitting it.
Diffie-Hellman is used in many secure communication protocols, such as SSL/TLS and SSH, to establish a secure channel between two parties. Virtual Private Networks (VPNs) also often use Diffie-Hellman for secure key exchange and server authentication when establishing a VPN connection.
Simplified Explanation:
In the Diffie-Hellman key exchange protocol, Alice and Bob (hypothetical characters commonly used in cryptographic explanations) follow these steps:
Private Values:
Alice and Bob each generate a private value that they keep secret. Let’s denote Alice’s private value as xxx and Bob’s private value as yyy. These private values are randomly chosen and not shared with anyone.
Computing Public Values:
Alice and Bob use their private values to compute their public values. Alice computes her public value AAA by raising the base number aaa to the power of her private value xxx (i.e., A=axA = a^xA=ax). Similarly, Bob computes his public value BBB by raising the base number aaa to the power of his private value yyy (i.e., B=ayB = a^yB=ay). These computed values AAA and BBB are then shared with each other.
Shared Secret:
Alice and Bob can independently compute the same shared secret key using their private values and the public value received from the other party. Alice computes the shared secret key by raising Bob’s public value BBB to the power of her private value xxx (i.e., key = BxB^xBx). Similarly, Bob computes the shared secret key by raising Alice’s public value AAA to the power of his private value yyy (i.e., key = AyA^yAy). Due to the properties of exponentiation, Alice and Bob end up with the same shared secret key.
This shared secret key can then be used for encrypting and decrypting messages between the two parties using a symmetric key algorithm like AES.
ECC is a modern and increasingly popular cryptographic algorithm that provides equivalent security to RSA but with much smaller key sizes. It leverages the mathematical properties of elliptic curves to generate keys and perform encryption and decryption operations.
ECC is used in various applications, including secure web communication (SSL/TLS), Internet of Things (IoT) device security, smart cards, embedded systems, and mobile device security. Cryptocurrencies like Bitcoin and Ethereum use ECC specifically for signing transactions. VPNs also commonly use ECC for secure key exchange and server authentication when establishing a VPN connection.
Basic Understanding of ECC: Key Generation
Similar to RSA, ECC uses private numbers and performs mathematical operations on points of an elliptic curve to generate a public and private key pair. The private key is a randomly chosen number, and the public key is derived from the private key through elliptic curve point multiplication.
Encryption and Decryption
In ECC, encryption and decryption involve complex mathematical operations on elliptic curve points. The public key is used for encrypting messages, while the private key is used for decrypting messages encrypted with the corresponding public key. Due to the inherent difficulty of the elliptic curve discrete logarithm problem, ECC ensures a high level of security with smaller key sizes compared to traditional algorithms like RSA.
These algorithms form the foundation of public key cryptography and enable the secure transmission of information across insecure networks
Public Key Infrastructure (PKI)

Public Key Infrastructure (PKI) is a system that enables secure, encrypted communication and the validation of identities in the digital context. It uses cryptographic keys and digital certificates to establish a trusted environment, ensuring the authenticity and integrity of data and entities involved in electronic transactions.
PKI manages the generation, distribution, storage, and revocation of digital certificates, which are essential for verifying the legitimacy of public keys and the identities associated with them. This framework creates a chain of trust, allowing users and systems to confidently engage in secure communications and transactions. Here's how PKI works:
- Certificate Authorities (CAs): These are trusted third-party organizations responsible for issuing digital certificates. CAs verify the identity of entities requesting certificates and vouch for the authenticity of their public keys.
- Digital Certificates: A digital certificate contains key information, including the owner's public key, identity information, and the CA's digital signature. It serves as a digital passport, allowing parties to verify the legitimacy of a public key and establish secure communication.
- Trust Models: PKI relies on a hierarchical trust model. There are root CAs at the top, considered the most trusted entities in the system. These root CAs issue certificates to intermediate CAs, who in turn can issue certificates to end entities (individuals or organizations). Each certificate verifies the legitimacy of the entity below it in the hierarchy.
Importance of PKI for Secure Communication
PKI is the backbone of secure digital communication, playing a crucial role in activities where simple passwords are inadequate, and more rigorous proof is required to confirm the identities of the parties involved in the communication and to validate the information being transferred. PKI works in cryptocurrency in the following ways:
Wallet Creation and Transaction Signing
PKI is an essential part of cryptocurrency protocols like Bitcoin and Ethereum. The creation of wallets and the signing of transactions, which are core components of any cryptocurrency, rely heavily on public key cryptography.
For instance, Bitcoin’s protocol uses the Elliptic Curve Digital Signature Algorithm (ECDSA) to create a new set of private keys and corresponding public keys. When a user generates a new Bitcoin wallet, ECDSA generates a private and corresponding public key, enabling secure transactions.
Address Generation
The public key is used with a hash function to create the public address cryptocurrency users use to send and receive funds. The private key is kept secret and used to sign a digital transaction to ensure the transaction's origin is legitimate.
For example, in Bitcoin, the public key is hashed using SHA-256 followed by RIPEMD-160 to produce the public address. This address is what users share to receive funds, ensuring that the transaction can be securely validated against the private key.
Digital Signatures
Digital signatures are important in cryptocurrencies. Every transaction has a unique digital signature that depends on the private key of the user. Given the message, the public key of the user, and the signature, it is non-trivial to check if the signature is authentic.
For instance, when Alice sends Bitcoin to Bob, she uses her private key to sign the transaction. This signature can then be verified by anyone using Alice's public key, ensuring the transaction's authenticity without revealing her private key.
Security and Anonymity
PKI in cryptocurrencies not only ensures the security of transactions but also provides a level of anonymity. While the transaction data is public, the identity of the users remains hidden behind their public keys.
Monero, a privacy-focused cryptocurrency, uses advanced cryptographic techniques such as ring signatures and stealth addresses to enhance anonymity. Users' public keys are obfuscated, making it extremely difficult to trace transactions back to the individuals involved.
Practical Uses of Public Key Cryptography in Cryptocurrency

Now that we have a solid understanding of the workings of Public Key Infrastructure (PKI), let’s explore how public key cryptography is fundamental to the functioning of cryptocurrencies. Here are some of its practical uses:
Cryptocurrency Wallet
When you create a cryptocurrency wallet, it generates a pair of cryptographic keys: a private key and a public key. The private key must be kept secret because it authorizes transactions. The public key, derived from the private key, is used to create your public address, which you can share to receive funds.
For example, Bitcoin wallets generate a private key that is kept secret and a public key used to create a public address for receiving Bitcoin.
Address Generation
Cryptocurrency addresses are derived from the public key using a hash function. This address is what users share to receive funds. It provides a layer of security and anonymity since the private key remains hidden. For example, Ethereum addresses are created by hashing the public key, producing a unique address that users can share to receive Ether.
Securing the Blockchain
Public key cryptography secures the blockchain by ensuring that only authorized transactions are added to the blockchain. This is done through digital signatures and cryptographic proofs. For instance, Bitcoin uses digital signatures to ensure that only the owner of a private key can spend the Bitcoins associated with a given public address.
Smart Contracts
Smart contracts are self-executing contracts with the terms directly written into code. Public key cryptography ensures these contracts are secure by verifying the identity of the parties involved and ensuring the integrity of the contract. On Ethereum, smart contracts use digital signatures to verify that only authorized parties can execute the contract's functions.
Privacy Coins
Some cryptocurrencies like Monero and Zcash use advanced cryptographic techniques for enhanced privacy. For example, Ring Signatures obscure the sender’s identity by mixing multiple public keys in a transaction while Zero-Knowledge Proofs allow verification of transactions without revealing details like the sender, recipient, or amount.
Distributed Applications (DApps)
Public key cryptography is used in DApps to authenticate users and secure interactions. Users sign messages with their private keys to prove ownership of their public keys, enabling secure, trustless interactions within the DApp.
For example, many Ethereum-based DApps, like Uniswap (a decentralized exchange) and CryptoKitties (a blockchain-based game), use cryptographic wallets such as MetaMask for user authentication. This ensures that only authorized users can perform specific actions within the application.
Quantum Computing Threats and Future-Proofing
Quantum computing poses a potential threat to current cryptographic algorithms. There is ongoing research into quantum-resistant algorithms to ensure the continued security of cryptocurrencies in the future.
For instance, Blockchain projects like Quantum Resistant Ledger (QRL) and Bitcoin Post-Quantum (BPQ) are exploring quantum-resistant cryptographic techniques. QRL uses hash-based signatures, which are believed to be resistant to quantum attacks, while BPQ focuses on integrating post-quantum secure protocols into the Bitcoin ecosystem.
Security Considerations
Public key cryptography offers a robust security framework for our digital interactions. However, to maintain its effectiveness, it's crucial to be aware of certain security considerations:
Trapdoor Functions
A trapdoor function is a function that is easy to compute in one direction, yet difficult to compute in the opposite direction without special information, called the “trapdoor”.
In the context of public key cryptography, the encryption function serves as the trapdoor function. The public key is used for encryption (easy direction), and the private key serves as the trapdoor, allowing for decryption (hard direction).
Key Size and Cryptographic Strength
The size of the keys used in public key cryptography plays a vital role in its security. Larger key sizes offer greater protection against brute-force attacks where attackers try every possible combination to crack the encryption.
As computing power increases, so too should the key size to maintain an adequate level of security. Cryptographic standards and best practices define recommended key sizes for different algorithms and security requirements.
Quantum Computing Threats
Quantum computers are a new type of computer that use the rules of quantum mechanics, a branch of physics that describes the strange, counter-intuitive behavior of very small particles. These computers can process information in a fundamentally different way from traditional computers, making them incredibly powerful for certain tasks.
This advanced capability means that some widely used public key cryptography algorithms, like RSA, could be broken by sufficiently powerful quantum computers. Quantum computers can solve complex mathematical problems much faster than classical computers, and this includes the kind of problems that secure many cryptographic systems today.
For example, Shor's algorithm, a quantum algorithm, can factor large numbers efficiently, potentially rendering RSA encryption insecure. Therefore, as quantum computing technology advances, there is an increasing need to develop new cryptographic algorithms that can resist quantum attacks.
Essential Security Practices

While public key cryptography offers strong protection, its effectiveness relies on you using it correctly. Here are some essential practices to maximize the security of your encrypted messages and private information:
Strong Passwords and Two-Factor Authentication (2FA)
Public key systems often rely on passwords to access your private key. Choose strong, unique passwords using apps like 2FA whenever possible for an extra layer of security.
Private Key Protection
Your private key is like the key to your apartment – keep it safe! Avoid storing it on easily accessible devices or sharing it with anyone. Some systems offer secure storage options for private keys.
Secure Software
Keep your operating system, web browser, and other software up to date with the latest security patches to address vulnerabilities that attackers might exploit.
Beware of Phishing
Don't click on suspicious links or attachments in emails, even if they appear to come from a trusted source. Phishing attacks can try to trick you into revealing your private key or other sensitive information.
Benefits and Limitations of Public Key Cryptography
Public Key Cryptography offers numerous advantages in securing digital communication and data protection, but it also presents certain limitations that need to be addressed. Let's examine the benefits and limitations:
Benefits of Public Key Cryptography
The benefits of Public key cryptography are as follows:
Enhanced Security and Confidentiality
Public key cryptography offers a significant advantage over traditional symmetric encryption. By eliminating the need for pre-shared secret keys, it significantly reduces the risk of exposure and unauthorized access to sensitive information.
Digital Signatures and Authentication
Public key cryptography enables the use of digital signatures for authentication. A digital signature is a mathematical scheme for verifying the authenticity of digital messages or documents. It provides a layer of validation and security to messages sent through a non-secure channel.
Key Distribution and Management
Public key cryptography simplifies key distribution compared to traditional methods. Public keys can be freely shared, eliminating the need for a secure exchange of secret keys with every new communication.
Limitations of Public Key Cryptography
The limitations of Public key cryptography are as follows:
Computational Overhead
Public key cryptography algorithms can be computationally more expensive than symmetric encryption algorithms. This can impact performance, especially for resource-constrained devices or for bulk encryption tasks.
A study conducted by researchers from IBM and the University of Waterloo analyzed the impact of public key cryptography on the performance of IoT devices. They found that using RSA for securing communications in smart meters, which are part of the IoT infrastructure for smart grids, led to significant delays and increased power consumption.
This reduced the efficiency of the smart meters, highlighting the need for more lightweight cryptographic solutions in such resource-constrained environments.
Alteration of Public Keys
If an attacker can alter the public keys in a public key infrastructure, they can decrypt messages or impersonate other users. This is why it’s crucial to ensure the integrity of public keys.
For example, in 2011, a hacker breached the security of DigiNotar, a Dutch certificate authority, and issued fraudulent certificates for several high-profile domains, including Google and Microsoft. These certificates could have been used for man-in-the-middle attacks, allowing the attacker to decrypt and alter communications or impersonate these sites. The breach undermined trust in the PKI and led to DigiNotar's bankruptcy.
Quantum Computing Threats
As discussed earlier, the potential rise of powerful quantum computers poses a future threat to some public key cryptography algorithms. Ongoing research and development of quantum-resistant algorithms are essential to address this challenge.
Conclusion
Public key cryptography is essential for modern digital security, providing robust data transfer and communication protection. Despite facing challenges, the ongoing research is focused on strengthening its resilience and adapting to emerging threats.
However, in cryptocurrency, public key cryptography underpins the security and functionality of the entire system. It ensures the secure creation and management of wallets, enables the signing and verification of transactions, and supports the development of secure smart contracts and decentralized applications (DApps).
Nevertheless, public key cryptography shows remarkable durability and versatility. It demonstrates human creativity in establishing a secure communication system amidst a digitally interconnected world.