{"id":40859,"date":"2026-08-25T04:07:24","date_gmt":"2026-08-25T11:07:24","guid":{"rendered":"https:\/\/www.privateinternetaccess.com\/blog\/?p=40859"},"modified":"2026-08-26T00:05:41","modified_gmt":"2026-08-26T07:05:41","slug":"rsa-encryption","status":"publish","type":"post","link":"https:\/\/www.privateinternetaccess.com\/blog\/rsa-encryption\/","title":{"rendered":"RSA Encryption: Asymmetric Cryptography for Data Authenticity and Integrity"},"content":{"rendered":"\n

The RSA encryption method is a form of asymmetric cryptography, also called public-key cryptography, that uses a pair of mathematically linked keys so that encrypted data can only be read by the intended recipient<\/strong>.<\/p>\n\n\n\n

It\u2019s a reliable method for securing data transfers, but it limits the amount of data you can transfer and is computationally heavy. As a result, it\u2019s usually used to protect the exchange of faster symmetric keys or confirm the identity of the data sender.<\/p>\n\n\n\n

This guide explains what RSA encryption is, the mathematics it relies on, how the encryption and decryption process works, and how it holds up against modern cybersecurity threats.<\/p>\n\n\n\n

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Table of Contents<\/h4>\nWhat Is RSA Encryption?<\/a>
\nHow Does RSA Encryption Work?<\/a>
\nWhere Is RSA Encryption Used?<\/a>
\nRSA Security Risks and Limitations<\/a>
\nRSA Compared to Other Popular Types of Encryption<\/a>
\nFAQ<\/a>
<\/div>\n\n\n\n\n

What Is RSA Encryption?<\/h2>\n\n\n\n

As a public-key cryptosystem, RSA asymmetric encryption secures data using two mathematically linked keys: a public key and a private key<\/strong>. The sender shares the public key and anyone can use it. On the other hand, the sender never shares the private key.\u00a0<\/p>\n\n\n\n

RSA encryption pairs the two keys so that data processed with one key can only be reversed with the other<\/strong>. This allows the system to work bidirectionally, which lets people communicate securely without ever having to share their private keys.<\/p>\n\n\n\n

For example, a sender can encrypt data with a recipient\u2019s public key so that only the intended recipient can decrypt it using their private key. The owner of a private key can also use it to encrypt a message and prove that the communication came from them.<\/p>\n\n\n\n

The whole system relies on a mathematical algorithm built on the integer factorization problem.<\/strong> This is the art of finding the prime factors of a composite number <\/strong>(i.e., finding factors that can only be divided by themselves and one to produce a whole number \u2013 like three, five, seven, and so on, but with much larger numbers).\u00a0<\/p>\n\n\n\n

The calculation is quick to run in one direction but difficult to reverse.<\/strong> That imbalance is what keeps RSA-encrypted data secure. It\u2019s much more time-consuming and resource-intensive to use a public key to work out the private key.<\/p>\n\n\n\n

Three researchers at the Massachusetts Institute of Technology: Ron Rivest, Adi Shamir, and Leonard Adleman developed the method in 1977. The \u201cRSA\u201d comes from the initial letters of their surnames.1<\/sup><\/p>\n\n\n\n

The researchers were looking for a practical way to solve a long-standing problem in cryptography: how can two people communicate privately without first meeting to agree on a shared secret key.<\/p>\n\n\n\n

Symmetric vs. Asymmetric Encryption<\/h3>\n\n\n\n

The RSA system uses asymmetric encryption to secure and exchange data<\/strong>, while many other commonly-used ciphers (e.g., AES) use symmetric encryption. Understanding the difference between these two types of encryption can make it easier to follow how RSA encryption works.<\/p>\n\n\n\n

Symmetric encryption uses a single shared key for both encrypting and decrypting data.<\/strong> The sender and recipient must both hold an identical copy of the key because it turns readable data into ciphertext and back to readable data.\u00a0<\/p>\n\n\n\n

This setup is fast and efficient, but comes with significant limitations. Sending the shared key to the recipient can potentially allow an attacker to intercept and read every message that\u2019s encrypted with it. Equally, if not more importantly, it doesn\u2019t work in a scenario where you want to limit a user to either encryption or decryption privileges only.<\/p>\n\n\n\n

Asymmetric encryption solves these problems by using a linked key pair instead of one key.<\/strong> You can share the public key while the private key stays secret, so there\u2019s no need to distribute it. The trade-off is speed since asymmetric methods are slower and more computationally demanding.<\/p>\n\n\n\n

Here\u2019s a side-by-side comparison:<\/p>\n\n\n\n

Feature<\/strong><\/td>Symmetric Encryption<\/strong><\/td>Asymmetric Encryption<\/strong><\/td><\/tr>
Keys<\/td>One shared key for both encryption and decryption<\/td>A linked public and private key pair<\/td><\/tr>
Key distribution<\/td>The sender and recipient securely share the secret key beforehand<\/td>The sender shares the public key while the private key stays secret<\/td><\/tr>
Speed<\/td>Fast and efficient, even for large files<\/td>Slower and more computationally demanding<\/td><\/tr>
Best for<\/td>Encrypting large amounts of data<\/td>Key exchange, digital signatures, and identity verification<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

The Math Behind RSA Encryption<\/h3>\n\n\n\n

The security of the RSA encryption algorithm comes from two mathematical concepts: Large prime numbers and modular arithmetic.<\/p>\n\n\n\n

RSA encryption multiplies two large prime numbers to produce a much larger number called the modulus.<\/strong> In a modern 2048-bit RSA key, that modulus can run to roughly 600 digits when written out in full.\u00a0<\/p>\n\n\n\n

We use modular arithmetic, a system where numbers \u201cwrap around\u201d after reaching a set value, to generate the public and private key values. This might sound a bit complicated, but you already use it every time you read a 12-hour analog clock.\u00a0<\/p>\n\n\n\n

Looking at a clock face, you\u2019ll see that once the clock passes 12, it wraps back around to 1. If the time is 10:00 a.m. and you add five hours, the result is 3:00 p.m. because the count starts again after it reaches 12.<\/p>\n\n\n\n

Modular arithmetic extends this theory to work with any number. The modulus is the \u201creset point.\u201d When a number goes past that value, you divide by the modulus and keep only the remainder.<\/strong><\/p>\n\n\n\n

Let\u2019s consider a simple example. In a system with a modulus of 3, the number 5 becomes 2 because 3 goes into 5 once with 2 left over. The number 7 would become 1, because 3 fits into 7 twice with 1 left over.<\/p>\n\n\n\n

The first operation \u2013 multiplying two primes \u2013 is quick to do, but working out which two primes produced the modulus (i.e., factoring) is currently impractical even for powerful computers<\/strong>.\u00a0<\/p>\n\n\n\n

For a sense of scale, researchers factored a 250-digit number known as RSA-250 in 2020, but only after the equivalent of about 2,700 years of processing time spread across many machines working in parallel.2<\/sup><\/p>\n\n\n\n

That number is smaller than the roughly 600-digit modulus used in a standard 2048-bit key, so this would make it challenging to derive the private key from the public key.<\/p>\n\n\n\n

RSA Key Sizes<\/h3>\n\n\n\n

Key size in RSA refers to the length of the modulus, measured in bits.<\/strong> Longer keys are harder to break but slower to use, so the choice is a balance between security and performance.<\/p>\n\n\n\n

In the early 2000s, 1024-bit keys were common but they\u2019re now considered obsolete. They provide only around 80 bits of security, which measures how difficult it is to break a cryptographic system. Certificate authorities stopped issuing 1024-bit certificates in 2013. A well-resourced attacker could realistically factor a key of this size.<\/p>\n\n\n\n

Today, 2048-bit keys are the baseline.<\/strong> The National Institute of Standards and Technology (NIST) treats 2048-bit RSA as acceptable through 2030, after which it recommends moving to 3072-bit and 4096-bit keys.3<\/sup><\/p>\n\n\n\n

How Does RSA Encryption Work?<\/h2>\n\n\n\n

The RSA method solves the key distribution problem: how to communicate securely without first sharing a key. To do this, the algorithm follows a defined set of steps for RSA encryption and decryption.<\/p>\n\n\n

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\"Encryption<\/figure>\n<\/div>\n\n\n

Step 1: Key Generation<\/h3>\n\n\n\n

Key generation puts the math behind RSA encryption into practice. It produces the public and private keys as a set of numbers, through the following steps:<\/p>\n\n\n\n