# How RSA Public-Key Encryption Keeps Digital Messages Secret > This patent describes the foundational RSA algorithm, a method for securely sending messages where anyone can encrypt a message using a public key, but only the intended recipient can decrypt it using a secret private key. - **Patent:** US 4405829 - **Original title:** Cryptographic communications system and method - **Owner:** Massachusetts Institute of Technology - **Granted:** 1983 - **Status:** Public domain (expired) - **Times cited:** 1,015 - **Field:** software, telecommunications, cybersecurity, finance, ecommerce, consumer_electronics ## What it does This patent outlines a cryptographic system for secure communication. A sender transforms a message, represented as a number M, into a secret ciphertext C. This is done by calculating M raised to a specific power 'e' and then finding the remainder when that result is divided by a large composite number 'n' (C ≡ M^e (mod n)), as described in Claim 1. The numbers 'e' and 'n' form the public key. The intended receiver then takes this ciphertext C and transforms it back into the original message M' using their secret private key, which involves raising C to a different power 'd' and again finding the remainder when divided by 'n' (M' ≡ C^d (mod n)). For example, if Alice wants to send a secret message to Bob, she uses Bob's public key (e, n) to encrypt her message. Only Bob, who knows the secret 'd' (his private key), can decrypt it. ## What it does NOT cover - Does not cover symmetric encryption systems where the same key is used for both encryption and decryption. - Does not cover cryptographic methods that do not rely on modular exponentiation (M^e mod n) for encryption and decryption. - Does not cover systems where the modulus 'n' is not the product of two prime numbers, 'p' and 'q', as specified in Claim 1. - Does not cover encryption schemes that do not use a public exponent 'e' that is relatively prime to lcm(p-1, q-1), as defined in Claim 1. - Does not cover methods for key exchange that don't rely on the specific mathematical properties of RSA, such as Diffie-Hellman. ## The clever bit The true innovation lies in the 'trapdoor function': it's easy to encrypt a message using a public key, but incredibly difficult to reverse the process without a specific piece of secret information (the private key). This asymmetry relies on the mathematical difficulty of factoring large prime numbers. ## Real-world examples 1. Secure Sockets Layer (SSL) and Transport Layer Security (TLS) protocols 2. Pretty Good Privacy (PGP) for email encryption 3. Digital signatures for software updates and documents 4. Virtual Private Networks (VPNs) 5. Cryptocurrency wallets and transactions ## Why it matters This patent describes the RSA algorithm, a cornerstone of modern cryptography. It enabled secure digital communications by solving the problem of key distribution, allowing parties to communicate securely without first needing to share a secret key through a secure channel. RSA became widely adopted for securing internet transactions, email, and data storage, fundamentally changing how digital information is protected. ## Frequently asked questions ### What does How RSA Public-Key Encryption Keeps Digital Messages Secret cover? This patent describes the foundational RSA algorithm, a method for securely sending messages where anyone can encrypt a message using a public key, but only the intended recipient can decrypt it using a secret private key. ### Who owns patent US 4405829? Massachusetts Institute of Technology owns this patent, granted in 1983. ### When does this patent expire? This patent has expired and is now in the public domain — anyone can use the invention freely. ### What is patent US 4405829 cited by? This patent has been cited by 1015 later patents that build on its ideas. ### What problem does this patent solve? This patent describes the RSA algorithm, a cornerstone of modern cryptography. It enabled secure digital communications by solving the problem of key distribution, allowing parties to communicate securely without first needing to share a secret key through a secure channel. RSA became widely adopted for securing internet transactions, email, and data storage, fundamentally changing how digital information is protected. ### What does this patent NOT cover? Does not cover symmetric encryption systems where the same key is used for both encryption and decryption. **Full plain-English explainer:** https://patentbrief.org/patent/us/4405829/rsa-encryption **Original patent:** https://patents.google.com/patent/US4405829 --- _Source: PatentBrief — https://patentbrief.org. Patent facts are from public records; the plain-English explanation is PatentBrief's._ ## Related patents Semantically similar inventions in the PatentBrief corpus: - [How to Create a Secret Code Key Without Meeting First](https://patentbrief.org/patent/us/4200770/diffie-hellman-public-key-exchange) — This 1980 patent describes a way for two people to create a secret code key over a public channel, like the internet, without ever meeting or sharing the key directly. - [How Netscape Created the Secure Socket Layer (SSL) for Web Security](https://patentbrief.org/patent/us/5657390/secure-socket-layer-application-program-apparatus-and-method) — Netscape's 1995 patent defining the architecture for SSL, the foundational technology that allows browsers to securely transmit encrypted data over the internet. - [Using Transcendental Math to Generate Better Random Numbers](https://patentbrief.org/patent/us/12200123/starship-orbital-test-flight) — A method for creating high-quality random numbers by using complex transcendental math equations to process raw data. - [How Pulse Code Modulation Digitizes Analog Signals](https://patentbrief.org/patent/us/2266401/pcm-pulse-code-modulation-reeves) — A foundational 1938 patent describing how to convert continuous sound waves into a stream of digital numbers for transmission. - [How Computers Use Hardware to Stop Software Piracy and Cracking](https://patentbrief.org/patent/us/4558176/computer-systems-to-inhibit-unauthorized-copying-unauthorized-usage-and-automated-cracking-of-protected-software) — A 1982 hardware-based security system that prevents software from being copied or cracked by destroying sensitive data if the computer detects unauthorized access or execution.