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.
Original patent title: “Cryptographic communications system and method”
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. Granted to Massachusetts Institute of Technology in 1983 with 52 claims and 1,015 forward citations, and it is now in the public domain.
Coverage
What does this patent actually cover?
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 ClaimclaimA numbered sentence at the end of a patent that legally defines what the inventor owns. The most important section.Read more → 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.
The gap
What does this patent 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 ClaimclaimA numbered sentence at the end of a patent that legally defines what the inventor owns. The most important section.Read more → 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 ClaimclaimA numbered sentence at the end of a patent that legally defines what the inventor owns. The most important section.Read more → 1.
- Does not cover methods for key exchange that don't rely on the specific mathematical properties of RSA, such as Diffie-Hellman.
These exclusions are unique to PatentBrief — derived from the actual claim language, not patent-office boilerplate.
Key facts
What made this novel
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.
The Patent Drawing
Schematic visualization of the patent's claim structure. Hand-drawn diagrams in progress for each landmark patent.
Where you've seen this
Real-world examples
Secure Sockets Layer (SSL) and Transport Layer Security (TLS) protocols
Pretty Good Privacy (PGP) for email encryption
Digital signatures for software updates and documents
Virtual Private Networks (VPNs)
Cryptocurrency wallets and transactions
Why it matters
The bigger picture
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.
Filed
December 14, 1977
Granted
September 20, 1983
Market context
Who's building on this
Companies in this space
Many companies and organizations continue to build on the principles of RSA. Major technology companies like Google, Apple, Microsoft, and Amazon rely on RSA for securing their online services and protecting user data. Cybersecurity firms like Palo Alto Networks and Fortinet integrate RSA into their security products. Open-source projects like OpenSSL also widely implement RSA for various cryptographic tasks.
Market impact
The granting of this patent and the widespread adoption of the RSA algorithm created the foundation for modern secure digital communication. It enabled the growth of e-commerce, secure banking, and private online interactions by providing a robust method for public-key cryptography. This technology became essential for protocols like SSL/TLS, which secure web traffic, making it a critical component of the internet's infrastructure and fostering trust in digital transactions globally.
Claim 1 — Plain English
What this patent covers
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.
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.
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.
Patent timeline
Application submitted to the patent office
Application published, typically 18 months after filing
Patent officially issued
Patent enters public domain
This patent is in the public domain
See the Freedom to Build guide — what is free to use, what is not, and how to cite this patent.
PatentBrief Score
Impact Score
High impact
Citation count
40/40
Highly cited
Claim breadth
20/20
Very broad protection
Recency
0/20
Older than 20 years
Assignee scale
20/20
Major company or institution
PatentBrief Impact Score — based on citation count, claim breadth, recency, and assignee scale. Not a legal assessment.
Heuristic Value Estimate
What this patent might be worth
$90K – $288K
Midpoint $180K · expired or expiring · industry ×1.5
Heuristic only — blends forward/backward citation counts, claim scope, time remaining, litigation history, and CPC-derived industry baseline. Real valuations need a professional appraisal.
Patent Claims
0 independent claims · 1 dependent
Claims are the legal boundaries of the patent. An independent claim stands alone. A dependent claim adds limitations to its parent, narrowing — but not broadening — the scope.
The original legal language
Original claims
52 claims as filed with the patent office.
Concepts involved
Citations
Patent lineage
Cite this patent
Adleman, L. M., Rivest, R. L., & Shamir, A. (1983). How RSA Public-Key Encryption Keeps Digital Messages Secret (U.S. Patent No. 4,405,829). U.S. Patent and Trademark Office. https://patentbrief.org/patent/us/4405829/rsa-encryption
Auto-generated from the patent record. Double-check author order and the issue date against the official USPTO document before submitting.
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Common Questions
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.
Same assignee
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