{
  "patent_number": "US 4405829",
  "country": "US",
  "title": "How RSA Public-Key Encryption Keeps Digital Messages Secret",
  "original_title": "Cryptographic communications system and method",
  "summary": "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.",
  "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."
  ],
  "filed": "1977-12-14",
  "granted": "1983-09-20",
  "expires": "2000-09-20",
  "status": "expired",
  "holder": "Massachusetts Institute of Technology",
  "holder_url": "https://patentbrief.org/company/massachusetts-institute-of-technology",
  "inventors": [
    {
      "name": "Leonard M. Adleman",
      "url": "https://patentbrief.org/inventor/leonard-m-adleman"
    },
    {
      "name": "Ronald L. Rivest",
      "url": "https://patentbrief.org/inventor/ronald-l-rivest"
    },
    {
      "name": "Adi Shamir",
      "url": "https://patentbrief.org/inventor/adi-shamir"
    }
  ],
  "times_cited": 1015,
  "tags": [
    "software",
    "telecommunications",
    "cybersecurity",
    "finance",
    "ecommerce",
    "consumer_electronics"
  ],
  "abstract": "A cryptographic communications system and method. The system includes a communications channel coupled to at least one terminal having an encoding device and to at least one terminal having a decoding device. A message-to-be-transferred is enciphered to ciphertext at the encoding terminal by first encoding the message as a number M in a predetermined set, and then raising that number to a first predetermined power (associated with the intended receiver) and finally computing the remainder, or residue, C, when the exponentiated number is divided by the product of two predetermined prime numbers (associated with the intended receiver). The residue C is the ciphertext. The ciphertext is deciphered to the original message at the decoding terminal in a similar manner by raising the ciphertext to a second predetermined power (associated with the intended receiver), and then computing the residue, M', when the exponentiated ciphertext is divided by the product of the two predetermined prime numbers associated with the intended receiver. The residue M' corresponds to the original encoded message M.",
  "url": "https://patentbrief.org/patent/us/4405829/rsa-encryption",
  "markdown_url": "https://patentbrief.org/patent/us/4405829/rsa-encryption/md",
  "google_patents_url": "https://patents.google.com/patent/US4405829",
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}