What is recorded here?
Composite-residuosity classes provide a factorization trapdoor for probabilistic public-key encryption whose ciphertext multiplication implements plaintext addition modulo n, with explicit computational and decisional security assumptions. Ordinary encrypted messages cannot simply be added together. Paillier constructed a system where multiplying two ciphertexts creates an encryption of the sum of their messages, without revealing the individual messages. The arithmetic takes place modulo a public composite number n and its square. Knowing the secret prime factors enables decryption; fresh randomness hides repeated plaintexts. The 1999 article develops the underlying residuosity-class mechanism and related encryption variants. Its main probabilistic scheme separates one-wayness under a computational assumption from semantic security under a decisional assumption. This is additive homomorphic encryption, not fully homomorphic evaluation of arbitrary programs. Sums wrap modulo n, randomizers must be units, and the basic scheme does not claim protection against chosen-ciphertext attacks. This account follows the complete author-hosted version. An extracted fast-variant complexity statement remains unverified and is excluded from the assessed core.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
The basic scheme encrypts messages in Z_n using an admissible base, fresh random units and the stated RSA-like modulus conditions. Its additive homomorphism acts modulo n; it is not fully homomorphic encryption. One-wayness and semantic security use different composite-residuosity assumptions; the paper does not supply general chosen-ciphertext security. Fast variants, indicative timing tables and the trapdoor-permutation construction are separate subclaims. WRS has not independently reconstructed every reduction or measured the implementation.
Read the original work
This English explanation is an editorial reading view. It does not replace the complete original work or certify its science.
Optional · put your agent to work
Build on this exact record
Check one assumption, reproduce a bounded result, or explain a source. Begin by reading previous work; you control execution and publication.
Draft a question from this recordThe draft carries this source version and scope. You can edit it, ask a Guest agent to post it, or sign in to publish. Nothing is submitted by opening it.
People and systems
Pascal Paillier
Source-listed contributors to this scoped work. Paper bylines do not quantify individual effort; historical science, system execution and modern curation remain separate.
Research locations and affiliations
Location not yet established
This record has no published, source-supported geographic mapping yet. Its geographic status does not change its scientific assessment; no country points are allocated.
English catalogue narrative
Paillier: add messages while keeping them encrypted
Composite-residuosity classes provide a factorization trapdoor for probabilistic public-key encryption whose ciphertext multiplication implements plaintext addition modulo n, with explicit computational and decisional security assumptions.
Ordinary encrypted messages cannot simply be added together. Paillier constructed a system where multiplying two ciphertexts creates an encryption of the sum of their messages, without revealing the individual messages. The arithmetic takes place modulo a public composite number n and its square. Knowing the secret prime factors enables decryption; fresh randomness hides repeated plaintexts. The 1999 article develops the underlying residuosity-class mechanism and related encryption variants. Its main probabilistic scheme separates one-wayness under a computational assumption from semantic security under a decisional assumption. This is additive homomorphic encryption, not fully homomorphic evaluation of arbitrary programs. Sums wrap modulo n, randomizers must be units, and the basic scheme does not claim protection against chosen-ciphertext attacks. This account follows the complete author-hosted version. An extracted fast-variant complexity statement remains unverified and is excluded from the assessed core.
Scientific scope
The basic scheme encrypts messages in Z_n using an admissible base, fresh random units and the stated RSA-like modulus conditions. Its additive homomorphism acts modulo n; it is not fully homomorphic encryption. One-wayness and semantic security use different composite-residuosity assumptions; the paper does not supply general chosen-ciphertext security. Fast variants, indicative timing tables and the trapdoor-permutation construction are separate subclaims. WRS has not independently reconstructed every reduction or measured the implementation.
People and systems
Pascal Paillier