# Public-key cryptosystems based on composite degree residuosity classes

##### Citations

4,940 citations

### Cites background from "Public-key cryptosystems based on c..."

...Other additively homomorphic encryption schemes with proofs of semantic security are Benaloh [8], Naccache-Stern [42], Okamoto-Uchiyama [46], Paillier [ 47 ], and Damgard-Jurik [19]....

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1,979 citations

### Cites methods from "Public-key cryptosystems based on c..."

...It can be converted to one which computes P (z) using the methods of Paillier [18], who presented a trapdoor for computing discrete logs....

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...[18] P. Paillier, Public-Key Cryptosystems Based on Composite Degree Residuocity Classes....

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...It can be converted to one which computes P (z) using the methodsof Paillier [18], who presented a trapdoor for computing discrete logs....

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1,588 citations

### Cites background or methods from "Public-key cryptosystems based on c..."

...These interactive zero knowledge proofs of bit encryption are efficiently constructed (using zero knowledge identification protocols) for standard homomorphic encryption schemes such as ElGamal [13, 21], Pedersen [29, 10], or Paillier [28, 12]....

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...Using a construction along the lines of Paillier [28], we obtain a system with an additive homomorphism....

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...Current homomorphic public key systems [20, 13, 28] have limited homomorphic properties: given two ciphertexts Encrypt(PK, x) and Encrypt(PK, y), anyone can compute either the sum Encrypt(PK, x+y), or the product Encrypt(PK, xy), but not both....

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...The system resembles the Paillier [28] and the Okamoto-Uchiyama [27] encryption schemes....

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1,450 citations

^{1}, Catherine M. S. Redfield

^{1}, Nickolai Zeldovich

^{1}, Hari Balakrishnan

^{1}•Institutions (1)

1,148 citations

##### References

14,611 citations

14,068 citations

### "Public-key cryptosystems based on c..." refers background in this paper

...Since the discovery of public-key cryptography by Die and Hellman [ 5 ], very few convincingly secure asymetric schemes have been discovered despite considerable research eorts....

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6,871 citations

### "Public-key cryptosystems based on c..." refers methods in this paper

...Another famous technique, related to Die-Hellman-type schemes (El Gamal [ 7 ], DSA, McCurley [14], etc.) combines the homomorphic properties of the modular exponentiation and the intractability of extracting discrete logarithms over nite groups....

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4,977 citations

### "Public-key cryptosystems based on c..." refers methods in this paper

...Finally, denoting by h : N 7→ {0, 1}k ⊂ Zn2 a hash function see as a random oracle [2], we obtain a digital signature scheme as follows....

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1,352 citations