### Table III. Additively Homomorphic Encryption Scheme

### Table 2. Communication efficiency of the homomorphic scheme (for both generic a2

2002

"... In PAGE 13: ... For these special cases, efficiency comparison of the ho- momorphic scheme from Section 5.2 with the Naor-Pinkas-Sumner scheme [NPS99] is presented in Table2 . (For the homomorphic scheme, this table shows the combined total length of a range proof and a range proof in exponents, since both are used in the correctness proof.... In PAGE 13: ... This table also presents two versions of the homomorphic scheme, one that works with a generic a38 and another one which works only with a prime a38 .) As seen from Table2 , if a38a232a185 a217 a112 then the seller-authority interaction in the prime- a38 homomorphic scheme is less than a24a122a112a122a49a141a51a25a53a121a55a122a57 a1 a38 bytes. The prime-a38 homomorphic scheme and the Naor-Pinkas scheme have roughly equal communication complexity for small-scale auctions.... ..."

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### Table 6. Performance Comparison of Additive Homomorphic Cryptosystems Scheme Addition Decryption Bandwidth

2006

"... In PAGE 8: ... The number of 1024-bit mod- ular multiplications will de ne the computational cost of summing ciphertexts at the server and decryption of aggregate values at the client. Table6 shows the comparison of the three homo- morphic cryptosystems. The size of ciphertexts re- ects both the overhead of storage at the server and transmission of aggregate values.... In PAGE 9: ... The size of these tables directly affect the ef ciency of the search in that the larger the tables the faster the search. When deriving the results in Table6 , we assumed aggre- gation of 10,000 20-bit bit values (e.g.... ..."

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### Table 2 Computational complexity in homomorphic encryption Volume One bidder

"... In PAGE 3: ... Therefore, the computation and communication complexity of e-auction based on homomorphic encryption are increased in opening stage. Table2 shows the computational complexity of [CLK03] scheme based on homomorphic encryption. Table 2 Computational complexity in homomorphic encryption Volume One bidder ... ..."

### Table 4. Performance Comparison of Additive Homomorphic Cryptosystems

2006

"... In PAGE 11: ...Table 4. Performance Comparison of Additive Homomorphic Cryptosystems Table4 shows the comparison of the three homomorphic cryptosystems. The size of ciphertexts reflects both the overhead of storage at the server and transmission of aggregate values.... In PAGE 12: ... The size of these tables directly affect the efficiency of the search in that the larger the tables the faster the search. When deriving the results in Table4 , we assumed aggregation of 10,000 20-bit bit values (e.g.... ..."

Cited by 4