J. Feigenbaum, M. Merritt, Open questions, talk abstracts, and summary of discussions, DIMACS series in discrete mathematics and theoretical computer science, 2 (1991), 1--45.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....time without revealing x or y. The existence of these schemes has been left open. In 1978, Rivest, Adleman, and Dertouzos [19] suggested investigating encryption schemes with additional homomorphic properties since they allow to compute with encrypted data. In 1991, Feigenbaum and Merritt [11] directly addressed algebraic homomorphic schemes of the form stated above. In [5] Boneh and Lipton showed that deterministic algebraically homomorphic encryption schemes over ring ZN can be broken in subexponential time under a (reasonable) number theoretic assumption. In their argument, it is ....

J. Feigenbaum and M. Merritt. Open Questions, Talks Abstracts, and Summary of Discussions. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 2:1-45, 1991.

....and E(y) without revealing x and y. The existence of these schemes has been left open. In 1978 Rivest, Adleman, and Dertouzos [34] suggested investigating encryption schemes with additional homomorphic properties since they allow one to compute with encrypted data. In 1991 Feigenbaum and Merritt [15] questioned directly for algebraic homomorphic schemes [15] in the form stated above. The most interesting case is an algebraic homomorphic encryption scheme over Z=2Z. Such a scheme would allow one to compute arbitrary functions with encrypted data. An algebraic homomorphic encryption scheme ....

....schemes has been left open. In 1978 Rivest, Adleman, and Dertouzos [34] suggested investigating encryption schemes with additional homomorphic properties since they allow one to compute with encrypted data. In 1991 Feigenbaum and Merritt [15] questioned directly for algebraic homomorphic schemes [15] in the form stated above. The most interesting case is an algebraic homomorphic encryption scheme over Z=2Z. Such a scheme would allow one to compute arbitrary functions with encrypted data. An algebraic homomorphic encryption scheme that is additionally inattentive (i.e. where the result of ....

J. Feigenbaum, M. Merritt. Open Questions, Talk Abstracts, and Summary of Discussions. DIMACS Series in Discrete Mathematics and Theoretical Computer Science. v. 2, pages 1--45, 1991.

....Schemes What are the structural requirements of encryption functions that can map one function to another one We start this investigation by looking at systems which enable to do computations on encrypted data. In the beginning of the 90s Feigenbaum and Merritt asked the following question [6]: Is there an encryption function E such that both E(x y) and E(xy) are easy to compute from E(x) and E(y) Encryption functions E : R S for rings R and S having the property stated above are called algebraic homomorphic encryption schemes. Their ability to serve as encryption schemes for ....

....x and y, mixed multiplicatively homomorphic if there is an efficient algorithm MIXED MULT to compute E(xy) from E(x) and y that does not reveal x, algebraically homomorphic if it is additively and multiplicatively homomorphic. 4. 1 Homomorphic Schemes for Computing with Encrypted Data In [6] Feigenbaum and Merritt wonder whether there exist algebraic homomorphic encryption schemes. The reason for this is the following Proposition 2. Algebraic homomorphic one way trapdoor functions E : R S allow non interactive CED for the evaluation of polynomials (resp. algebraic circuits) p 2 ....

J. Feigenbaum and M. Merritt. Open questions, talk abstracts, and summary of discussions. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 2:1--45, 1991.

....Schemes What are the structural requirements of encryption functions that can map one function to another one We start this investigation by looking at systems which enable to do computations on encrypted data. In the beginning of the 90s Feigenbaum and Merritt asked the following question [5]: Is there an encryption function E such that both E(x y) and E(xy) are easy to compute from E(x) and E(y) Encryption functions E : R S for rings R and S having the property stated above are called algebraic homomorphic encryption schemes. Their ability to serve as encryption schemes for ....

....x and y, mixed multiplicatively homomorphic if there is an efficient algorithm MIXED MULT to compute E(xy) from E(x) and y that does not reveal x, algebraically homomorphic if it is additively and multiplicatively homomorphic. 4. 1 Homomorphic Schemes for Computing with Encrypted Data In [5] Feigenbaum and Merritt wonder whether there exist algebraic homomorphic encryption schemes. The reason for this is the following Proposition 2. Algebraic homomorphic one way trapdoor functions E : R S allow non interactive CED for the evaluation of polynomials (resp. algebraic circuits) p 2 ....

J. Feigenbaum and M. Merritt. Open questions, talk abstracts, and summary of discussions. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 2:1--45, 1991.

....together with the encrypted data E(x) and E permits two ecient operations on ciphertexts that are homomorphic to addition and multiplication on the message space, then Bob can without interaction compute E(f(x) and send it back to Alice. Although this has been a prominent open problem for years [16], it is still unknown whether such homomorphic encryption schemes exist. On the one hand, Boneh and Lipton [8] have shown that all such deterministic encryption schemes are insecure; on the other hand, Sander, Young, and Yung [27] propose a scheme that allows the necessary operations on encrypted ....

J. Feigenbaum and M. Merritt, \Open questions, talk abstracts, and summary of discussions," in Distributed Computing and Cryptography, vol. 2 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, AMS, 1991.

....Alice and Bob and thus violates our non interactiveness requirement. Also motivated by the problem of processing encrypted data, Rivest et al. 9] asked in 1978 for encryption schemes having certain additional homomorphic properties. In 1991 Feigenbaum and Merritt asked more specifically [5]: Is there a public key encryption function E such that both E(x y) and E(xy) are easy to compute from E(x) and E(y) It is easy to see that an encryption function having these properties allows to evaluate polynomial expressions in the encrypted data without revealing the input and the result. ....

J. Feigenbaum and M. Merritt. Open questions, talk abstracts, and summary of discussions. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 2:1--45, 1991.

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J. Feigenbaum, M. Merritt, Open questions, talk abstracts, and summary of discussions, DIMACS series in discrete mathematics and theoretical computer science, 2 (1991), 1--45.

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