A public key cryptosystem and a signature scheme based on discrete logarithms
Proceedings of CRYPTO 84 on Advances in cryptology
Oblivious transfer and polynomial evaluation
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Modern computer algebra
Communications of the ACM
Breaking the O(n1/(2k-1)) Barrier for Information-Theoretic Private Information Retrieval
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Privacy Preserving Data Mining
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Oblivious Polynomial Evaluation and Oblivious Neural Learning
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Oblivious Polynomial Evaluation
SIAM Journal on Computing
Constructions of truly practical secure protocols using standardsmartcards
Proceedings of the 15th ACM conference on Computer and communications security
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
Efficient Robust Private Set Intersection
ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Fast secure computation of set intersection
SCN'10 Proceedings of the 7th international conference on Security and cryptography for networks
Efficient and secure evaluation of multivariate polynomials and applications
ACNS'10 Proceedings of the 8th international conference on Applied cryptography and network security
(If) size matters: size-hiding private set intersection
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
Secure efficient multiparty computing of multivariate polynomials and applications
ACNS'11 Proceedings of the 9th international conference on Applied cryptography and network security
Keyword search and oblivious pseudorandom functions
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Privacy-preserving set operations
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Practical private set intersection protocols with linear complexity
FC'10 Proceedings of the 14th international conference on Financial Cryptography and Data Security
Efficient set operations in the presence of malicious adversaries
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Efficient polynomial operations in the shared-coefficients setting
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
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In this paper, we explore fast algorithms for computing on encrypted polynomials. More specifically, we describe efficient algorithms for computing the Discrete Fourier Transform, multiplication, division, and multipoint evaluation on encrypted polynomials. The encryption scheme we use needs to be additively homomorphic, with a plaintext domain that contains appropriate primitive roots of unity. We show that some modifications to the key generation setups and working with variants of the original hardness assumptions one can adapt the existing homomorphic encryption schemes to work in our algorithms. The above set of algorithms on encrypted polynomials are useful building blocks for the design of secure computation protocols. We demonstrate their usefulness by utilizing them to solve two problems from the literature, namely the oblivious polynomial evaluation (OPE) and the private set intersection but expect the techniques to be applicable to other problems as well.