Journal of Cryptology
Journal of Algorithms
A course in computational algebraic number theory
A course in computational algebraic number theory
A new public key cryptosystem based on higher residues
CCS '98 Proceedings of the 5th ACM conference on Computer and communications security
Practical multi-candidate election system
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Algorithms for Black-Box Fields and their Application to Cryptography (Extended Abstract)
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Non-interactive Private Auctions
FC '01 Proceedings of the 5th International Conference on Financial Cryptography
Sharing Decryption in the Context of Voting or Lotteries
FC '00 Proceedings of the 4th International Conference on Financial Cryptography
Verifiable secret-ballot elections
Verifiable secret-ballot elections
An Average-Case Analysis of the Gaussian Algorithm for Lattice Reduction
Combinatorics, Probability and Computing
A robust and verifiable cryptographically secure election scheme
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Elliptic curve cryptosystems using curves of smooth order over the ring Zn
IEEE Transactions on Information Theory
Oblivious neural network computing via homomorphic encryption
EURASIP Journal on Information Security
Linear Bandwidth Naccache-Stern Encryption
SCN '08 Proceedings of the 6th international conference on Security and Cryptography for Networks
On the implementation of spread spectrum fingerprinting in asymmetric cryptographic protocol
EURASIP Journal on Information Security
Secure computation with fixed-point numbers
FC'10 Proceedings of the 14th international conference on Financial Cryptography and Data Security
Towards secure bioinformatics services (short paper)
FC'11 Proceedings of the 15th international conference on Financial Cryptography and Data Security
Conversion of real-numbered privacy-preserving problems into the integer domain
ICICS'12 Proceedings of the 14th international conference on Information and Communications Security
Secure computations on non-integer values with applications to privacy-preserving sequence analysis
Information Security Tech. Report
Fault attacks on projective-to-affine coordinates conversion
COSADE'13 Proceedings of the 4th international conference on Constructive Side-Channel Analysis and Secure Design
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In this paper we describe a method to compute with encrypted rational numbers. It is well-known that homomorphic schemes allow calculations with hidden integers, i.e. given integers x and y encrypted in Ɛ(x) and Ɛ(y), one can compute the encrypted sum Ɛ(x + y) or the encrypted product Ɛ(kx) of the encrypted integer x and a known integer k without having to decrypt the terms Ɛ(x) or Ɛ(y). Such cryptosystems have a lot of applications in electronic voting schemes, lottery or in multiparty computation since they allow to keep the privacy of the terms and return the result in encrypted form. However, from a practical point of view, it might be interesting to compute with rationals. For instance, a lot of financial applications require algorithms to compute with rational values instead of integers such as bank accounts, electronic purses in order to make payments or micropayments, or secure spreadsheets. We present here a way to solve this problem using the Paillier cryptosystem which offers the largest bandwidth among all homomorphic schemes. The method uses two-dimensional lattices to recover the numerator and denominator of the rationals. Finally we implement this technique and our results in order to build an encrypted spreadsheet showing the practical possibilities of the homomorphic properties applied on rationals.