Generalized secret sharing and monotone functions
CRYPTO '88 Proceedings on Advances in cryptology
Elements of information theory
Elements of information theory
How to share a function securely
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Perfect Homomorphic Zero-Knowledge Threshold Schemes over any Finite Abelian Group
SIAM Journal on Discrete Mathematics
Existence of multiplicative secret sharing schemes with polynomial share expansion
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Communications of the ACM
A Comment on the Efficiency of Secret Sharing Scheme over Any Finite Abelian Group
ACISP '98 Proceedings of the Third Australasian Conference on Information Security and Privacy
Randomness Required for Linear Threshold Sharing Schemes Defined over Any Finite Abelian Group
ACISP '01 Proceedings of the 6th Australasian Conference on Information Security and Privacy
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
A Construction of Practical Secret Sharing Schemes using Linear Block Codes
ASIACRYPT '92 Proceedings of the Workshop on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Multiplicative Non-abelian Sharing Schemes and their Application to Threshold Cryptography
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
Optimal-resilience proactive public-key cryptosystems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Some results in linear secret sharing
Some results in linear secret sharing
Efficient multiplicative sharing schemes
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Practical threshold signatures
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
General secure multi-party computation from any linear secret-sharing scheme
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
On Unconditionally Secure Distributed Oblivious Transfer
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
Non-interactive Distributed-Verifier Proofs and Proving Relations among Commitments
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Span-program-based quantum algorithm for evaluating formulas
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Revisiting the Karnin, Greene and Hellman Bounds
ICITS '08 Proceedings of the 3rd international conference on Information Theoretic Security
Secure Arithmetic Computation with No Honest Majority
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Efficient multi-party computation over rings
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
An efficient group-based secret sharing scheme
ISPEC'11 Proceedings of the 7th international conference on Information security practice and experience
An efficient implementation of a threshold RSA signature scheme
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
CISC'05 Proceedings of the First SKLOIS conference on Information Security and Cryptology
On the size of monotone span programs
SCN'04 Proceedings of the 4th international conference on Security in Communication Networks
Black-box secret sharing from primitive sets in algebraic number fields
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Visual cryptographic protocols using the trusted initializer
ICICS'05 Proceedings of the 7th international conference on Information and Communications Security
Algebraic geometric secret sharing schemes and secure multi-party computations over small fields
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Linear integer secret sharing and distributed exponentiation
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Proactive verifiable linear integer secret sharing scheme
ICICS'09 Proceedings of the 11th international conference on Information and Communications Security
A generalization and a variant of two threshold cryptosystems based on factoring
ISC'07 Proceedings of the 10th international conference on Information Security
Efficient integer span program for hierarchical threshold access structure
Information Processing Letters
Hi-index | 0.00 |
A black-box secret sharing scheme for the threshold access structure Tt,n is one which works over any finite Abelian group G. Briefly, such a scheme differs from an ordinary linear secret sharing scheme (over, say, a given finite field) in that distribution matrix and reconstruction vectors are defined over Z and are designed independently of the group G from which the secret and the shares are sampled. This means that perfect completeness and perfect privacy are guaranteed regardless of which group G is chosen. We define the black-box secret sharing problem as the problem of devising, for an arbitrary given Tt,n, a scheme with minimal expansion factor, i.e., where the length of the full vector of shares divided by the number of players n is minimal.Such schemes are relevant for instance in the context of distributed cryptosystems based on groups with secret or hard to compute group order. A recent example is secure general multi-party computation over black-box rings.In 1994 Desmedt and Frankel have proposed an elegant approach to the black-box secret sharing problem based in part on polynomial interpolation over cyclotomic number fields. For arbitrary given Tt,n with O t n - 1, the expansion factor of their scheme is O(n). This is the best previous general approach to the problem.Using certain low degree integral extensions of Z over which there exist pairs of sufficiently large Vandermonde matrices with co-prime determinants, we construct, for arbitrary given Tt,n with O t n - 1, a black-box secret sharing scheme with expansion factor O(log n), which we show is minimal.