Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Multiparty unconditionally secure protocols
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Verifiable secret sharing and multiparty protocols with honest majority
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Communication complexity of secure computation (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Perfect Homomorphic Zero-Knowledge Threshold Schemes over any Finite Abelian Group
SIAM Journal on Discrete Mathematics
Universal Hashing and Geometric Codes
Designs, Codes and Cryptography
On the complexity of verifiable secret sharing and multiparty computation
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Tables of curves with many points
Mathematics of Computation
Communications of the ACM
Algebraic-Geometric Codes
Coding Constructions for Blacklisting Problems without Computational Assumptions
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Optimal Black-Box Secret Sharing over Arbitrary Abelian Groups
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Efficient multiparty computations secure against an adaptive adversary
EUROCRYPT'99 Proceedings of the 17th 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
Efficient multi-party computation over rings
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
On codes, matroids and secure multi-party computation from linear secret sharing schemes
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Black-box secret sharing from primitive sets in algebraic number fields
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
A note on authentication codes from algebraic geometry
IEEE Transactions on Information Theory
Constructions of authentication codes from algebraic curves over finite fields
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Zero-knowledge from secure multiparty computation
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Secure Computation from Random Error Correcting Codes
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Atomic Secure Multi-party Multiplication with Low Communication
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Founding Cryptography on Oblivious Transfer --- Efficiently
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Strongly Multiplicative and 3-Multiplicative Linear Secret Sharing Schemes
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Key Predistribution Schemes and One-Time Broadcast Encryption Schemes from Algebraic Geometry Codes
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Strongly multiplicative ramp schemes from high degree rational points on curves
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Isolated proofs of knowledge and isolated zero knowledge
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
OT-combiners via secure computation
TCC'08 Proceedings of the 5th conference on Theory of cryptography
P4P: practical large-scale privacy-preserving distributed computation robust against malicious users
USENIX Security'10 Proceedings of the 19th USENIX conference on Security
Cryptography and Communications
Correlation extractors and their applications
ICITS'11 Proceedings of the 5th international conference on Information theoretic security
Efficient reductions for non-signaling cryptographic primitives
ICITS'11 Proceedings of the 5th international conference on Information theoretic security
P3CA: private anomaly detection across ISP networks
PETS'11 Proceedings of the 11th international conference on Privacy enhancing technologies
Constant-rate oblivious transfer from noisy channels
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
The torsion-limit for algebraic function fields and its application to arithmetic secret sharing
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Perfectly secure multiparty computation and the computational overhead of cryptography
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
On constructing homomorphic encryption schemes from coding theory
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Bilinear complexity of algebras and the Chudnovsky-Chudnovsky interpolation method
Journal of Complexity
Coset bounds for algebraic geometric codes
Finite Fields and Their Applications
On the amortized complexity of zero knowledge protocols for multiplicative relations
ICITS'12 Proceedings of the 6th international conference on Information Theoretic Security
Commitments and efficient zero-knowledge proofs from learning parity with noise
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
A simple combinatorial treatment of constructions and threshold gaps of ramp schemes
Cryptography and Communications
Secret sharing schemes based on graphical codes
Cryptography and Communications
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We introduce algebraic geometric techniques in secret sharing and in secure multi-party computation (MPC) in particular. The main result is a linear secret sharing scheme (LSSS) defined over a finite field ${\mathbb F}_q$, with the following properties. 1. It is ideal. The number of players n can be as large as $\#C({\mathbb F}_q)$, where C is an algebraic curve C of genus g defined over ${\mathbb F}_q$. 2. It is quasi-threshold: it is t-rejecting and t+1+2g-accepting, but not necessarily t+1-accepting. It is thus in particular a ramp scheme. High information rate can be achieved. 3. It has strong multiplication with respect to the t-threshold adversary structure, if $tt-adversary. 4. The finite field ${\mathbb F}_q$ can be dramatically smaller than n. This is by using algebraic curves with many ${\mathbb F}_q$-rational points. For example, for each small enough ε, there is a finite field ${\mathbb F}_q$ such that for infinitely many n there is an LSSS over ${\mathbb F}_q$ with strong multiplication satisfying $(\frac{1}{3}- \epsilon) n\leq t 5. Shamir's scheme, which requires nq and which has strong multiplication for $tg=0. Now consider the classical (“BGW”) scenario of MPC unconditionally secure (with zero error probability) against an active t-adversary with $tn-player network with secure channels. By known results it now follows that there exist MPC protocols in this scenario, achieving the same communication complexities in terms of the number of field elements exchanged in the network compared with known Shamir-based solutions. However, in return for decreasing corruption tolerance by a small ε-fraction, q may be dramatically smaller than n. This tolerance decrease is unavoidable due to properties of MDS codes. The techniques extend to other models of MPC. Results on less specialized LSSS can be obtained from more general coding theory arguments.