Definition ∞ Span programs are a mathematical construct used in cryptography to represent access structures, particularly in secret sharing schemes and attribute-based encryption. They define how subsets of parties can collectively reconstruct a secret, while other subsets cannot. These programs offer a linear algebraic approach to expressing complex access policies.
Context ∞ In advanced cryptographic protocols relevant to digital assets, such as those enabling privacy-preserving transactions or complex access control for decentralized applications, span programs serve as a theoretical underpinning. They are instrumental in designing systems where specific conditions must be met to access or verify information, without revealing the underlying data itself. Research continues to explore their application in constructing more efficient and expressive zero-knowledge proofs and secure multi-party computation.
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