Definition ∞ Unknown order in cryptography refers to a mathematical group whose order, or the number of elements it contains, is not publicly known. Cryptographic schemes built upon groups of unknown order often derive their security from the computational difficulty of factoring large numbers. This property is used in certain zero-knowledge proofs and other advanced cryptographic constructions. It complicates attacks that rely on knowing the group’s structure.
Context ∞ Cryptographic systems relying on groups of unknown order are a subject of ongoing research, particularly in the context of privacy-preserving technologies and secure multi-party computation. Discussions often concern the trade-offs between the security assurances provided by unknown order groups and the computational efficiency of operations within them. Future developments will likely involve exploring new constructions and practical applications that effectively leverage the security properties of these mathematical structures.
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