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Universidad de los Andes

Academic institutionsouthamerica · co
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Selected work

Representative Papers

Optimal Small Set Expanders and Their Codes

Jun 22, 2026

This work investigates the optimal expansion properties of left-regular bipartite graphs over small vertex subsets. By leveraging combinatorial characteristics such as girth, it provides the first complete characterization of s-optimal small-set expanders, proving their existence for all values of s and establishing a transitive lower bound on neighborhood size for larger sets. Building on this theoretical foundation, the paper constructs efficient error-correcting codes tailored for post-quantum key exchange, simultaneously enhancing both small-set expansion performance and coding-based security. The approach integrates techniques from extremal graph theory, expander graph theory, and code construction, offering both theoretical novelty and practical relevance to cryptographic applications.

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Latest Papers

Optimal Small Set Expanders and Their Codes

Jun 22, 2026

This work investigates the optimal expansion properties of left-regular bipartite graphs over small vertex subsets. By leveraging combinatorial characteristics such as girth, it provides the first complete characterization of s-optimal small-set expanders, proving their existence for all values of s and establishing a transitive lower bound on neighborhood size for larger sets. Building on this theoretical foundation, the paper constructs efficient error-correcting codes tailored for post-quantum key exchange, simultaneously enhancing both small-set expansion performance and coding-based security. The approach integrates techniques from extremal graph theory, expander graph theory, and code construction, offering both theoretical novelty and practical relevance to cryptographic applications.

0 citationsRead paper