Cryptographic & Combinatorial Hardness Problems

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Abstractions about computationally hard problems and structured combinatorial objects, covering cryptographic hardness assumptions (Diffie-Hellman Problem, Short Integer Solution Problem), number-theoretic representability questions (Sums of Three Cubes), and interpolation or matrix structures like Newton Polynomial and Supnick Matrix.

5 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Diffie–Hellman problem — Compute the shared exponentiation result from two public powers in a specified cyclic group.
• Newton Polynomial — An interpolating polynomial expressed in a nested Newton basis with divided-difference coefficients at distinct nodes.
• Short Integer Solution Problem — Find a nonzero short integer vector in a stated matrix's modular kernel.
• Sums of three cubes — Integer representability by three signed cubes, subject to a modulo-nine obstruction.
• Supnick Matrix — A symmetric square Monge matrix, under a stated diagonal convention, with ordered quadrangle inequalities.