Growing-degree improvements to the lifting attack

Definitions and mathematical statement

The elliptic-curve discrete-logarithm problem takes points $P,Q$ on $E/\mathbb F_q$, with $P$ of known finite order $r$ and $Q\in\langle P\rangle$, and asks for $a\in\mathbb Z/r\mathbb Z$ such that $Q=aP$.

The source asks whether its lifting attack can be improved by permitting the degree $d=[K:\mathbb Q]$ of an auxiliary number field to grow. A typical lifting framework chooses a number field with a prime whose residue field supports the finite-field curve and lifts relevant geometric/arithmetic data. The precise Huang--Raskind-style construction and the role of Shafarevich--Tate arithmetic are not provided, so no specific lift existence or attack formula is asserted.

Determine whether a nonconstant choice of $d$ as the problem parameters grow gives a genuine improvement over the intended fixed-degree method. A comparison must specify the baseline complexity and success probability and include the cost of representing and constructing $K$, its arithmetic, discriminant/height growth, and every remaining attack phase. Allowing uncounted higher-degree arithmetic is not an algorithmic improvement. The source does not prescribe a degree-growth regime, computational model, heuristic/conditional assumptions, or even the exact baseline lifting algorithm, so no numerical speedup threshold can be formalized from the record alone.

Short English statement

Can growing the auxiliary number-field degree improve the source's elliptic-curve discrete-log lifting attack after all field-construction and arithmetic costs are counted? The attack details and comparison baseline are missing.

Sources

• Ming-Deh Huang, IPAM Workshop on Number Theory and Cryptography --- Open Problems (2006), attachment 6673, PDF page 9, schedule source https://www.ipam.ucla.edu/programs/workshops/workshop-i-number-theory-and-cryptography-open-problems/?tab=schedule; accessed 2026-07-29. The supplied provenance records a PDF/legacy-PPT visual audit.
• Huang--Raskind-style lifting and Shafarevich--Tate methods are named in the supplied summary without a full publication citation or exact attack statement.
• Local registry data/unsolvedmath/problems.json, permanent UnsolvedMath ID $8800093$, source code catalogue entry, Growing-degree improvements to the lifting attack. Dataset attribution: Ulam AI and the UnsolvedMath Contributors.