From the linked discussion (in which the withdrawal was announced) [0]:
Dear Colleagues,
This is a historic moment in cryptology: AI has beaten humans at cryptanalysis. We would like to share a few thoughts with the PQC community based on our own experience.
There are other dimension-reduction attacks on HAWK in literature. At Eurocrypt 2026, we proposed a dimension-halving algorithm for quaternion Ideal-SVP, which potentially implies that HAWK-n key recovery can be reduced to (cyclotomic) Ideal-SVP in dimension n:
However, one of these heuristics was soon found to be invalid by colleagues with the assistance of AI.
Apparently, we were outpaced by AI in both cases. A couple of lessons we have learned are: (a) humans can make mistakes; and (b) humans are slower than AI. Beyond cryptanalysis itself, the use of AI to check mathematical proofs is becoming an increasingly serious issue.
One can even imagine a crisis in cryptography: in the worst-case scenario, all human-designed cryptosystems are broken by AI. Whether or not that happens, a new era—Post-AI Cryptography—has arrived.
From the linked discussion (in which the withdrawal was announced) [0]:
Dear Colleagues,
This is a historic moment in cryptology: AI has beaten humans at cryptanalysis. We would like to share a few thoughts with the PQC community based on our own experience.
There are other dimension-reduction attacks on HAWK in literature. At Eurocrypt 2026, we proposed a dimension-halving algorithm for quaternion Ideal-SVP, which potentially implies that HAWK-n key recovery can be reduced to (cyclotomic) Ideal-SVP in dimension n:
https://eprint.iacr.org/2025/1448
Later, we proposed another guessing attack based on advanced number theory, under a few heuristic assumptions:
https://eprint.iacr.org/2026/1318
However, one of these heuristics was soon found to be invalid by colleagues with the assistance of AI.
Apparently, we were outpaced by AI in both cases. A couple of lessons we have learned are: (a) humans can make mistakes; and (b) humans are slower than AI. Beyond cryptanalysis itself, the use of AI to check mathematical proofs is becoming an increasingly serious issue.
One can even imagine a crisis in cryptography: in the worst-case scenario, all human-designed cryptosystems are broken by AI. Whether or not that happens, a new era—Post-AI Cryptography—has arrived.
Cong Ling
[0] https://groups.google.com/a/list.nist.gov/g/pqc-forum/c/2r2u...