The Google engineer racing to make the world's most dangerous algorithm actually runnable

[HollowSentinel]

Craig Gidney, a quantum software engineer at Google Quantum AI, has spent the past several years steadily and repeatedly slashing the estimated hardware resources needed to actually run Shor's algorithm, the quantum algorithm capable of breaking the RSA and elliptic curve cryptography protecting most of the internet's sensitive traffic today. Back in 2019, breaking RSA-2048 encryption was estimated to require roughly 20 million noisy qubits. By 2025, Gidney had published research showing the same task could theoretically be accomplished with less than 1 million qubits running for under a week, a twentyfold reduction achieved without changing the underlying quantum hardware architecture at all, purely through smarter algorithmic and error correction techniques.

The core technical trick behind Gidney's most recent improvements involves approximate modular arithmetic, a method originally developed by researchers Chevignard, Fouque, and Schrottenloher that computes the core exponentiation operation at the heart of Shor's algorithm in smaller pieces rather than requiring one enormous quantum register to hold an entire 2048 bit number at once. Gidney streamlined that approach further and estimated its actual physical cost once real world error correction overhead gets properly accounted for, essentially finding a way to compress how much quantum memory the calculation genuinely needs at any single moment, similar in spirit to how memory compression lets more data get reliably stored in less physical hardware.

Gidney and collaborators have applied similar techniques to elliptic curve cryptography too, the scheme underlying most cryptocurrency and much of the encryption securing everyday internet traffic. Their published resource estimates show 256 bit elliptic curve encryption could theoretically be broken using somewhere between 1,200 and 1,450 logical qubits and between 70 and 90 million Toffoli gates, figures that in one instance were verified using a zero knowledge proof specifically to avoid publishing an actual usable attack blueprint alongside the underlying research findings.

Gidney has been notably candid about the tension built into this kind of research. Publishing improved attack estimates arguably helps push the entire industry to actually take post quantum cryptography migration seriously well before real capability arrives, but each improvement also inches the field closer to knowing exactly how a working attack would need to be built. He has said he now believes openly publishing this kind of resource estimate research, rather than obscuring it behind more complicated proof mechanisms, is ultimately the better strategy, arguing the security benefits of transparency outweigh the costs given how much legitimate defensive planning depends on accurate, trustworthy threat estimates.

No quantum computer capable of actually running Shor's algorithm at this kind of scale exists yet, and Gidney's own estimates suggest current hardware remains a meaningful distance away from the million qubit, low error rate systems these calculations assume. But the steady, repeated downward revision of what's actually required, cut by a factor of twenty in just six years through algorithmic improvement alone, is precisely why organizations tracking post quantum migration timelines increasingly treat Gidney's specific published numbers as one of the most closely watched benchmarks in the entire field, a rare case where the exact person doing the mathematics that could someday break the internet's cryptography is also the same person warning everyone how seriously and how quickly to actually prepare for it

2581592 The Engineer Racing To Run The Worlds Most Dangerous Algorithmwww.newscientist.com

[FairDos47]

A twentyfold reduction in required qubits over just six years purely from algorithmic improvement, with no actual hardware changes involved at all, is a genuinely staggering rate of progress on the theoretical side of this specific problem. Makes we wonder how much further that same number could still realistically fall with a few more years of dedicated research effort behind it

[VB]

The decision to publish openly rather than obscure the findings behind something like a zero knowledge proof is the part of this whole story that actually deserves the most scrutiny and discussion. Gidney's own stated reasoning, that transparency helps drive faster and more serious post quantum migration efforts, makes real logical sense, but it's also exactly the kind of argument someone in his specific position would understandably want to genuinely believe regardless of whether it's fully correct

[Sophie92]

Approximate modular arithmetic as the core trick behind this whole improvement is a great, concrete example of how algorithmic cleverness alone can sometimes matter just as much as raw hardware progress in this field. Everyone tends to focus purely on qubit counts and error rates whenever quantum computing comes up in casual conversation, but the actual math and computer science running on top of that physical hardware matters just as much, if not more, for determining what's genuinely achievable in practice

[Patrick93]

The framing of Shor's algorithm as the world's most dangerous algorithm feels completely earned given just how much of the modern internet's security architecture rests entirely on the specific mathematical assumption that this exact algorithm is trying to systematically undermine. Very few pieces of pure applied mathematics carry genuinely civilization scale stakes quite this directly and quite this concretely

[SuperPosition]

Curious whether these specific resource estimates account properly for realistic physical error rates on actual current hardware platforms, or whether they're still largely idealized, best case theoretical numbers that assume error correction performance considerably better than what real systems can currently reliably achieve in practice. That distinction matters enormously for how urgently organizations should actually be treating these specific published numbers as a genuine planning deadline

[Pat82]

Six years from twenty million qubits down to under one million is honestly a faster pace of theoretical progress than most people working outside quantum computing specifically probably assume is even happening in this field right now. Public perception still seems stuck somewhere around thinking useful quantum computers remain purely distant science fiction, when the actual required resource estimates keep shrinking dramatically and steadily every single year through work exactly like this

[Robin13]

This is exactly the kind of research that should be driving urgency around post quantum cryptography migration timelines specifically, yet it still doesn't seem to have fully broken through into genuinely broad mainstream public awareness the way it probably should have by now given the stakes involved.

Most people have simply never heard of Craig Gidney specifically, despite the fact that his repeated resource estimate revisions arguably represent some of the most consequential, practically relevant research currently happening anywhere in applied cryptography today. The gap between how significant this specific work actually is and how little broad public attention it still receives feels like a real, ongoing communication and outreach failure across the wider field