Today's security is built on a number-theory bet
Every time a browser shows a padlock, a bank moves money, or a phone checks a software update, it relies on public-key cryptography. The two systems in near-universal use, RSA and elliptic-curve cryptography (ECC), are secure for exactly one reason: they are built on arithmetic problems that are easy to state but, as far as anyone knows, extraordinarily hard to reverse.
RSA rests on integer factorization. Multiplying two large primes together is fast; recovering those primes from the product is believed to be infeasible for numbers of a few thousand bits. ECC rests on the discrete logarithm problem, a cousin of factorization set on an elliptic curve. In both cases the security guarantee is not a law of physics, it is a bet that a certain number-theoretic problem has no efficient solution.
The confidentiality of the modern world is a wager on the difficulty of two questions about whole numbers: how do you factor a large integer, and how do you invert a discrete exponential? Change the answer to those questions and you change the security of everything built on top of them.
The quantum threat: Shor's algorithm
In 1994 the mathematician Peter Shor showed that a sufficiently large quantum computer could factor integers and compute discrete logarithms not merely faster, but exponentially faster, than any known classical method. Shor's algorithm turns the two hard problems underpinning RSA and ECC into problems a quantum machine can solve in practical time.
No quantum computer today is large or stable enough to run Shor's algorithm against real cryptographic key sizes. But the machines are improving, and the mathematics is not in doubt: the moment a "cryptographically relevant" quantum computer exists, RSA and ECC stop being secure. The threat is not that the number theory was wrong, it is that a new kind of computer can win the bet.
Why the deadline is already here: "harvest now, decrypt later"
A natural reaction is: if the quantum computer does not exist yet, why hurry? The answer is a strategy known as harvest now, decrypt later (HNDL). An adversary does not need a quantum computer today to benefit from one tomorrow. It can copy and store encrypted traffic now, then decrypt the archive once the hardware matures.
For data whose secrecy must last decades, medical records, state secrets, intellectual property, financial and biometric data, the clock has effectively already run out. Anything encrypted today with RSA or ECC and intercepted today could be exposed the day a capable quantum computer arrives. That is why migration cannot wait for the threat to become concrete.
The 2026 US mandate
On 22 June 2026, President Donald Trump signed two executive orders on quantum technology. One, Ushering in the Next Frontier of Quantum Innovation, funds the technology itself. The other, Securing the Nation Against Advanced Cryptographic Attacks (Executive Order 14412), addresses the defensive side: replacing vulnerable cryptography across the federal government.
The order sets concrete deadlines. Federal agencies must move their most sensitive systems to post-quantum encryption by 31 December 2030, and to post-quantum authentication by 31 December 2031. Federal contractors must comply with the post-quantum federal standards by the end of 2030, and the Department of Commerce is to run a migration pilot completed by 31 December 2027. The orders build on the previous administration's National Security Memorandum 10, which had targeted 2035, and compress that timeline substantially.
A government does not legislate deadlines for a mathematical migration unless the underlying problem is considered real, near, and expensive to ignore. The dates are a policy statement that the number-theoretic assumption behind current cryptography can no longer be assumed to hold for the lifetime of today's secrets.
The replacement: new hard problems
Post-quantum cryptography (PQC) does not use quantum computers. It is ordinary software that runs on ordinary machines, built on different mathematical problems, ones with no known efficient quantum attack. After a multi-year public competition, the US National Institute of Standards and Technology (NIST) published its first standards in August 2024:
203ML-KEM (FIPS 203)
204ML-DSA (FIPS 204)
205SLH-DSA (FIPS 205)
The strategy is deliberate diversity. Lattice problems provide efficient, general-purpose replacements; hash-based signatures provide a fallback that does not share the same assumptions, so that a future break in one family does not break everything at once.
Why this sits on a number-theory site
The Tesfa Grid programme studies the hidden structure of the primes, the same objects RSA is built from. The post-quantum transition is, at heart, a story about number theory meeting its limits: a security guarantee written in the language of integer factorization is being retired because a new machine can read that language too well, and it is being replaced by guarantees written in the language of lattices and hash functions.
Understanding why a problem is hard, and whether that hardness is durable, is number-theoretic and geometric work. The migration underway is the largest practical demonstration in a generation that the difficulty of arithmetic problems is not an abstraction. It is infrastructure.
In one paragraph
Modern encryption is secure because factoring large numbers and inverting discrete exponentials are hard. Shor's algorithm lets a large quantum computer do both easily, and because adversaries can store encrypted data now to decrypt later, the risk is present-tense. In June 2026 the US mandated a move to post-quantum cryptography, algorithms based on lattice and hash problems (NIST FIPS 203, 204, 205) with no known quantum attack, on a timeline running to 2030–2031. The whole episode is a number-theoretic bet being re-placed on new ground.
Executive Order 14412 — Securing the Nation Against Advanced Cryptographic Attacks (The White House, June 2026)
NIST FIPS 203 (ML-KEM), FIPS 204 (ML-DSA), and FIPS 205 (SLH-DSA) — the finalized post-quantum standards
Background: What post-quantum means for cyber-security (PQShield)