Why quantum computers threaten cryptography and why migration to PQC has begun

【Article Title】 Why quantum computers threaten cryptography and why migration to PQC has begun 【Article Body】 AI TRANSLATION This article is an AI-generated translation of the original Japanese article. For the authoritative version, please refer to the original. Read the original Japanese article → (https://quantumindex.jp/quantum-computing-threat-encryption-pqc-transition/) Quantum computers have not yet broken RSA-2048. Even so, the world has already begun transitioning to the “next cryptography.” Why prepare now for a threat that has not yet materialized? You don’t need deep expertise in cryptography or quantum mechanics to read this article. It’s enough to know that prime numbers are numbers like 2, 3, 5, 7, 11… that are divisible only by 1 and themselves, and that prime factorization means expressing an integer as a product of primes—for example, 21 = 3 × 7. Now, think about this briefly. If you factor 3233, what two numbers multiply to make it? The answer is, 3233 = 53 × 61 . It’s easy to multiply 53 × 61 to get 3233. But given only 3233, finding 53 and 61 is a bit more tedious. RSA, a widely used public-key cryptosystem, roughly exploits this asymmetry. Still, saying “factorization is hard, so it becomes encryption” can be hard to grasp. What RSA aims to achieve is a scheme where anyone can lock (encrypt) something, but only the intended recipient can unlock (decrypt) it. Imagine a padlock. If you distribute the open padlock to the world, anyone can use it to lock a box addressed to you. But only you hold the key that opens that closed padlock. The RSA public key is like that “padlock anyone can use.” For example, choose secret primes 53 and 61, and 53 × 61 = 3233 is computed. 3233 can be made public. The person who knows 53 and 61 can use them to construct the private key. An outsider trying to reach the same secret from 3233 must find the original 53 and 61. With a small number like 3233 that’s possible. But RSA-2048 uses integers as large as 617 decimal digits. That is where RSA’s strength lies. So do quantum computers simply try dividing a 617-digit number at crazy speed one-by-one? No. In 1994 Peter Shor published Shor’s algorithm, which transforms factorization into a problem of finding a period (a periodicity). A quantum computer is used not to accelerate brute force but to efficiently extract that period. The important point is that for factoring very large integers—an extremely hard problem for classical computers—efficient quantum algorithms are already known. The issue is not limited to RSA. Elliptic curve cryptography (ECC), widely used today, relies on a different mathematical hardness than RSA, but it is also vulnerable to Shor’s algorithm. In September 2026, IonQ published a fault-tolerant resource estimate for breaking the 256-bit elliptic curve secp256k1 used in Bitcoin and other systems, assuming a future fault-tolerant quantum computerfault-tolerant quantum computerFTQC / Fault-Tolerant Quantum Computing / FTQCA method for future large-scale quantum computing that uses quantum error correction to allow correct computation to continue even when physical errors occur.QI NoteA demonstration of quantum error correction is not the same as realizing FTQC. Logical error rates, the number of physical qubits required, logical gate performance, and so on are important.. The estimate indicated it would require 19,397 physical qubitsphysical qubitsPhysical Qubit / Physical QubitIndividual qubits that are physically created and manipulated on a quantum processor. They are also used to form logical qubits.QI NoteA large number of physical qubits does not by itself indicate practical computational capability. Error rates, connectivity, and the number of physical qubits required per logical qubit are also important., 1,457 logical qubitslogical qubitsLogical Qubit / Logical QubitA unit of information treated as a single qubit protected from errors by using multiple physical qubits and quantum error correction.QI NoteSimply having “created a logical qubit” does not necessarily mean fault-tolerant quantum computing (FTQC) has been achieved. One should verify logical error rates, operational/gate performance, and scalability., and 39 million Toffoli gates, with a runtime of 25.7 days. This did not mean IonQ actually broke Bitcoin’s cryptography; it was an estimate assuming a future quantum computer. (quantumindex.jp (https://en.quantumindex.jp/ionq-secp256k1-fault-tolerant-resource-estimate/)) Still, you can see that talk of “quantum computers can break cryptography” has progressed to the point where required qubitqubitQubit / Quantum Bit / QubitThe basic unit of information in a quantum computer. It can represent not only 0 or 1 but also a quantum state that is a superposition of them.QI NoteHaving more qubits does not necessarily mean higher performance. Error rates, connectivity, coherence time, and the number of logical qubits are also important. counts and operation counts are being debated. Many proposed quantum applications still lack clear proof of real advantage over classical computingclassical computingClassical Computing / Classical Computation / Classical Computing / Classical ComputationA computation method that uses bits of 0 and 1; the form of computation performed by the computers commonly used today.QI NoteUsed as a point of comparison with quantum computing, but it can encompass CPUs, GPUs, supercomputers, and specialized algorithms, so care should be taken about the conditions of comparison.. Cryptography is a somewhat different case. We are not searching for an application. The thing to be broken already exists. If those quantum computers do not yet exist, why not just wait until they’re completed and then switch cryptography? The issue here is time. The day encryption is broken lies in the future. Yet the data that will be read then may already be being stolen today. Attackers can store encrypted communications now and, once sufficiently powerful quantum computers appear, decrypt them later. This practice is called Harvest Now, Decrypt Later (HNDL). This is particularly problematic for long-lived sensitive data such as diplomatic and defense communications, trade secrets, and medical records. Moreover, replacing cryptographic systems themselves takes time. Cryptography is embedded in many parts of society—not only web browsers and servers but also communications equipment, operating systems, certificates, authentication infrastructure, and embedded devices. NIST notes that historically it can take 10–20 years from standardizing a new cryptographic algorithm until it becomes widely adopted. That is why the transition to post-quantum cryptographypost-quantum cryptography耐量子計算機暗号 / Post-Quantum Cryptography / PQCCryptographic techniques designed to be resistant to attacks by quantum computers. Schemes that can be used on conventional (classical) computers are the primary focus.QI NotePQC is not a technology that uses quantum communication; it is a class of cryptographic schemes that can be deployed in existing communications and computing environments. In news coverage, it is important to distinguish whether a scheme has been standardized and how far implementations and migrations have progressed. (PQC) is underway. Although PQC includes “quantum” in its name, it is not cryptography that uses quantum computers. PQC uses mathematical problems for which no efficient quantum algorithms are known and that run on conventional computers. In 2024, NIST formally announced ML-KEM, ML-DSA, and SLH-DSA as its initial PQC standards. An alternative approach to quantum-era security is QKDQKDQuantum Key Distribution / Quantum Key Distribution / QKDA technology that uses properties of quantum mechanics to securely share secret keys used for encrypted communications with a remote party. It is characterized by the ability to detect attempts at eavesdropping.QI NoteQKD itself does not encrypt data; it is a mechanism for sharing cryptographic keys. When evaluating practicality, attention should be paid to communication distance, key generation rate, and methods for connecting to existing networks., which uses quantum states to share keys. In September 2026, IonQ and Congruity360 announced an $8.18 million agreement to combine PQC and QKD for enterprise data protection. (quantumindex.jp (https://en.quantumindex.jp/ionq-congruity360-quantum-security-agreement/)) The critical point is that the shift to new cryptography did not begin because quantum computers have already broken existing systems. It began because the mathematical vulnerability is known, the data that must be protected already exists, and replacing cryptographic infrastructure can take a decade or more. That is precisely why we must replace cryptography before it is broken. NETWORKSee industry networks around quantum companies → (/qi-network/) Related articles • IonQ, Congruity360 sign $8.18M quantum security agreement to deploy PQC and QKD for enterprise data protection (https://en.quantumindex.jp/ionq-congruity360-quantum-security-agreement/) • IonQ provides fault-tolerant resource estimate for secp256k1 decryption via Shor’s algorithm: 19,397 physical qubits, 25.7 days (https://en.quantumindex.jp/ionq-secp256k1-fault-tolerant-resource-estimate/) • Pasqal and KACST launch multi-year collaboration on quantum-safe cryptography in Saudi Arabia (https://en.quantumindex.jp/pasqal-kacst-quantum-safe-cryptography-collaboration/) If you found this article useful, please consider sharing it. ──────────────────── 【AI Evaluation Request】 Evaluate the following article critically, not based on the quality of its writing, but on its **original informational value as a specialist publication**. 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Quantum computers have not yet broken RSA-2048.

Even so, the world has already begun transitioning to the “next cryptography.”

Why prepare now for a threat that has not yet materialized?

You don’t need deep expertise in cryptography or quantum mechanics to read this article.

It’s enough to know that prime numbers are numbers like 2, 3, 5, 7, 11… that are divisible only by 1 and themselves, and that prime factorization means expressing an integer as a product of primes—for example, 21 = 3 × 7.

Now, think about this briefly.

If you factor 3233, what two numbers multiply to make it?

The answer is,

3233 = 53 × 61

.

It’s easy to multiply 53 × 61 to get 3233. But given only 3233, finding 53 and 61 is a bit more tedious.

RSA, a widely used public-key cryptosystem, roughly exploits this asymmetry.

Still, saying “factorization is hard, so it becomes encryption” can be hard to grasp.

What RSA aims to achieve is a scheme where anyone can lock (encrypt) something, but only the intended recipient can unlock (decrypt) it.

Imagine a padlock. If you distribute the open padlock to the world, anyone can use it to lock a box addressed to you. But only you hold the key that opens that closed padlock.

The RSA public key is like that “padlock anyone can use.”

For example, choose secret primes 53 and 61, and

53 × 61 = 3233

is computed. 3233 can be made public.

The person who knows 53 and 61 can use them to construct the private key. An outsider trying to reach the same secret from 3233 must find the original 53 and 61.

With a small number like 3233 that’s possible. But RSA-2048 uses integers as large as 617 decimal digits.

That is where RSA’s strength lies.

So do quantum computers simply try dividing a 617-digit number at crazy speed one-by-one?

No.

In 1994 Peter Shor published Shor’s algorithm, which transforms factorization into a problem of finding a period (a periodicity). A quantum computer is used not to accelerate brute force but to efficiently extract that period.

The important point is that for factoring very large integers—an extremely hard problem for classical computers—efficient quantum algorithms are already known.

The issue is not limited to RSA.

Elliptic curve cryptography (ECC), widely used today, relies on a different mathematical hardness than RSA, but it is also vulnerable to Shor’s algorithm.

In September 2026, IonQ published a fault-tolerant resource estimate for breaking the 256-bit elliptic curve secp256k1 used in Bitcoin and other systems, assuming a future fault-tolerant quantum computerfault-tolerant quantum computerFTQC / Fault-Tolerant Quantum Computing / FTQCA method for future large-scale quantum computing that uses quantum error correction to allow correct computation to continue even when physical errors occur.QI NoteA demonstration of quantum error correction is not the same as realizing FTQC. Logical error rates, the number of physical qubits required, logical gate performance, and so on are important..

The estimate indicated it would require 19,397 physical qubitsphysical qubitsPhysical Qubit / Physical QubitIndividual qubits that are physically created and manipulated on a quantum processor. They are also used to form logical qubits.QI NoteA large number of physical qubits does not by itself indicate practical computational capability. Error rates, connectivity, and the number of physical qubits required per logical qubit are also important., 1,457 logical qubitslogical qubitsLogical Qubit / Logical QubitA unit of information treated as a single qubit protected from errors by using multiple physical qubits and quantum error correction.QI NoteSimply having “created a logical qubit” does not necessarily mean fault-tolerant quantum computing (FTQC) has been achieved. One should verify logical error rates, operational/gate performance, and scalability., and 39 million Toffoli gates, with a runtime of 25.7 days. This did not mean IonQ actually broke Bitcoin’s cryptography; it was an estimate assuming a future quantum computer. (quantumindex.jp)

Still, you can see that talk of “quantum computers can break cryptography” has progressed to the point where required qubitqubitQubit / Quantum Bit / QubitThe basic unit of information in a quantum computer. It can represent not only 0 or 1 but also a quantum state that is a superposition of them.QI NoteHaving more qubits does not necessarily mean higher performance. Error rates, connectivity, coherence time, and the number of logical qubits are also important. counts and operation counts are being debated.

Many proposed quantum applications still lack clear proof of real advantage over classical computingclassical computingClassical Computing / Classical Computation / Classical Computing / Classical ComputationA computation method that uses bits of 0 and 1; the form of computation performed by the computers commonly used today.QI NoteUsed as a point of comparison with quantum computing, but it can encompass CPUs, GPUs, supercomputers, and specialized algorithms, so care should be taken about the conditions of comparison..

Cryptography is a somewhat different case.

We are not searching for an application. The thing to be broken already exists.

If those quantum computers do not yet exist, why not just wait until they’re completed and then switch cryptography?

The issue here is time.

The day encryption is broken lies in the future. Yet the data that will be read then may already be being stolen today.

Attackers can store encrypted communications now and, once sufficiently powerful quantum computers appear, decrypt them later.

This practice is called Harvest Now, Decrypt Later (HNDL).

This is particularly problematic for long-lived sensitive data such as diplomatic and defense communications, trade secrets, and medical records.

Moreover, replacing cryptographic systems themselves takes time.

Cryptography is embedded in many parts of society—not only web browsers and servers but also communications equipment, operating systems, certificates, authentication infrastructure, and embedded devices.

NIST notes that historically it can take 10–20 years from standardizing a new cryptographic algorithm until it becomes widely adopted.

That is why the transition to post-quantum cryptographypost-quantum cryptography耐量子計算機暗号 / Post-Quantum Cryptography / PQCCryptographic techniques designed to be resistant to attacks by quantum computers. Schemes that can be used on conventional (classical) computers are the primary focus.QI NotePQC is not a technology that uses quantum communication; it is a class of cryptographic schemes that can be deployed in existing communications and computing environments. In news coverage, it is important to distinguish whether a scheme has been standardized and how far implementations and migrations have progressed. (PQC) is underway.

Although PQC includes “quantum” in its name, it is not cryptography that uses quantum computers. PQC uses mathematical problems for which no efficient quantum algorithms are known and that run on conventional computers.

In 2024, NIST formally announced ML-KEM, ML-DSA, and SLH-DSA as its initial PQC standards.

An alternative approach to quantum-era security is QKDQKDQuantum Key Distribution / Quantum Key Distribution / QKDA technology that uses properties of quantum mechanics to securely share secret keys used for encrypted communications with a remote party. It is characterized by the ability to detect attempts at eavesdropping.QI NoteQKD itself does not encrypt data; it is a mechanism for sharing cryptographic keys. When evaluating practicality, attention should be paid to communication distance, key generation rate, and methods for connecting to existing networks., which uses quantum states to share keys. In September 2026, IonQ and Congruity360 announced an $8.18 million agreement to combine PQC and QKD for enterprise data protection. (quantumindex.jp)

The critical point is that the shift to new cryptography did not begin because quantum computers have already broken existing systems. It began because the mathematical vulnerability is known, the data that must be protected already exists, and replacing cryptographic infrastructure can take a decade or more. That is precisely why we must replace cryptography before it is broken.

NETWORKSee industry networks around quantum companies →

Related articles

• IonQ, Congruity360 sign $8.18M quantum security agreement to deploy PQC and QKD for enterprise data protection
• IonQ provides fault-tolerant resource estimate for secp256k1 decryption via Shor’s algorithm: 19,397 physical qubits, 25.7 days
• Pasqal and KACST launch multi-year collaboration on quantum-safe cryptography in Saudi Arabia