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Post-Quantum Cryptography & Shor's Algorithm Qubit Simulator (2026)

Execute Shor's quantum period-finding algorithm ($a^r \equiv 1 \pmod N$) step-by-step on toy RSA moduli and calculate logical vs physical surface-code qubits required to break RSA-2048 and ECC P-256.Documentation & FAQs ↓

Post-Quantum Cryptography & Shor's Algorithm Qubit Simulator — Interactive Console
Runs locally in your browser • Instant output
Logical vs Physical Qubits
4,099 Logical Qubits
~20,000,000 Physical (d=27)
Post-Quantum Security
0 bits (Broken in polynomial time O((log N)^3))
2.7 × 10^10 Toffoli gates (~8 hours on Surface Code)
"Harvest Now, Decrypt Later" Risk
CRITICAL (Decryptable by CRQC)
NIST Fix: ML-KEM-768 (FIPS 203) + ML-DSA-65 (FIPS 204)
NIST FIPS 203 (ML-KEM-768) Drop-In Migration Snippet (Nginx & OpenSSH 9.9+)
# Nginx / OpenSSL 3.5+ Post-Quantum Hybrid Key Exchange
ssl_protocols TLSv1.3;
ssl_ecdh_curve X25519MLKEM768:X25519:secp384r1;

# OpenSSH 9.9+ sshd_config (Defends against Harvest-Now-Decrypt-Later)
KexAlgorithms mlkem768x25519-sha256,sntrup761x25519-sha512@openssh.com
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2026 Quick-Reference Cheat Sheet & Benchmark Table: Post-Quantum Cryptography & Shor's Algorithm Qubit Simulator

Quick Answer & 2026 Technical Summary (quantum computing rsa qubit calculator)Updated 2026 Standard

RSA security relies on the hardness of factoring a large semiprime $N = p \times q$. Number theory shows that factoring $N$ can be reduced to finding the even period $r$ of the modular exponentiation function $f(x) = a^x \bmod N$ (such that $a^r \equiv 1 \pmod N$). Once a quantum computer finds $r$ using Quantum Phase Estimation and the Quantum Fourier Transform (QFT), a classical computer immediately extracts the factors via Euclidean $\gcd(a^{r/2} - 1, N)$ and $\gcd(a^{r/2} + 1, N)$. Use this interactive quantum computing rsa qubit calculator above to test shors algorithm simulator online, qubits needed to break rsa 2048, and nist post quantum cryptography ml-kem ml-dsa locally in your browser with zero server uploads.

Target Keyword Spec: quantum computing rsa qubit calculator | Modules: Interactive Shor's Period-Finding ($a^x \bmod N$) Engine • Logical vs Physical Surface-Code Qubit Calculator • Grover's Algorithm vs Symmetric AES-128/256 Analyzer
Primary Focus: quantum computing rsa qubit calculator
Core Capability: shors algorithm simulator online
Privacy Mode: 100% Client-Side (Zero Upload)
Technical Parameter / ModuleStandard / Keyword SpecArchitecture & Validation RuleOperational Use Case (2026)
Interactive Shor's Period-Finding ($a^x \bmod N$) Engineshors algorithm simulator onlinePick a semiprime $N = p \times q$ (15, 21, 33, 35, 55, 77, 91, 143, 221) an...'Harvest Now, Decrypt Later' (HNDL) Threat Modeling
Logical vs Physical Surface-Code Qubit Calculatorqubits needed to break rsa 2048Calculates the $2n + 3$ Beauregard logical qubits, Toffoli gate depth ($O(n...Quantum Computing & Cryptography University Education
Grover's Algorithm vs Symmetric AES-128/256 Analyzernist post quantum cryptography ml-kem ml-dsaDemonstrates why Shor's algorithm devastates asymmetric RSA/ECC (exponentia...Enterprise TLS & PKI Post-Quantum Bandwidth Planning
Tokenizer & Model Architecturetiktoken (o200k_base / cl100k_base) + GGUF1 Token ≈ 0.75 English Words (~4 Chars)Calibrated for 2026 Frontier & Open-Weight LLMs
Context Window & KV Cache Scaling8k / 32k / 128k / 1M+ Token ContextsFP16 vs Q8_0 vs Q4_K_M QuantizationAccounts for FlashAttention & prompt caching
Inference Cost & Throughput MetricUSD per 1M Input / Cached / Output TokensMemory Bandwidth (GB/s) ÷ Model Size (GB)Optimizes self-hosted GPU vs cloud API ROI
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Step-by-Step Workflow

4 Easy Steps
01Phase 1

Select an Algorithm to Audit in the CRQC Qubit Estimator

Pick RSA-2048, RSA-4096, ECC P-256, AES-128, AES-256, or ML-KEM-768 (Kyber) to inspect logical qubits, physical qubits, and quantum resistance status.

02Phase 2

Choose a Semiprime N & Coprime Base a in the Shor's Simulator

Select a composite number $N = p \times q$ (e.g., $N = 15$, $21$, $35$, or $91$) and a coprime base $a$ in the interactive period-finding lab.

03Phase 3

Inspect the Modular Exponentiation Wave & Period r

Trace the repeating sequence of $f(x) = a^x \bmod N$ across $x = 0, 1, 2, \dots$ to see how quantum superposition and QFT isolate the period $r$.

04Phase 4

Review Classical GCD Factor Extraction & NIST PQC Replacements

Verify how $\gcd(a^{r/2} - 1, N)$ and $\gcd(a^{r/2} + 1, N)$ reveal the secret prime factors $p$ and $q$, then review the NIST FIPS 203/204 migration guide.

Real-World Applications

'Harvest Now, Decrypt Later' (HNDL) Threat Modeling

Evaluate whether long-lived confidential data encrypted over classic TLS/RSA/ECDHE must transition immediately to hybrid X25519MLKEM768 key exchange.

Quantum Computing & Cryptography University Education

See exactly how integer factorization reduces to finding the period $r$ of $f(x) = a^x \bmod N$ and why odd periods or $a^{r/2} \equiv -1 \pmod N$ require selecting a new base $a$.

Enterprise TLS & PKI Post-Quantum Bandwidth Planning

Compare the network packet overhead of migrating from 32-byte X25519 keys to 1,184-byte ML-KEM-768 public keys and 3,309-byte ML-DSA-65 signatures.

Related Editorial GuideWhy Quantum Computing Threatens RSA Encryption & NIST Post-Quantum Guide
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