Profil de Moonax | Binance Square

·

--

Voir la traduction

shots algorithmShor’s algorithm, developed by Peter Shor in 1994, is a quantum algorithm that factors large integers into their prime factors exponentially faster than the best known classical algorithms. This makes it a major threat to RSA encryption (and similar systems like ECDSA in crypto), since breaking large composites is the security foundation of those schemes. Why It Matters in Crypto Factoring a 2048-bit RSA modulus classically takes enormous time (sub-exponential but impractical). Shor’s algorithm runs in polynomial time — roughly O((log N)³) operations — so a sufficiently large, fault-tolerant quantum computer could break current public-key crypto in hours or days. High-Level Idea (in Simple Terms) algorithm cleverly reduces factoring to a much easier quantum-friendly problem: finding the period (or “order”) of a modular exponential function. Imagine you want to factor N (e.g., N = 15, but in practice N is huge like a 2048-bit number). 1. Pick a random number a (2 ≤ a < N) such that gcd(a, N) = 1 (they share no common factors). • If gcd(a, N) > 1, you’ve already found a factor of N — lucky! (happens sometimes). 2. Define the function f(x) = a^x mod N. This function is periodic: it repeats every r steps, where r is the smallest positive integer such that a^r ≡ 1 mod N (called the order of a modulo N). 3. The quantum part magically finds this period r very efficiently. 4. Once you have r: • If r is even, compute a^(r/2) mod N. • Let b = a^(r/2) mod N. Then compute gcd(b-1, N) and gcd(b+1, N) — at least one of these will (with good probability) be a non-trivial factor of N. 5. If it fails (e.g., r odd or factors trivial), just pick a new random a and repeat. Success probability is typically >40% per run. The Quantum Magic: How Period Finding Works The exponential speedup comes from quantum parallelism + Quantum Fourier Transform (QFT): • Create a superposition of many x values at once (using ~2n qubits for an n-bit N). • Compute a^x mod N for all x in superposition simultaneously (via repeated squaring in quantum circuits — this is efficient). • This creates a state where the amplitudes are periodic with period r. • Apply the QFT (quantum version of the Fourier transform) → it turns the periodic pattern into sharp peaks at frequencies related to 1/r. • Measure → you get a value that approximates k/r for some integer k (continued fraction approximation classically extracts r). In essence: Classical computers check one x at a time → slow for huge periods. Quantum computer evaluates exponentially many x “at once” and uses interference (via QFT) to reveal the hidden period. Success Rate & Practical Notes • ~50–100% chance per trial of getting a useful even r that yields factors (re-run if needed). • Only needs a fault-tolerant quantum computer with thousands to millions of logical qubits (far beyond 2026 hardware). • Doesn’t break symmetric crypto (AES) or hash functions directly — Grover’s algorithm gives only quadratic speedup there. Shor’s algorithm remains the poster child for why quantum computing could disrupt cryptography, driving the push toward post-quantum cryptography (e.g., lattice-based schemes like Kyber/Dilithium used in projects like Naoris Protocol).#StrategyBTCPurchase #BTC100kNext? #BTC走势分析 #Binance #CPIWatch

shots algorithm

Shor’s algorithm, developed by Peter Shor in 1994, is a quantum algorithm that factors large integers into their prime factors exponentially faster than the best known classical algorithms. This makes it a major threat to RSA encryption (and similar systems like ECDSA in crypto), since breaking large composites is the security foundation of those schemes.

Why It Matters in Crypto
Factoring a 2048-bit RSA modulus classically takes enormous time (sub-exponential but impractical). Shor’s algorithm runs in polynomial time — roughly O((log N)³) operations — so a sufficiently large, fault-tolerant quantum computer could break current public-key crypto in hours or days.
High-Level Idea (in Simple Terms)
algorithm cleverly reduces factoring to a much easier quantum-friendly problem: finding the period (or “order”) of a modular exponential function.
Imagine you want to factor N (e.g., N = 15, but in practice N is huge like a 2048-bit number).
1. Pick a random number a (2 ≤ a < N) such that gcd(a, N) = 1 (they share no common factors).
• If gcd(a, N) > 1, you’ve already found a factor of N — lucky! (happens sometimes).
2. Define the function f(x) = a^x mod N.

This function is periodic: it repeats every r steps, where r is the smallest positive integer such that a^r ≡ 1 mod N (called the order of a modulo N).
3. The quantum part magically finds this period r very efficiently.
4. Once you have r:
• If r is even, compute a^(r/2) mod N.
• Let b = a^(r/2) mod N.
Then compute gcd(b-1, N) and gcd(b+1, N) — at least one of these will (with good probability) be a non-trivial factor of N.
5. If it fails (e.g., r odd or factors trivial), just pick a new random a and repeat. Success probability is typically >40% per run.

The Quantum Magic: How Period Finding Works
The exponential speedup comes from quantum parallelism + Quantum Fourier Transform (QFT):
• Create a superposition of many x values at once (using ~2n qubits for an n-bit N).
• Compute a^x mod N for all x in superposition simultaneously (via repeated squaring in quantum circuits — this is efficient).
• This creates a state where the amplitudes are periodic with period r.
• Apply the QFT (quantum version of the Fourier transform) → it turns the periodic pattern into sharp peaks at frequencies related to 1/r.
• Measure → you get a value that approximates k/r for some integer k (continued fraction approximation classically extracts r).
In essence: Classical computers check one x at a time → slow for huge periods.
Quantum computer evaluates exponentially many x “at once” and uses interference (via QFT) to reveal the hidden period.

Success Rate & Practical Notes
• ~50–100% chance per trial of getting a useful even r that yields factors (re-run if needed).
• Only needs a fault-tolerant quantum computer with thousands to millions of logical qubits (far beyond 2026 hardware).
• Doesn’t break symmetric crypto (AES) or hash functions directly — Grover’s algorithm gives only quadratic speedup there.
Shor’s algorithm remains the poster child for why quantum computing could disrupt cryptography, driving the push toward post-quantum cryptography (e.g., lattice-based schemes like Kyber/Dilithium used in projects like Naoris Protocol).#StrategyBTCPurchase #BTC100kNext? #BTC走势分析 #Binance #CPIWatch

Moonax

shots algorithm

Informatique quantique

NAORISUSDT

Beyond moving

comparer la croix de la mort vs croix dorée

Croisement de la mort de Bitcoin

Implications du croisement mort

BTCUSDT perpétuel

Graphique de 15m

Signaux MACD contre RSI

lecture actuelle

Sujets d’actualité