Barazanar Kwamfyuta ta Quantum ga Bitcoin da Maganganun Bayan-Quantum

1.1 Gabatarwa ga Barazanar Quantum

Kwamfyutocin Quantum suna haifar da barazana mai gamsarwa ga tsarin cryptographic na yanzu da ke kare Bitcoin da sauran kudade na sirri. Ci gaban manyan kwamfyutocin quantum masu isa zai iya karya algorithm na sa hannu na elliptic curve digital (ECDSA) da ake amfani da shi a Bitcoin, wanda zai yiwu a farkon shekara ta 2027 bisa ga kyakkyawan kiyasi.

1.2 Tushen Tsaron Bitcoin

Tsaron Bitcoin ya dogara ne da manyan sassa guda biyu: tsarin yarjejeniyar proof-of-work da cryptography na elliptic curve don ba da izinin ma'amala. Yanayin rarrabuwar kawuna na Bitcoin ya nuna juriya sosai ga hare-haren kwamfyuta na gargajiya tun lokacin da aka ƙaddamar da shi a shekara ta 2008.

2. Binciken Harin Quantum

2.1 Juriyar Proof-of-Work

Proof-of-work na Bitcoin na tushen SHA-256 yana nuna juriya mai dangi ga saurin quantum. Masu hakar ma'adinai na ASIC na yanzu suna kai ga yawan hash na ~100 TH/s, yayin da kwamfyutocin quantum na kusa an kiyasta zasu kai saurin agogo kawai 100 MHz-1 GHz. Saurin quantum na algorithm na Grover da ake amfani da shi wajen hakar ma'adinai yana ba da fa'ida mai murabba'i kawai, wanda ke haifar da ingantu kusan 2-4x maimakon ribobi masu yawa.

2.2 Raunin Elliptic Curve

Tsarin sa hannu na elliptic curve da ake amfani da shi a Bitcoin yana da rauni sosai ga algorithm na Shor, wanda zai iya warware matsalar lissafi ta elliptic curve discrete a cikin lokaci mai yawa. Taga harin mai mahimmanci yana wanzuwa tsakanin watsa ma'amala da tabbatar da blockchain (yawanci mintuna 10).

3. Mafita Masu Jure Quantum

3.1 Momentum Proof-of-Work

Momentum proof-of-work, dangane da gano karon hash, yana ba da ƙarfin juriya na quantum idan aka kwatanta da hakar ma'adinai na SHA-256 na Bitcoin. Sabon abu na ranar haihuwa yana ba da juriya ta halitta tare da fa'idar quantum kawai $O(2^{n/3})$ sabanin $O(2^{n/2})$ na gargajiya.

function momentum_mining(difficulty):
    while True:
        nonce1 = random()
        nonce2 = random()
        hash1 = sha256(block_header + nonce1)
        hash2 = sha256(block_header + nonce2)
        if hamming_distance(hash1, hash2) < difficulty:
            return (nonce1, nonce2)
    

3.2 Tsare-tsare na Sa hannu Bayan-Quantum

Tsare-tsare da yawa na sa hannu bayan-quantum suna nuna alƙawari don aikace-aikacen blockchain:

• Sa hannu na tushen Hash: SPHINCS+ da XMSS suna ba da tabbataccen tsaro
• Tushen Lattice: Dilithium da Falcon suna ba da halayen aiki masu kyau
• Tushen Code: Classic McEliece yana ba da tsaro mai ra'ayin mazan jiya

4. Aiwatar da Fasaha

Tushen lissafi na hare-haren quantum ya dogara ne akan algorithm na Shor don lissafin discrete. Don elliptic curve $E$ a kan filin iyaka $F_p$ tare da madaidaicin batu $G$, maɓalli na jama'a $P = kG$, algorithm na Shor yana gano maɓalli na sirri $k$ ta hanyar warwarewa:

$k = \log_G P$ a cikin $E(F_p)$

Canjin Fourier na quantum yana ba da damar samun lokaci mai inganci a cikin matsalar ƙungiya ta ɓoye, yana ba da sauri mai yawa fiye da algorithms na gargajiya.

5. Aikace-aikacen Gaba

Canjin zuwa kudade na sirri masu jure quantum zai bi hanyoyi da yawa:

• Gajeren Lokaci (2023-2027): Bincike da daidaita ma'auni na algorithms bayan-quantum
• Matsakaicin Lokaci (2027-2035): Aiwar da tsare-tsaren sa hannu na haɗaka
• Dogon Lokaci (2035+): Ƙaura cikakke zuwa ka'idojin jure quantum

Fasahohi masu tasowa kamar quantum blockchain da quantum-secure distributed ledgers na iya amfani da haɗin gwiwar quantum don ingantaccen tsaro, kamar yadda aka bincika a cikin bincike na baya-bayan nan daga Cibiyar Ƙididdiga da Fasaha ta Ƙasa (NIST) tsarin daidaita ma'auni na cryptography bayan-quantum.

6. Bayanan Kara

1. Aggarwal, D., et al. "Quantum attacks on Bitcoin, and how to protect against them." arXiv:1710.10377 (2017).
2. Shor, P. W. "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer." SIAM Journal on Computing 26.5 (1997): 1484-1509.
3. NIST. "Post-Quantum Cryptography Standardization." National Institute of Standards and Technology (2022).
4. Nakamoto, S. "Bitcoin: A Peer-to-Peer Electronic Cash System." (2008).
5. Bernstein, D. J., et al. "SPHINCS: practical stateless hash-based signatures." EUROCRYPT 2015.
6. Alagic, G., et al. "Status report on the second round of the NIST post-Quantum cryptography standardization process." NIST IR 8309 (2020).