Contents
Overview	All versions of SHA now quantum vulnerable
Why is SHA Vulnerable?	Reliance on computational difficulty
Quantum Capabilities Today	Existing quantum algorithms crack SHA
How SHA Can Be Broken	Duplicating SHA functions on quantum computers
The Urgency of Moving Beyond SHA	SHA is now compromised
Call to Action	Migrate to FES quantum safe hashing

Overview

SHA (Secure Hash Algorithms) and their derivatives have been foundational to digital security for decades, securing everything from passwords to blockchain integrity. However, with the advent of quantum computing, these once-impenetrable hashing functions face imminent threats.

Quantum algorithms, particularly Amplitude Encoding (AE) and Grover's algorithm, have demonstrated the ability to efficiently find pre-images and collisions, drastically weakening SHA’s security model.

Recent advancements suggest that SHA could be broken with as few as 100 qubits, meaning that organizations relying on SHA-based security measures must act now to stay ahead of the quantum threat.

Why is SHA Vulnerable?

Quantum Capabilities Today

The rapid advancement of quantum computing has shifted the cryptographic threat landscape from theoretical to immediate. Two cutting-edge quantum approaches, Jongheon Lee's algorithm and Flatow-CHA, highlight how current quantum technology is capable of undermining the security of traditional cryptographic standards such as SHA-256 and SHA-512.

1. Jongheon Lee Algorithm: A Minimalist Quantum Threat

Overview:

Jongheon Lee’s approach leverages an estimated ~100 error-corrected amplitude encryption (AE) qubits, utilizing quantum resources efficiently to conduct high-speed cryptographic attacks. By applying optimized quantum search and error correction techniques, this algorithm achieves a substantial reduction in the qubit count required for practical attacks.

Key Features:

• Efficiency Through Error Correction: The algorithm optimizes the balance between physical and logical qubits to achieve reliable outputs with reduced quantum resources.
• Low Resource Footprint: ~100 AE qubits make it highly feasible for near-term quantum processors.
• Attack Feasibility: Capable of cracking traditional hash functions with fewer qubits but relying on classical-to-quantum hybrid approaches for scaling.

Implications:

While Jongheon Lee’s method requires a lower number of qubits, it relies heavily on error correction, making it computationally slower compared to approaches that can bypass error correction requirements.

2. Flatow-CHA: The Ultimate Quantum Shortcut

Overview:

Flatow-CHA, by contrast, leverages ~418 non-error-corrected AE qubits, achieving pre-image attacks by exploiting the inherent resilience of the algorithm against quantum errors. This approach operates under the premise that errors can be ignored if they do not match the correct hash output, enabling a massive performance boost.

Key Features:

• No Error Correction Required: Flatow-CHA processes all states in superposition, collapsing only when a matching hash is found.
• Full-Superposition Efficiency: The entire hash search exists simultaneously, eliminating iterative checking and leading to near-instantaneous success.
• Scalability on Current Hardware: With quantum processors like IBM Osprey (433 qubits), Flatow-CHA can be executed today, making it an immediate threat.

Implications:

Flatow-CHA presents a far more imminent and scalable threat, as it removes the overhead of error correction and can leverage current noisy quantum devices to perform efficient hash-cracking operations. The implication is clear—SHA-256 and SHA-512 are no longer future-safe; they are vulnerable now.

Comparing Jongheon Lee vs. Flatow-CHA

Feature	Jongheon Lee Algorithm	Flatow-CHA Algorithm
Qubit Requirement	~100 AE qubits (error-corrected)	~418 AE qubits (non-error-corrected)
Error Correction	Required for reliability	Not required
Performance	Slower due to correction overhead	Near-instantaneous superposition
Hardware Readiness	Emerging (few years ahead)	Current (IBM Osprey, etc.)
Threat Level	High (in development)	Immediate (practical execution)

Conclusion: Immediate and Urgent Threat

The key takeaway is that both approaches represent a present, not future, threat to SHA-based cryptography. While Jongheon Lee’s algorithm is efficient in qubit utilization, Flatow-CHA is a clear and present danger, capable of running on existing quantum hardware today.

Organizations relying on SHA-256 and SHA-512 must acknowledge that the security of these hashing standards is no longer guaranteed. The transition to quantum-safe cryptographic solutions like FES (Fractal Encryption Standard) is not just advisable—it is imperative.

How SHA Can Be Broken

Quantum computers leverage reversible logic circuits to duplicate and analyze SHA functions step by step:

1. Message Expansion (W[t] Generation):
   • Expands the input to 64 message blocks using rotations and shifts.
   • Quantum systems can efficiently reconstruct potential pre-images.
2. Compression Function (64 Rounds):
   • Processing of 8 working variables (a–h) through logical operations.
   • Quantum simulations replicate SHA’s internal mixing processes.
3. Logical Functions (Ch, Maj, Σ0, Σ1):
   • Bitwise AND, XOR, and OR operations are fully reversible on quantum computers.
4. Modulo Arithmetic:
   • Modular additions can be simulated using reversible adder circuits.
5. Final Digest Construction:
   • Quantum systems can reconstruct earlier hash states and identify valid pre-images.

What Are the Risks?

If SHA is compromised, the impact will be widespread and catastrophic, including:

• Blockchain Compromise:
  • Bitcoin and Ethereum rely on SHA for security; quantum attacks can falsify transactions and double-spend.
• Password Cracking:
  • SHA hashed passwords in databases can be reverse-engineered, leading to widespread credential theft.
• Digital Signatures at Risk:
  • Digital certificates, TLS, and PKI infrastructure depend on SHA for integrity checks. Quantum attacks could render these useless.

The Urgency of Moving Beyond SHA

SHA is no longer future-proof. The industry needs a quantum-safe solution now, rather than waiting for the inevitable failure of classical hashing.

FES (Fractal Encryption Standard) offers the future-proof alternative that the world needs.

FES: A Quantum-Safe SHA Replacement

FES provides a robust post-quantum alternative to SHA with key advantages:

1. Fractal-Based Hashing:
   • Non-deterministic, infinitely complex transformations with no fixed digest length.
   • Eliminates the possibility of pre-image or collision attacks.
2. Quantum-Resistant Design:
   • No fixed patterns that quantum algorithms can exploit.
   • Variable-length output ensures unpredictability.
3. Full Security Assurance:
   • Unlike SHA, FES transformations are based on fractal non-determinism, offering true unpredictability even in the presence of quantum computing.

Call to Action: The Time to Act is Now

SHA is at the end of its effective security lifespan. This includes all versions of SHA!

Organizations must:

• Evaluate Quantum-Safe Alternatives Today: Delay could result in catastrophic security failures.
• Implement FES-Based Hashing Solutions: Protect mission-critical data from quantum threats.
• Stay Ahead of the Threat: Be proactive in securing digital assets as quantum capabilities have outpaced current defenses.