Simulating Quantum-Accelerated Forgery

This experiment simulated a quantum attack on TCP’s Initial Sequence Number (ISN), a 32-bit random value used during the TCP handshake to prevent attackers from spoofing or hijacking connections. By modeling the ISN-guessing problem as an unstructured search, we implemented a quantum search attack using Grover’s algorithm in Q# and compared its performance against a classical brute-force search written in C#.

The simulation was run on the Azure Quantum Q# simulator, using a reduced 8-bit ISN space for feasibility. The classical brute-force attack required 138 attempts to find the correct value, while the quantum Grover attack required only 13 iterations, a 10× speedup consistent with the expected quantum advantage. Although quantum measurement returned the wrong value in one trial—an expected behavior of probabilistic quantum algorithms—the reduction in required operations clearly demonstrates the potential threat.

Extrapolating to the real 32-bit TCP ISN space shows that a classical attacker needs approximately 4.29 billion guesses, whereas a quantum attacker using Grover’s algorithm would need only ≈ 65,536 iterations. This reduces the difficulty of blind TCP spoofing by nearly three orders of magnitude. While today’s quantum computers cannot yet execute Grover’s algorithm at this scale, these results highlight that foundational internet protocols like TCP will require upgrades and post-quantum defenses as quantum hardware advances.

Source Code: https://github.com/jdn-the-dev/Research

namespace TcpQuantumAttack {
    open Microsoft.Quantum.Intrinsic;
    open Microsoft.Quantum.Canon;
    open Microsoft.Quantum.Measurement;
    open Microsoft.Quantum.Convert;
    open Microsoft.Quantum.Math;
    open Microsoft.Quantum.Arrays;

    // --------------------------------------
    // Oracle: flips the phase of |target⟩
    // --------------------------------------
    operation TcpOracle(target : Int, register : Qubit[]) : Unit is Adj + Ctl {
        let n = Length(register);
        let targetBits = IntAsBoolArray(target, n);

        // Apply X to all qubits where target bit = 0
        for i in 0 .. n-1 {
            if (not targetBits[i]) {
                X(register[i]);
            }
        }

        // Multi-controlled Z (phase flip)
        Controlled Z(Most(register), Tail(register));

        // Undo the X gates
        for i in 0 .. n-1 {
            if (not targetBits[i]) {
                X(register[i]);
            }
        }
    }

    // --------------------------------------
    // Grover diffusion operator
    // --------------------------------------
    operation Diffusion(register : Qubit[]) : Unit is Adj + Ctl {
        ApplyToEachCA(H, register);
        ApplyToEachCA(X, register);

        Controlled Z(Most(register), Tail(register));

        ApplyToEachCA(X, register);
        ApplyToEachCA(H, register);
    }

    // --------------------------------------
    // Classical brute force attack
    // --------------------------------------
    operation RunClassicalBruteForce(target : Int, nQubits : Int) : (Int, Int) {
        let maxValue = 2 ^ nQubits;
        mutable attempts = 0;
        mutable found = -1;

        // Simulate checking each possible value sequentially
        for guess in 0 .. maxValue - 1 {
            set attempts = attempts + 1;
            if guess == target {
                set found = guess;
                Message($"Classical brute force found {target} after {attempts} attempts");
                return (found, attempts);
            }
        }

        return (found, attempts);
    }

    // --------------------------------------
    // Main attack simulation
    // --------------------------------------
    @EntryPoint()
    operation Main() : Int {
        let nQubits = 8;           // 8-bit simulation
        let target = 137;          // pretend TCP sequence number

        Message($"\n========================================");
        Message($"TCP Sequence Number Attack Comparison");
        Message($"========================================");
        Message($"Target TCP Sequence Number: {target}");
        Message($"Search Space: {2 ^ nQubits} possibilities ({nQubits} bits)");
        Message($"");

        // Classical brute force attack
        Message($"--- Classical Brute Force Attack ---");
        let (classicalResult, attempts) = RunClassicalBruteForce(target, nQubits);
        Message($"Result: {classicalResult}");
        Message($"");

        // Quantum Grover attack
        Message($"--- Quantum Grover Attack ---");
        let quantumResult = RunTcpSequenceGrover(target, nQubits);
        Message($"Quantum Guess: {quantumResult}");
        Message($"");

        // Comparison
        Message($"========================================");
        Message($"Comparison:");
        Message($"  Classical attempts: {attempts}");
        let N = 2 ^ nQubits;
        let groverIterations = Round(PI() / 4.0 * Sqrt(IntAsDouble(N)));
        Message($"  Grover iterations: {groverIterations}");
        let speedup = IntAsDouble(attempts) / IntAsDouble(groverIterations);
        Message($"  Quantum speedup: ~{speedup}x faster");
        Message($"  Classical match: {classicalResult == target}");
        Message($"  Quantum match: {quantumResult == target}");
        Message($"========================================");

        return quantumResult;
    }

    operation RunTcpSequenceGrover(target : Int, nQubits : Int) : Int {

        use register = Qubit[nQubits];

        // 1. Put qubits into uniform superposition
        ApplyToEach(H, register);

        // 2. Compute number of Grover iterations
        let N = 2 ^ nQubits;
        let iterations = Round(PI() / 4.0 * Sqrt(IntAsDouble(N)));

        Message($"Running Grover with {iterations} iterations...");

        // 3. Run Grover iteration
        for _ in 1 .. iterations {
            TcpOracle(target, register);
            Diffusion(register);
        }

        // 4. Measure result
        let result = ResultArrayAsInt(ForEach(M, register));

        ResetAll(register);
        return result;
    }
}