To simulate Birthday Attack in MATLAB that is a kind of cryptographic attack according to the birthday paradox. It aims hash functions by utilizing the probability of collisions — the chance, which two distinct inputs will generate the similar hash value. In the context of cryptographic security, the birthday attack is utilized to discover the hash collisions and show the vulnerabilities of particular hashing algorithms.
We will guide you through the simulation steps for birthday attack’s simulation using MATLAB in which the aim is to determine two diverse inputs with the similar hash output or collisions with the help of a simple hash function.
Steps to Simulate a Birthday Attack in MATLAB
- Define the Hash Function
- Signify a vulnerable hash algorithm using a basic hash function. For instance, we can utilize modulo operation on the total of ASCII values of a string, which replicating a hash function with restricted output size.
- Generate Random Inputs
- Make random inputs that normally strings, and calculate its hash values.
- Save each input and their hash within a list or dictionary.
- Check for Collisions
- Equate each new hash with earlier generated hashes to verify for a collision.
- End the simulation once a collision is discovered.
- Evaluate the Probability of a Collision
- Monitor the number of tries until the initial collision is discovered. With a small hash space, the collision’s probability maximizes as additional inputs are hashed.
MATLAB Code to Simulate a Birthday Attack
Below is a simple instance in MATLAB to replicate a birthday attack with a simple hash function.
% Parameters
hashSpace = 100; % Define a small hash space for simplicity (e.g., 0 to 99)
numAttempts = 1000; % Maximum number of attempts to find a collision
foundCollision = false; % Flag to indicate if collision was found
% Initialize a dictionary to store inputs and their hash values
inputHashes = containers.Map(‘KeyType’, ‘double’, ‘ValueType’, ‘char’);
% Function to simulate a simple hash (e.g., sum of ASCII values modulo hashSpace)
simpleHash = @(inputStr) mod(sum(double(inputStr)), hashSpace);
% Collision search
for attempt = 1:numAttempts
% Generate a random string of characters (input)
inputStr = char(randi([32, 126], 1, 5)); % Random 5-character string
% Calculate hash for this input
hashValue = simpleHash(inputStr);
% Check if this hash already exists in the dictionary
if isKey(inputHashes, hashValue)
% Collision found
fprintf(‘Collision found!\n’);
fprintf(‘Attempt %d: Input “%s” and “%s” have the same hash value %d.\n’, …
attempt, inputHashes(hashValue), inputStr, hashValue);
foundCollision = true;
break;
else
% Store the input and hash in the dictionary
inputHashes(hashValue) = inputStr;
end
end
% Results if no collision is found within the maximum attempts
if ~foundCollision
fprintf(‘No collision found within %d attempts.\n’, numAttempts);
end
Explanation of Code
- Hash Space: The hash space is set to a small value (100) to maximize the likelihood of a collision and illustrate the attack successfully.
- Hash Function: simpleHash is described as a basic modulo hash function. The total of ASCII values of characters within the input string is computed then the outcome is taken modulo hashSpace.
- Collision Detection: Each random input made, if the hash already calculated for a distinct input then the code verifies. If a collision is discovered then it indicates both inputs with the similar hash value.
Example Output
If a collision is discovered, we could observe output like this:
Collision found!
Attempt 23: Input “hello” and “world” have the similar hash value 56.
Extending the Simulation
- Different Hash Spaces: Test with diverse hash spaces like 256, 512 to monitor how larger hash spaces minimize the likelihood of a collision.
- Complex Hash Functions: Substitute simpleHash with a more complex hashing function such as using hash function of MATLAB that to replicate more realistic situations.
- Statistics Collection: Monitor how many tries on average lead to a collision. Do again the simulation several times to examine the efficiency of the birthday attack.
Visualization (Optional)
We can envision the collision’s probability by plotting the amount of attempts against collision success rate.
% Run multiple simulations to gather statistics
numTrials = 100; % Number of trials for statistical analysis
collisionAttempts = zeros(1, numTrials);
for trial = 1:numTrials
inputHashes = containers.Map(‘KeyType’, ‘double’, ‘ValueType’, ‘char’);
foundCollision = false;
for attempt = 1:numAttempts
inputStr = char(randi([32, 126], 1, 5));
hashValue = simpleHash(inputStr);
if isKey(inputHashes, hashValue)
collisionAttempts(trial) = attempt;
foundCollision = true;
break;
else
inputHashes(hashValue) = inputStr;
end
end
if ~foundCollision
collisionAttempts(trial) = numAttempts;
end
end
% Plotting the distribution of attempts to collision
figure;
histogram(collisionAttempts);
title(‘Distribution of Attempts to Collision’);
xlabel(‘Attempts’);
ylabel(‘Frequency’);
Here, we had discussed about the simulation approach that were used to simulate the Birthday Attack projects using MATLAB tool and it contains the essential information like step-by step procedure, explanation along with coding. If you require further innovative information relevant to this topic then feel free to ask!
