A birthday attack is a type of brute force attack that is derived from the probability theorem. A birthday attack is a form of cryptographic attack that cracks mathematical algorithms by looking for matches in the hash function. The strategy relies upon the birthday paradox via which the probability of sharing one birthday with two persons is significantly larger than it appears. Similarly, the probability of collision detection is increased within the target hash function, allowing the attacker to locate similar pieces with a few rounds. The attack is used largely for manipulating communication between the two parties. The type of attack is determined by collisions between random attacks and the degree of permutation.
What is a Birthday Attack?
The probability theory explains the birthday paradox problem as follows: if there are ‘n’ people in the room, there is a chance that some of them will have their birthdays on the same day. However, one crucial consideration is that we do not concentrate on matching birth dates, but instead on two people sharing the same birthday.
As a result, birthday attacks adopt the probability strategy to minimize the difficulty in the matched collision and to obtain the estimated hash collision risk in a given number. It also demonstrates that finding a specific hash collision is more difficult than finding matched hash collisions with the same values. Let’s look at an example to better understand the concept:
- Assume an average year has 365 days.
- Put 23 people in the room.
- So, if “A” has a 1/365 chance of sharing your birthday with some other 22 people, your probability is 22/365.
- If “A’s” birthday doesn’t quite match, “B” has a 21/365 chance of having its birthday match with the rest of the people in the room.
- If “B” too fails to find a match, “C” will have a chance of 20/365, and so on.
- If you add up all the possibilities of everyone in the room, i.e. 22/365+21/365+20/365, you get a total chance of 50%.
- Similarly, to get a probability of 99.9 per cent, you need 70 people in the room, and to get a probability of 100 per cent, you need 366 people.
Birthday attacks, then, apply probabilistic logic to minimize the complexity of obtaining a hash collision and determining the estimated risk of the presence of a hash mismatch within a given number. Therefore, finding a particular hash collision is more challenging than finding a matched hash collision with the same values.
Digital signature susceptibility is one of the most common applications of the birthday paradox attack. Continue reading to gain a basic understanding of the concept.
Digital signature susceptibility
A digital signature is one place that is extremely susceptible to a birthday attack.
- f denotes a cryptographic function.
- M denotes a message signed as f(m) using a certain secret key.
- Assume Noah wants to defraud Lucas by having a malicious document signed by him.
- Noah prepares a legal document called (m) and a malicious one designated as (m’)
- Noah can generate multiple variations of the legal document by changing (m) to (m’) in several spots (m).
- Noah, too, prepared many types of fraudulent papers.
- Noah can use the hash function to get hash values that match f(m)= f(m’).
- Even if Lucas signs the legal document, Noah can simply replace it with a similar malicious document and claim that Lucas signed the malicious document originally.
Noah can uncover numerous methods to subtly change each contract without changing its meaning. For example, you may change the amount of white space at the end of each line, tweak the pixels in a logo, or make minor formatting modifications. This results in millions of technically distinct but semantically similar texts, all of which would receive Lucas’s approval. It also provides Noah with millions of variations on the forged document. If Noah identifies a pair of documents, one real and one fake, that create the same hash, he can have Lucas sign the valid one and then use that signature to “prove” the legitimacy of the fraudulent contract.
Given the wide range of the hash function, the risk of at least one hash value collision between one of the genuine and one of the fraudulent documents is substantially higher than may be predicted. In fact, the number of documents required is about equal to the square root of the set of possible hash function outputs. This is made easier by the fact that no hash function is perfectly evenly distributed, which has led to the insecurity of several popular hashing methods.
How to Prevent Birthday Attack?
- To prevent the birthday attack, the duration output for the hashing algorithm of the signature scheme might be chosen to be big enough that the birthday attack gets computationally impractical.
- In addition to using the longer bit length, the signer can avoid the attack by making some innocent but random alterations to the document before signing it and keeping the contract copy in their possession. Such that he can demonstrate inside the court that the sign matches the agreement.
Conclusion
By matching the hashing algorithm, the birthday attack solves the mathematical algorithm. The probability theory is the best way to compute the birthday attack. The attack, although, can be avoided by increasing the bit length and having the signer make some random alterations to the document.