Туған күн шабуылы: Қақтығыс пен цифрлық қолтаңбалардың осалдығы

Type of cryptographic attack
A birthday attack is a bruteforce collision attack that exploits the mathematics behind the birthday problem in probability theory. This attack can be used to abuse communication between two or more parties. The attack depends on the higher likelihood of collisions found between random attack attempts and a fixed degree of permutations (pigeonholes). With a birthday attack, it is possible to find a collision of a hash function with chance in , There is a general (though disputed) result that quantum computers can perform birthday attacks, thus breaking collision resistance, in
Although there are some digital signature vulnerabilities associated with the birthday attack, it cannot be used to break an encryption scheme any faster than a brute force attack.

As an example, consider the scenario in which a teacher with a class of 30 students (n = 30) asks for everybody's birthday (for simplicity, ignore leap years) to determine whether any two students have the same birthday (corresponding to a hash collision as described further). Intuitively, this chance may seem small. Counter intuitively, the probability that at least one student has the same birthday as any other student on any day is around 70% (for n = 30), from the formula
If the teacher had picked a specific day (say, 16 September), then the chance that at least one student was born on that specific day is , about 7.9%. In a birthday attack, the attacker prepares many different variants of benign and malicious contracts, each having a digital signature. A pair of benign and malicious contracts with the same signature is sought. In this fictional example, suppose that the digital signature of a string is the first byte of its SHA 256 hash. The pair found is indicated in green – note that finding a pair of benign contracts (blue) or a pair of malicious contracts (red) is useless. After the victim accepts the benign contract, the attacker substitutes it with the malicious one and claims the victim signed it, as proven by the digital signature.

Digital signatures can be susceptible to a birthday attack or more precisely a chosen prefix collision attack. A message is typically signed by first computing , where is a cryptographic hash function, and then using some secret key to sign Suppose Mallory wants to trick Bob into signing a fraudulent contract. Mallory prepares a fair contract and a fraudulent one She then finds a number of positions where can be changed without changing the meaning, such as inserting commas, empty lines, one versus two spaces after a sentence, replacing synonyms, etc. By combining these changes, she can create a huge number of variations on which are all fair contracts. In a similar manner, Mallory also creates a huge number of variations on the fraudulent contract She then applies the hash function to all these variations until she finds a version of the fair contract and a version of the fraudulent contract which have the same hash value, She presents the fair version to Bob for signing. After Bob has signed, Mallory takes the signature and attaches it to the fraudulent contract. This signature then "proves" that Bob signed the fraudulent contract. The probabilities differ slightly from the original birthday problem, as Mallory gains nothing by finding two fair or two fraudulent contracts with the same hash. Mallory's strategy is to generate pairs of one fair and one fraudulent contract. For a given hash function is the number of possible hashes. The birthday problem equations does not exactly apply here, the number of hashes Mallory actually generates for a chance is twice as much as required for a simple collision which corresponds to
To avoid this attack, the output length of the hash function used for a signature scheme can be chosen large enough so that the birthday attack becomes computationally infeasible, i. e. about twice as many bits as are needed to prevent an ordinary brute force attack. Besides using a larger bit length, the signer (Bob) can protect himself by making some random, inoffensive changes to the document before signing it, and by keeping a copy of the contract he signed in his own possession, so that he can at least demonstrate in court that his signature matches that contract, not just the fraudulent one. Pollard's rho algorithm for logarithms is an example for an algorithm using a birthday attack for the computation of discrete logarithms.

The same fraud is possible if the signer is Mallory, not Bob. Bob could suggest a contract to Mallory for a signature. Mallory could find both an inoffensively modified version of this fair contract that has the same signature as a fraudulent contract, and Mallory could provide the modified fair contract and signature to Bob. Later, Mallory could produce the fraudulent copy. If Bob doesn't have the inoffensively modified version contract (perhaps only finding their original proposal), Mallory's fraud is perfect. If Bob does have it, Mallory can at least claim that it is Bob who is the fraudster.