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# 数学代写|密码学代写Cryptography Theory代考|Standard assumptions

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## 数学代写|密码学Cryptography Theory代考|Standard assumptions

In order to assess the security of a cryptosystem, we must first establish exactly what assumptions we are making about potential attackers of the cryptosystem. Identifying assumptions about the capabilities of attackers is standard practice in all areas of information security and forms part of the larger process of risk assessment. If we underestimate an attacker’s capabilities, the resulting security might be inadequate. It thus makes sense to be slightly conservative and take a worst-case view.

In cryptography there are three standard assumptions that are almost always made concerning an attacker’s ability. These are that the attacker knows the following:

All ciphertexts sent using the cryptosystem. It is entirely reasonable to assume that an attacker has access to all the ciphertexts sent using the cryptosystem. These are not hidden from public view by the encryption process.

Some corresponding pairs of plaintexts and ciphertexts. At first glance, this might not seem such an obvious assumption to make; however, there are many circumstances where an attacker could have access to corresponding pairs of plaintexts and ciphertexts. Just some possible scenarios are:

• The receiver has been careless in failing to keep decrypted ciphertexts secret.
• The attacker has intelligently guessed some predictable plaintexts. Agood example is predictable document headers.
• The attacker has been able to influence the choice of plaintexts encrypted by the sender.
• The attacker has (temporary) access to either the encryption or decryption device. Note this does not imply that the attacker knows the encryption or decryption key. The keys might be embedded in secure hardware and the attacker only has access to the interface of the machine that conducts the encryption (decryption) process. Obviously, we assume that the attacker does not have permanent access to the decryption device, otherwise they are in a very strong position!
• We are using a public-key cryptosystem, where the encryption key is known to any potential attacker. Thus, an attacker can generate pairs of corresponding plaintexts and ciphertexts at leisure.

## 数学代写|密码学Cryptography Theory代考|Theoretical attack models

Attacks on cryptosystems have historically been classified using the following terminology:
ciphertext-only attacks assume the attacker knows the encryption algorithm and some ciphertext;
known-plaintext attacks assume the attacker knows the encryption algorithm and some arbitrary plaintext/ciphertext pairs;
chosen-plaintext attacks assume the attacker knows the encryption algorithm and some plaintext/ciphertext pairs that correspond to plaintexts chosen by the attacker;
chosen-ciphertext attacks assume the attacker knows the encryption algorithm and some plaintext/ciphertext pairs that correspond either to plaintexts or to ciphertexts chosen by the attacker.

These are increasingly powerful attacks since, for example, an attacker who can choose which plaintext/ciphertext pairs to examine is clearly in a better position than an attacker who can only see arbitrary plaintext/ciphertext pairs.

Our ‘standard assumptions’ do not clearly differentiate between the last three of these attacks. It is safest to assume that an attacker has been able to at least choose the plaintexts for which they know plaintext/ciphertext pairs. Modern cryptosystems should thus be able to withstand at least chosenplaintext attacks. However, to be on the safe side, they are usually designed to protect against chosenciphertext attacks.

While it will suffice for us to remember the three standard assumptions about the knowledge of an attacker, it is worth recognising that cryptographic researchers tend to have even more stringent assumptions about the possible attack model. For example, in one strong theoretical model of the security of a cryptosystem, an attacker should not be able to tell the difference between ciphertext that is produced using the cryptosystem and randomly generated data. While this is a property any good cryptosystem should possess, for some practical applications it might be questionable whether it is strictly necessary to pass this ‘test’.

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