# Security of RSA

Security of RSA-Below mention four possible approaches/method  to attacking the RSA algorithm and damage it.

Brute force:

• This involves trying all possible private keys.
• A brute force attack is a trial-and-error method used to obtain information such as a user password or personal identification number (PIN).
• In a brute force attack, automated software is used to generate a large number of consecutive guesses as to the value of the desired data.
• Brute force attacks may be used by criminals to crack encrypted data, or by security analysts to test an organization’s network security.
• A brute force attack is also known as brute force cracking or simply brute force.

Mathematical attacks:

• The solution to a number of the types of attack outlined above has involved the use of encryption.
• A mathematical attack involves the use of computation based on the mathematical properties of the encryption algorithm to attempt to decrypt data.
• The best way to avoid the decryption of data is to use strong encryption (128-bit) rather than rely on weaker encryption (both 40-bit and 56-bit encryption can easily be broken).

Timing attacks:

• These depend on the running time of the decryption algorithm.
• Atiming attack is a side channel attack in which the attacker attempts to compromise a cryptosystem by analyzing the time taken to execute cryptographic algorithms.
• Every logical operation in a computer takes time to execute, and the time can differ based on the input; with precise measurements of the time for each operation, an attacker can work backwards to the input.
• Information can leak from a system through measurement of the time it takes to respond to certain queries. How much such information can help an attacker depends on many variables: crypto system design, the CPU running the system, the algorithms used, assorted implementation details, timing attack countermeasures, the accuracy of the timing measurements, etc.
• Timing attacks are often overlooked in the design phase because they are so dependent on the implementation and can be introduced inadvertently with compiler optimisations. Avoidance of timing attacks involves design of constant-time functions and careful testing of the final executable code.

Chosen ciphertext attacks:

• This type of attack exploits properties of the RSA algorithm.
• In achosen-ciphertext attack, the attacker is assumed to have a way to trick someone who knows the secret key into decrypting arbitrary message blocks and tell him the result.
• The attacker can choose some arbitrary nonsense as an “encrypted message” and ask to see the (usually) different nonsense it decrypts to, and he can do this a number of times.
• Having this capability obviously already allows the attacker to read an intercepted message, since he can just ask to have it decrypted.
• But in this attack his goal is more ambitious than that: he wants to deducewhat the secret key is, such that he can encrypt messages himself, and also keep decrypting after his access to having things decrypted for him vanishes.
• The attack is successful if if an attacker has a significant chance of being able to deduce the key after having “relatively few” blocks decrypted and without doing so much work himself that he could just as well have brute-forced it.
• The term “chosen-ciphertext attack” does not in itself say anything about how the attacker chooses the nonsense blocks he asks to have decrypted, or what kind of computations he does in order to recover the key from the responses.