# Security of RSA

• Difficulty Level : Basic
• Last Updated : 06 Sep, 2022

Prerequisite – RSA Algorithm in Cryptography

Security of RSA:-
These are explained as following below.

1. Plain text attacks:
It is classified into 3 subcategories:-

• Short message attack:
In this we assume that attacker knows some blocks of plain text and tries to decode cipher text with the help of that. So, to prevent this pad the plain text before encrypting.
• Cycling attack:
In this attack, the attacker thinks that the cipher text has been generated by using some permutation. He uses all possible permutations of plain text to decipher the cipher text by ‘cycling’ the permutations.
• Unconcealed Message attack:
Sometimes it happens that plain text is same as cipher text after encryption. So it must be checked or it will be of no use as the attacker will see right through it.

2. Chosen cipher attack:
In this attacker is able to find out plain text based on cipher text using the Extended Euclidean Algorithm.

3. Factorization attack:
If the attacker is able to know P and Q using N, then he can find out value of private key. This fails when N contains at least 300 longer digits in decimal terms, attacker will not able to find it. Hence this is infeasible for larger numbers.

4. Attacks on Encryption key:
If we take smaller value of E in RSA this may occur so to avoid this take value of E = 2^16+1 (at least).

5. Attacks on Decryption key:

• Revealed decryption exponent attack:
If attacker somehow guess decryption key D, not only the cipher text generated by encryption the plain text with corresponding encryption key is in danger, but even future messages are also in danger. So, it is advised to take fresh values of two prime numbers (i.e.:  P and Q), N and E.
• Low decryption exponent attack:
If we take smaller value of D in RSA this may occur so to avoid this take value of D = 2^16+1(at least).

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