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A modern form of padding for asymmetric primitives is OAEP applied to the RSA algorithm, when it is used to encrypt a limited number of bytes. The operation is referred to as "padding" because originally, random material was simply appended to the message to make it long enough for the primitive.
However, the original scheme was proved in the random oracle model to be IND-CCA2 secure when OAEP is used with the RSA permutation using standard encryption exponents, as in the case of RSA-OAEP. [2] An improved scheme (called OAEP+) that works with any trapdoor one-way permutation was offered by Victor Shoup to solve this problem. [3]
The public key in the RSA system is a tuple of integers (,), where N is the product of two primes p and q.The secret key is given by an integer d satisfying (() ()); equivalently, the secret key may be given by () and () if the Chinese remainder theorem is used to improve the speed of decryption, see CRT-RSA.
More specifically, the RSA problem is to efficiently compute P given an RSA public key (N, e) and a ciphertext C ≡ P e (mod N). The structure of the RSA public key requires that N be a large semiprime (i.e., a product of two large prime numbers), that 2 < e < N, that e be coprime to φ(N), and that 0 ≤ C < N.
The RSA problem is defined as the task of taking e th roots modulo a composite n: recovering a value m such that c ≡ m e (mod n), where (n, e) is an RSA public key, and c is an RSA ciphertext. Currently the most promising approach to solving the RSA problem is to factor the modulus n .
The attack uses the padding as an oracle. [4] [5] PKCS #1 was subsequently updated in the release 2.0 and patches were issued to users wishing to continue using the old version of the standard. [3] However, the vulnerable padding scheme remains in use and has resulted in subsequent attacks:
The authors of Rijndael used to provide a homepage [2] for the algorithm. Care should be taken when implementing AES in software, in particular around side-channel attacks. The algorithm operates on plaintext blocks of 16 bytes. Encryption of shorter blocks is possible only by padding the source bytes, usually with null bytes. This can be ...
PKCS Standards Summary; Version Name Comments PKCS #1: 2.2: RSA Cryptography Standard [1]: See RFC 8017. Defines the mathematical properties and format of RSA public and private keys (ASN.1-encoded in clear-text), and the basic algorithms and encoding/padding schemes for performing RSA encryption, decryption, and producing and verifying signatures.