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The McEliece cryptosystem is the asymmetric type of cryptography which is
based on error correction code. The classical McEliece used irreducible binary
Goppa code which considered unbreakable until now especially with parameter
[1024, 524, 101] which is suggested by McEliece, but it is suffering from large
public key matrix which leads to be diffi...
Contexts in source publication
Context 1
... decryption includes: Import Random Generator Polynomial and Parity Check Sum: The random polynomial imported first, built the range of Goppa code, and then check if the generator polynomial is irreducible or separable polynomial. Partition Ciphered Message and Inverse of Permutation Matrix: This stage of decryption process classified into three commands (as shown in Figure (11), the first command starts to partition ciphered message, where each partition include number of rows of secret generator matrix in bits. The second command is to find the inverse of permutation matrix, and then multiply each partitioned message by the inverse of permutation matrix. ...
Context 2
... and Error Locater: The most important form in decryption process because it finds the error locater in each partitioned message. This form include three commands (as shown in Figure (12)), the first bottom find the syndrome for each partitioned cipher message. The second bottom locates the errors in each partitioned message depending on type of Goppa code (irreducible or separable), each type have its own process. ...
Context 3
... removing the errors from the ciphered message, it is added to the secret generator matrix, as shown in Figure (13), while the second command remove the secret generator matrix from ciphered message by calculating Gaussian elimination method for the created matrix. Inverse of Nonsingular Matrix: Determining the original message in binary form by multiplying the message, which is founded in previous form, with the inverse of Nonsingular matrix. ...
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The Gaussian sampler is an integral part in lattice-based cryptography as it has a direct connection to security and efficiency. Although it is theoretically secure to use the Gaussian sampler, the security of its implementation is an open issue. Therefore, researchers have started to investigate the security of the Gaussian sampler against side-ch...
Citations
... A public key is published and used to cipher a message, while a private key must keep it secret and use it to decipher the message. To prepare keys depending on Goppa code, the following steps as shown in Figure (3)should be followed [15]: ...
... To encrypt any message, the block diagram asshown in Figure (4)) should be followed [15]: ...
Side channel attack is the most efficient attack against original McEliece cryptosystem, especially ball-collision and Bernstein et al. Stern attacks. The modified Stern attack has an ability to break original McEliece cryptosystem with parameter [1024, 524, 101] in 1400 days with personal computers. While with 200 clusters CPU breaking could be done in 7 days. While ball-collision attacks have smaller exponent time than Stern algorithm. This paper will present a modified version of Patterson decoding algorithm using a new evaluation for finding error locations. This approach gave the sender an opportunity to choose errors less than identified errors in public key without notifying the receiver; therefore, it reduces the probability of modified Stern attack against McEliece cryptosystem to (0.02) and increases exponent time of ball-collision attack. In this paper also the leakage of proposed implementation has been measured using a measurement type for possible leakage in Patterson’s decoding algorithm suggested by previous work, and we concluded that the designed system have fewer leakage compared to previous implementation. The work has done using Visual Studio C#.
