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The McEliece cryptosystem is an asymmetric type of cryptography based on error correction code. The classical McEliece used irreducible binary Goppa code which considered unbreakable until now especially with parameter [1024, 524, and 101], but it is suffering from large public key matrix which leads to be difficult to be used practically. In this...
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Citations
... The Binary Goppa code is denoted by Γ(g(z); L), where g(z) is a Goppa generator polynomial of degree t over the extension field GF(2 m ) and L is the range of code such that L⊆GF(2 m ) [14]. ...
... When the errors are fixed, the received message can be decoded [14], using equation (5), which can be written as matrix representation: ...
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#.
