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Chapter and Conference Paper
An Efficient \(F_4\) -style Based Algorithm to Solve MQ Problems
The multivariate public key cryptosystem (MPKC) is a potential post-quantum cryptosystem. Its safety depends on the hardness of solving systems of algebraic equations over finite fields. In particular, the mul...
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Article
Open AccessImprovement of FPPR method to solve ECDLP
Solving the elliptic curve discrete logarithm problem (ECDLP) by using Gröbner basis has recently appeared as a new threat to the security of elliptic curve cryptography and pairing-based cryptosystems. At Eur...
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Chapter and Conference Paper
Recovering RSA Secret Keys from Noisy Key Bits with Erasures and Errors
We discuss how to recover RSA secret keys from noisy key bits with erasures and errors. There are two known algorithms recovering original secret keys from noisy keys. At Crypto 2009, Heninger and Shacham prop...
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Chapter and Conference Paper
Improvement of Faugère et al.’s Method to Solve ECDLP
Solving the elliptic curve discrete logarithm problem (ECDLP) by using Gröbner basis has recently appeared as a new threat to the security of elliptic curve cryptography and pairing-based cryptosystems. At Eur...
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Chapter and Conference Paper
Breaking Pairing-Based Cryptosystems Using η T Pairing over GF(397)
In this paper, we discuss solving the DLP over GF(36·97) by using the function field sieve (FFS) for breaking paring-based cryptosystems using the η T pairing o...
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Chapter and Conference Paper
A Unified Framework for Small Secret Exponent Attack on RSA
We address a lattice based method on small secret exponent attack on RSA scheme. Boneh and Durfee reduced the attack into finding small roots of a bivariate modular equation:
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Chapter and Conference Paper
Key Length Estimation of Pairing-Based Cryptosystems Using η T Pairing
The security of pairing-based cryptosystems depends on the difficulty of the discrete logarithm problem (DLP) over certain types of finite fields. One of the most efficient algorithms for computing a pairing i...
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Chapter and Conference Paper
Solving a 676-Bit Discrete Logarithm Problem in GF(36n )
Pairings on elliptic curves over finite fields are crucial for constructing various cryptographic schemes. The η T pairing on supersingular curves over GF(3 ...
