Name
Abstract | ||
|---|---|---|
In 1995, Kuwakado, Koyama and Tsuruoka presented a new RSA-type scheme based on singular cubic curves $$y^2\\equiv x^3+bx^2\\pmod N$$ where $$N=pq$$ is an RSA modulus. Then, in 2002, Elkamchouchi, Elshenawy and Shaban introduced an extension of the RSA scheme to the field of Gaussian integers using a modulus $$N=PQ$$ where P and Q are Gaussian primes such that $$p=|P|$$ and $$q=|Q|$$ are ordinary primes. Later, in 2007, Castagnos proposed a scheme over quadratic field quotients with an RSA modulus $$N=pq$$. In the three schemes, the public exponent e is an integer satisfying the key equation $$ed-k\\left p^2-1\\right \\left q^2-1\\right =1$$. In this paper, we apply the continued fraction method to launch an attack on the three schemes when the private exponent d is sufficiently small. Our attack can be considered as an extension of the famous Wiener attack on the RSA. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1007/978-3-319-40367-0_16 | ACISP |
Field | DocType | Citations |
Integer,Discrete mathematics,Gaussian integer,Exponent,Quotient,Cryptosystem,Quadratic field,Mathematics,Elliptic curve | Conference | 4 |
PageRank | References | Authors |
0.52 | 4 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Martin W. Bunder | 1 | 64 | 16.78 |
| Abderrahmane Nitaj | 2 | 72 | 15.00 |
| Willy Susilo | 3 | 4823 | 353.18 |
| Joseph Tonien | 4 | 8 | 2.68 |