Abstract: Recently, Jia et al. proposed a remote user authentication scheme using bilinear pairings and an Elliptic Curve Cryptosystem (ECC). However, the scheme is vulnerable to privileged insider attack at their proposed registration phase and to forgery attack at their proposed authentication phase. In addition, the scheme can be vulnerable to server spoofing attack because it does not provide mutual authentication between the user and the remote server. Therefore, this paper points out that the Jia et al. scheme is vulnerable to the above three attacks.
Abstract: Key management represents a major and the most
sensitive part of cryptographic systems. It includes key generation,
key distribution, key storage, and key deletion. It is also considered
the hardest part of cryptography. Designing secure cryptographic
algorithms is hard, and keeping the keys secret is much harder.
Cryptanalysts usually attack both symmetric and public key
cryptosystems through their key management. We introduce a
protocol to exchange cipher keys over insecure communication
channel. This protocol is based on public key cryptosystem,
especially elliptic curve cryptosystem. Meanwhile, it tests the cipher
keys and selects only the good keys and rejects the weak one.
Abstract: Polynomial bases and normal bases are both used for
elliptic curve cryptosystems, but field arithmetic operations such as
multiplication, inversion and doubling for each basis are implemented
by different methods. In general, it is said that normal bases, especially
optimal normal bases (ONB) which are special cases on normal bases,
are efficient for the implementation in hardware in comparison with
polynomial bases. However there seems to be more examined by
implementing and analyzing these systems under similar condition. In
this paper, we designed field arithmetic operators for each basis over
GF(2233), which field has a polynomial basis recommended by SEC2
and a type-II ONB both, and analyzed these implementation results.
And, in addition, we predicted the efficiency of two elliptic curve
cryptosystems using these field arithmetic operators.
Abstract: The major building block of most elliptic curve cryptosystems
are computation of multi-scalar multiplication. This paper
proposes a novel algorithm for simultaneous multi-scalar multiplication,
that is by employing addition chains. The previously known
methods utilizes double-and-add algorithm with binary representations.
In order to accomplish our purpose, an efficient empirical
method for finding addition chains for multi-exponents has been
proposed.
Abstract: Groups where the discrete logarithm problem (DLP) is believed to be intractable have proved to be inestimable building blocks for cryptographic applications. They are at the heart of numerous protocols such as key agreements, public-key cryptosystems, digital signatures, identification schemes, publicly verifiable secret sharings, hash functions and bit commitments. The search for new groups with intractable DLP is therefore of great importance.The goal of this article is to study elliptic curves over the ring Fq[], with Fq a finite field of order q and with the relation n = 0, n ≥ 3. The motivation for this work came from the observation that several practical discrete logarithm-based cryptosystems, such as ElGamal, the Elliptic Curve Cryptosystems . In a first time, we describe these curves defined over a ring. Then, we study the algorithmic properties by proposing effective implementations for representing the elements and the group law. In anther article we study their cryptographic properties, an attack of the elliptic discrete logarithm problem, a new cryptosystem over these curves.