216 research outputs found
[[alternative]]Computing and Crypto Applications of Discrete Algebraic Structures
計畫編號:NSC93-2115-M032-008研究期間:200408~200507研究經費:398,000[[sponsorship]]行政院國家科學委員
Cryptography from tensor problems
We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler
Certificateless Signature Scheme Based on Rabin Algorithm and Discrete Logarithm
Certificateless signature can effectively immue the key escrow problem in the identity-based signature scheme. But the security of the most certificateless signatures usually depends on only one mathematical hard problem, which makes the signature vulnerable when the underlying hard problem has been broken. In order to strengthen the security, in this paper, a certificateless signature whose security depends on two mathematical hard problems, discrete logarithm and factoring problems, is proposed. Then, the proposed certificateless signature can be proved secure in the random oracle, and only both of the two mathematical hard problems are solved, can the proposed signature be broken. As a consequence, the proposed certificateless signature is more secure than the previous signatures. On the other hand, with the pre-computation of the exponential modular computation, it will save more time in the signature signing phase. And compared with the other schemes of this kind, the proposed scheme is more efficient
Assessing security of some group based cryptosystems
One of the possible generalizations of the discrete logarithm problem to
arbitrary groups is the so-called conjugacy search problem (sometimes
erroneously called just the conjugacy problem): given two elements a, b of a
group G and the information that a^x=b for some x \in G, find at least one
particular element x like that. Here a^x stands for xax^{-1}. The computational
difficulty of this problem in some particular groups has been used in several
group based cryptosystems. Recently, a few preprints have been in circulation
that suggested various "neighbourhood search" type heuristic attacks on the
conjugacy search problem. The goal of the present survey is to stress a
(probably well known) fact that these heuristic attacks alone are not a threat
to the security of a cryptosystem, and, more importantly, to suggest a more
credible approach to assessing security of group based cryptosystems. Such an
approach should be necessarily based on the concept of the average case
complexity (or expected running time) of an algorithm.
These arguments support the following conclusion: although it is generally
feasible to base the security of a cryptosystem on the difficulty of the
conjugacy search problem, the group G itself (the "platform") has to be chosen
very carefully. In particular, experimental as well as theoretical evidence
collected so far makes it appear likely that braid groups are not a good choice
for the platform. We also reflect on possible replacements.Comment: 10 page
Proposal of a Signature Scheme based on STS Trapdoor
A New digital signature scheme based on Stepwise Triangular Scheme (STS) is proposed. The proposed trapdoor has resolved the vulnerability of STS and secure against both Gröbner Bases and Rank Attacks. In addition, as a basic trapdoor, it
is more efficient than the existing systems. With the efficient implementation, the Multivariate Public Key Cryptosystems (MPKC) signature public key has the signature
longer than the message by less than 25 %, for example
MI-T-HFE, a New Multivariate Signature Scheme
In this paper, we propose a new multivariate signature scheme named MI-T-HFE as a competitor of QUARTZ. The core map of MI-T-HFE is of an HFEv type but more importantly has a specially designed trapdoor. This special trapdoor makes MI-T-HFE have several attractive advantages over QUARTZ. First of all, the core map and the public map of MI-T-HFE are both surjective. This surjectivity property is important for signature schemes because any message should always have valid signatures; otherwise it may be troublesome to exclude those messages without valid signatures. However this property is missing for a few major signature schemes, including QUARTZ. A practical parameter set is proposed for MI-T-HFE with the same length of message and same level of security as QUARTZ, but it has smaller public key size, and is more efficient than (the underlying HFEv- of) QUARTZ with the only cost that its signature length is twice that of QUARTZ
A study on the fast ElGamal encryption
ElGamal cryptosystem is typically developed in the multiplicative group ( is a prime number), but it can be applied to the other groups in which discrete logarithm problem should be computationally infeasible. Practically, instead of ElGamal in , various variants such as ECElGamal (ElGamal in elliptic curve group), CRTElGamal (ElGamal in subgroup of where and are primes) have already been used for the semantic security.
In this paper, for the fast decryption, we reduced the private CRT exponent () and ()maintaining full sized private exponent () in CRTElGamal as reducing () and () in RSA for the fast decryption. (i.e. as in rebalanced RSA).
In this case, unlike rebalanced RSA, decryption of CRTElGamal can be done faster without losing of encryption speed. As a result, it is possible to propose the fast public key cryptosystem that has fast encryption and fast decryption
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