*15:17* [Pub][ePrint]
A New Approach to Discrete Logarithm Problem with Auxiliary Inputs, by Taechan Kim and Jung Hee Cheon
Embedding an element of a finite field into auxiliary groups such as elliptic curve groups or extension fields of finite fields has been useful tool for analysis of cryptographic problems such as establishing the equivalence between the discrete logarithm problem and Diffie-Hellman problem or solving the discrete logarithm problem with auxiliary inputs (DLPwAI). Actually, Cheon\'s algorithm solving the DLPwAI can be regarded as a quantitative version of den Boer and Maurer. Recently, Kim showed in his dissertation that the generalization of Cheon\'s algorithm using embedding technique including Satoh\'s \\cite{Sat09} is no faster than Pollard\'s rho algorithm when $d\\nmid (p\\pm 1)$. In this paper, we propose a new approach to solve DLPwAI concentrating on the behavior of function mapping between the finite fields rather than using an embedding to auxiliary groups. This result shows the relation between the complexity of the algorithm and the number of absolutely irreducible factors of the substitution polynomials, hence enlightens the research on the substitution polynomials.

More precisely, with a polynomial $f(x)$ of degree $d$ over $\\mathbf{F}_p$, the proposed algorithm shows the complexity $O\\left(\\sqrt{p^2/R}\\log^2d\\log p\\right)$ group operations to recover $\\alpha$ with $g, g^{\\alpha}, \\dots, g^{\\alpha^{d}}$, where $R$ denotes the number of pairs $(x, y)\\in\\mathbf{F}_p\\times \\mathbf{F}_p$ such that $f(x)-f(y)=0$. As an example using the Dickson polynomial, we reveal $\\alpha$ in $O(p^{1/3}\\log^2{d}\\log{p})$ group operations when $d|(p+1)$. Note that Cheon\'s algorithm requires $g, g^{\\alpha}, \\dots, g^{\\alpha^{d}}, \\dots, g^{\\alpha^{2d}}$ as an instance for the same problem.

*15:17* [Pub][ePrint]
Candidate Multilinear Maps from Ideal Lattices and Applications, by Sanjam Garg and Craig Gentry and Shai Halevi
We describe plausible lattice-based constructions with properties thatapproximate the sought-after multilinear maps in hard-discrete-logarithm

groups, and show that some applications of such multi-linear maps can

be realized using our approximations.

The security of our constructions relies on seemingly hard problems in

ideal lattices, which can be viewed as extensions of the assumed

hardness of the NTRU function.

*00:17* [Pub][JoC]
A One-Time Stegosystem and Applications to Efficient Covert Communication
Abstract We present the first information-theoretic steganographic protocol with an asymptotically optimal ratio of key length to message length that operates on arbitrary covertext distributions with constant min-entropy. Our results are also applicable to the computational setting: our stegosystem can be composed over a pseudorandom generator to send longer messages in a computationally secure fashion. In this respect our scheme offers a significant improvement in terms of the number of pseudorandom bits generated by the two parties in comparison to previous results known in the computational setting. Central to our approach for improving the overhead for general distributions is the use of combinatorial constructions that have been found to be useful in other contexts for derandomization: almost *t*-wise independent function families.

- Content Type Journal Article
- Pages 1-22
- DOI 10.1007/s00145-012-9135-4
- Authors

- Aggelos Kiayias, Department of Computer Science and Engineering, University of Connecticut, Storrs, CT, USA
- Yona Raekow, Fraunhofer Institute for Algorithms and Scientific Computing, St. Augustin, Germany
- Alexander Russell, Department of Computer Science and Engineering, University of Connecticut, Storrs, CT, USA
- Narasimha Shashidhar, Department of Computer Science, Sam Houston State University, Huntsville, TX, USA

- Journal Journal of Cryptology
- Online ISSN 1432-1378
- Print ISSN 0933-2790

From: Wed, 24 Oct 2012 17:55:35 GMT
*15:17* [Pub][ePrint]
Secure Outsourced Attribute-Based Signatures, by Jin Li, Xiaofeng Chen, Jingwei Li, Chunfu Jia, Duncan S. Wong, Willy Susilo
Attribute-based signature (ABS) is a useful variant of digital signature, which enables users to sign messages over attributes without revealing any information other than the fact that they have attested to the messages. However, heavy computational cost is required during signing in existing work of ABS, which grows linearly with the size of the predicate formula. As a result, this presents a significant challenge for resource-limited users (such as mobile devices) to perform such heavy computation independently. Aiming at tackling the challenge above, we propose and formalize anew paradigm called OABS, in which the computational overhead at user side is greatly reduced through outsourcing such intensive computation to an untrusted signing-cloud service provider (S-CSP). Furthermore, we apply this novel paradigm to existing ABS to reduce complexity and present two schemes, i) in the first OABS scheme, the number of exponentiations involving in signing is reduced from $O(d)$ to $O(1)$ (nearly three), where $d$ is the upper bound of threshold value defined in the predicate; ii) our second scheme is built on Herranz et al\'s construction with constant-size signatures. The number of exponentiations in signing is reduced from $O(d^2)$ to $O(d)$ and the communication overhead is $O(1)$. Security analysis demonstrates that both OABS schemes are secure in terms of the unforgeability and attribute-signer privacy definitions specified in the proposed security model. Finally, to allow for high efficiency and flexibility, we discuss extensions of OABS and show how to achieve accountability and outsourced verification as well.

*15:17* [Pub][ePrint]
Breaking Public Keys - How to Determine an Unknown RSA Public Modulus, by Hans-Joachim Knobloch
Not surprisingly, the common use of any public key crypto system involves publishing the public key and keeping the private key secret. There are however a few applications where both the private and public key are kept secret, thereby effectively converting a public key crypto algorithm to a symmetric algorithm.We show that if the RSA cryptosystem is used in such a symmetric application, it is possible to determine the public RSA modulus if the public exponent is known and short, such as 3 or F4=65537, and two or more plaintext/ciphertext (or, if RSA is used for signing, signed value/signature) pairs are known.

*15:17* [Pub][ePrint]
An Efﬁcient Three-Party Authenticated Key Exchange Protocol for Mobile-Commerce Environments Using Elliptic Curve Cryptography, by Nishant Doshi
In the three party authentication key exchange(3PAKE) protocol, more than two parties can communicate and

set up common shared secret key using the server. Recently,

Tan et al. proposed an enhanced 3PAKE scheme based on

elliptic curve cryptography (ECC) to minimize the operations and

make compatible for mobile commerce environments. However,

Nose showed the scheme of Tan et al. is susceptible to the

impersonation attack and the man-in-middle attack. However, in

this paper we have shown that Tan et al. protocol is susceptible to

the known session-speciﬁc temporary information attack and the

clock synchronization attack too. Afterwards, we have proposed

the protocol that withstands against the above mentioned attacks.

In addition, our proposed approach is based on the hash function

in place of the encryption/decryption function that was used in

Tan et al. scheme.