On the Security of the Hashing Scheme Based on SL2
نویسندگان
چکیده
Tillich and Zémor proposed a hashing scheme based on the group of unimodular matrices SL2(Fq) over a finite field Fq of q = 2 elements. Charnes and Pieprzyk studied the security of this scheme. They showed that for n = 131 and for some irreducible polynomial P131(x) this scheme is weak. We show that with sufficiently high probability the polynomials Pn(x) can be chosen in such a way that this type of attack can be avoided. Futhermore, we generalize the Tillich-Zémor hashing scheme for any finite field Fq and show that the new generalized scheme has similar properties.
منابع مشابه
Image authentication using LBP-based perceptual image hashing
Feature extraction is a main step in all perceptual image hashing schemes in which robust features will led to better results in perceptual robustness. Simplicity, discriminative power, computational efficiency and robustness to illumination changes are counted as distinguished properties of Local Binary Pattern features. In this paper, we investigate the use of local binary patterns for percep...
متن کاملWeaknesses in the SL2(IFs2) Hashing Scheme
We show that for various choices of the parameters in the SL2(IF2n) hashing scheme, suggested by Tillich and Zémor, messages can be modified without changing the hash value. Moreover, examples of hash functions “with a trapdoor” within this family are given. Due to these weaknesses one should impose at least certain restrictions on the allowed parameter values when using the SL2(IF2n) hashing s...
متن کاملOn the design and security of a lattice-based threshold secret sharing scheme
In this paper, we introduce a method of threshold secret sharing scheme (TSSS) in which secret reconstruction is based on Babai's nearest plane algorithm. In order to supply secure public channels for transmitting shares to parties, we need to ensure that there are no quantum threats to these channels. A solution to this problem can be utilization of lattice-based cryptosystems for these channe...
متن کاملAn efficient secure channel coding scheme based on polar codes
In this paper, we propose a new framework for joint encryption encoding scheme based on polar codes, namely efficient and secure joint secret key encryption channel coding scheme. The issue of using new coding structure, i.e. polar codes in Rao-Nam (RN) like schemes is addressed. Cryptanalysis methods show that the proposed scheme has an acceptable level of security with a relatively smaller ke...
متن کاملNavigating in the Cayley graph of SL2(Fp) and applications to hashing
Cayley hash functions are based on a simple idea of using a pair of (semi)group elements, A and B, to hash the 0 and 1 bit, respectively, and then to hash an arbitrary bit string in the natural way, by using multiplication of elements in the (semi)group. In this paper, we focus on hashing with 2× 2 matrices over Fp. Since there are many known pairs of 2× 2 matrices over Z that generate a free m...
متن کامل