Simona Samardjiska

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In this paper we describe two methods for constructing Multivariate Quadratic Quasigroups (MQQ) in Galois fields of any characteristic and order. Our constructions extend the previously known constructions defined for operations over the prime field of characteristic 2. Application of these new constructions can reduce the public key size of the recently(More)
We present a new family of linear binary codes of length n and dimension k accompanied with a fast list decoding algorithm that can correct up to n 2 errors in a bounded channel with an error density ρ. The decisional problem of decoding random codes using these generalized error sets is NP-complete. Next we use the properties of these codes to design both(More)
We introduce a new family of binary linear codes suitable for steganographic matrix embedding. The main characteristic of the codes is the staircase random block structure of the generator matrix. We propose an efficient list decoding algorithm for the codes that finds a close codeword to a given random word. We provide both theoretical analysis of the(More)
We propose a new multivariate probabilistic encryption scheme with decryption errors MQQ-ENC that belongs to the family of MQQ-based public key schemes. Similarly to MQQ-SIG, the trapdoor is constructed using quasigroup string transformations with multivariate quadratic quasi-groups, and a minus modifier with relatively small and fixed number of removed(More)
Staircase-Generator codes (St-Gen codes) have recently been introduced in the design of code-based public key schemes and in the design of steganographic matrix embedding schemes. In this paper we propose a method for random splitting of St-Gen Codes and use it to design a new coding based public key encryption scheme. The scheme uses the known list(More)
This paper presents MQDSS, the first signature scheme with a security reduction based on the problem of solving a multivariate system of quadratic equations (MQ problem). In order to construct this scheme we give a new security reduction for the Fiat-Shamir transform from a large class of 5-pass identification schemes and show that a previous attempt from(More)
We investigate the security of the family of MQQ public key cryptosystems using multivari-ate quadratic quasigroups (MQQ). These cryptosystems show especially good performance properties. In particular, the MQQ-SIG signature scheme is the fastest scheme in the ECRYPT benchmarking of cryptographic systems (eBACS). We show that both the signature scheme(More)
Recently we have defined Staircase-Generator codes (St-Gen codes) and their variant with a random split of the generator matrix of the codes. One unique property of these codes is that they work with arbitrary error sets. In this paper we give a brief overview of St-Gen codes and the list decoding algorithm for their decoding. We also analyze the semantic(More)
One of the crucial factors for enabling fast and secure computations in the Zettabyte era is the use of incremental cryptographic primitives. For files ranging from several megabytes up to hundreds of gigabytes, incremental cryptographic primitives offer speedup factors measured in multiple orders of magnitude. In this paper we define two incremental hash(More)