Ayineedi Venkateswarlu

Error linear complexity measures for multisequences

Complexity measures for sequences over finite fields, such as the linear complexity and the k-error linear complexity, play an important role in cryptology. Recent developments in stream ciphers point towards an interest in word-based stream ciphers, which require the study of the complexity of multisequences. We introduce various options for error linear complexity measures for multisequences. For finite multisequences as well as for periodic multisequences with prime period, we present formulas for the number of multisequences with given error linear complexity for several cases, and we present lower bounds for the expected error linear complexity.

Results on multiples of primitive polynomials and their products over GF(2)

Linear feedback shift registers (LFSR) are important building blocks in stream cipher cryptosysterns. To be cryptographically secure, the connection polynomials of the LFSRs need to be primitive over GF(2). Moreover, the polynomials should have high weight and they should not have sparse multiples at low or moderate degree. Here we provide results on t-nomial multiples of primitive polynomials and their products. We present results for counting t-nomial multiples and also analyse the statistical distribution of their degrees. The results in this paper helps in deciding what kind of primitive polynomial should be chosen and which should be discarded in terms of cryptographic applications. Further the results involve important theoretical identities in terms of t-nomial multiples which were not known earlier.

Partial Key Exposure Attack on CRT-RSA

In Eurocrypt 2005, Ernst et al. proposed an attack on RSA allowing to recover the secret key when the most or least significant bits of the decryption exponent \(d\) are known. In Indocrypt 2011, Sarkar generalized this by considering the number of unexposed blocks in the decryption exponent is more than one. In this paper, for the first time, we study this situation for CRT-RSA. Further, we consider the case when random bits of one decryption exponent are exposed in this model. These results have implications in side channel attacks.

Multiples of Primitive Polynomials and Their Products over GF(2)

A standard model of nonlinear combiner generator for stream cipher system combines the outputs of several independent Linear Feed-back Shift Register (LFSR) sequences using a nonlinear Boolean function to produce the key stream. Given such a model, cryptanalytic attacks have been proposed by finding the sparse multiples of the connection polynomials corresponding to the LFSRs. In this direction recently a few works are published on t-nomial multiples of primitive polynomials. We here provide further results on degree distribution of the t-nomial multiples. However, getting the sparse multiples of just a single primitive polynomial does not suffice. The exact cryptanalysis of the nonlinear combiner model depends on finding sparse multiples of the products of primitive polynomials. We here make a detailed analysis on t-nomial multiples of products of primitive polynomials. We present new enumeration results for these multiples and provide some estimation on their degree distribution.

On the direct construction of recursive MDS matrices

MDS matrices allow to build optimal linear diffusion layers in the design of block ciphers and hash functions. There has been a lot of study in designing efficient MDS matrices suitable for software and/or hardware implementations. In particular recursive MDS matrices are considered for resource constrained environments. Such matrices can be expressed as a power of simple companion matrices, i.e., an MDS matrix

Towards a general construction of recursive MDS diffusion layers

M = C_g^k

Periodic multisequences with large error linear complexity

M=Cgk for some companion matrix corresponding to a monic polynomial