Showing papers by "Sedat Akleylek published in 2016"

An Efficient Lattice-Based Signature Scheme with Provably Secure Instantiation

Abstract: In view of the expected progress in cryptanalysis it is important to find alternatives for currently used signature schemes such as RSA and ECDSA. The most promising lattice-based signature schemes to replace these schemes are CRYPTO 2013 and GLP CHES 2012. Both come with a security reduction from a lattice problem and have high performance. However, their parameters are not chosen according to their provided security reduction, i.e., the instantiation is not provably secure. In this paper, we present the first lattice-based signature scheme with good performance when provably secure instantiated. To this end, we provide a tight security reduction for the new scheme from the ring learning with errors problem which allows for provably secure and efficient instantiations. We present experimental results obtained from a software implementation of our scheme. They show that our scheme, when provably secure instantiated, performs comparably with BLISS and the GLP scheme.

An Efficient Lattice-Based Signature Scheme with Provably Secure Instantiation.

Abstract: In view of the expected progress in cryptanalysis it is important to find alternatives for currently used signature schemes such as RSA and ECDSA. The most promising lattice-based signature schemes to replace these schemes are CRYPTO 2013 and GLP CHES 2012. Both come with a security reduction from a lattice problem and have high performance. However, their parameters are not chosen according to their provided security reduction, i.e., the instantiation is not provably secure. In this paper, we present the first lattice-based signature scheme with good performance when provably secure instantiated. To this end, we provide a tight security reduction for the new scheme from the ring learning with errors problem which allows for provably secure and efficient instantiations. We present experimental results obtained from a software implementation of our scheme. They show that our scheme, when provably secure instantiated, performs comparably with BLISS and the GLP scheme.

Sparse polynomial multiplication for lattice-based cryptography with small complexity

Abstract: In this paper, we propose efficient modular polynomial multiplication methods with applications in lattice-based cryptography. We provide a sparse polynomial multiplication to be used in the quotient ring $$({\mathbb {Z}}/ p{\mathbb {Z}}) [x] / (x^{n}+1)$$(Z/pZ)[x]/(xn+1). Then, we modify this algorithm with sliding window method for sparse polynomial multiplication. Moreover, the proposed methods are independent of the choice of reduction polynomial. We also implement the proposed algorithms on the Core i5-3210M CPU platform and compare them with number theoretic transform multiplication. According to the experimental results, we speed up the multiplication operation in $$({\mathbb {Z}}/ p{\mathbb {Z}}) [x] / (x^{n}+1)$$(Z/pZ)[x]/(xn+1) at least $$80~\%$$80% and improve the performance of the signature generation and verification process of GLP scheme significantly.

Generating binary diffusion layers with maximum/high branch numbers and low search complexity

Abstract: In this paper, we propose a new method to generate n × n binary matrices for n = ki¾ź2t where k and t are positive integers with a maximum/high of branch numbers and a minimum number of fixed points by using 2t×2t Hadamard almost maximum distance separable matrices and k × k cyclic binary matrix groups. By using the proposed method, we generate n × n for n = 6, 8, 12, 16, and 32 binary matrices with a maximum of branch numbers, which are efficient in software implementations. The proposed method is also applicable with m × m circulant matrices to generate n × nfor n = ki¾źm binary matrices with a maximum/high of branch numbers. For this case, some examples for 16 × 16, 48 × 48, and 64 × 64 binary matrices with branch numbers of 8, 15, and 18, respectively, are presented. Copyright © 2016 John Wiley & Sons, Ltd.