We give an alternative proof of a result of Miyazaki and Yasuhara that there exists links that are not smoothly slice in 𝑆 2 × 𝑆 2 . We discuss potential applications to the detection of exotic 𝑆 2 × 𝑆 2 . This is a follow-up note to a similar paper for the ℂℙ 2 # case.
In the practical application of pseudorandom binary sequences (e.g., in cryptography or signal processing), a need often arises for a long binary sequence while only much shorter binary sequences with suitable properties are readily available. In this paper, an N-2-element pseudorandom binary lattice is constructed from two shorter, N-length binary sequences with strong pseudorandom properties. Next, this N-2 -element binary lattice is 'unrolled' (using a row-major order) to generate a significantly longer N-2-element pseudorandom sequence. While optimal upper bounds for the pseudorandom measures of this new lattice and sequence are not established, we provide non-trivial upper bounds for these measures, demonstrating their strong pseudorandom properties.
This paper presents a further development of a well-known construction that relies on polynomials and the Legendre symbol. To address theoretical security concerns regarding the original method, which used a single polynomial, we introduce a new approach that combines three different polynomials to generate the sequence, thereby enhancing its security. We prove that the sequences produced by this new construction also exhibit strong pseudorandom properties with respect to the pseudorandom measures introduced by Mauduit and S & aacute;rk & ouml;zy.
SLIM and LBCIoT are lightweight block ciphers proposed for IoT applications. We present differential meet-in-the-middle attacks on these ciphers, attacking up to 18-rounds of SLIM and 26-rounds of LBCIoT. We discuss several implementation variants and possible improvements of these attacks. Experimental validation also shows some results that may be of independent interest in the cryptanalysis of other ciphers. Namely, the problems with low-probability differentials and the questionable accuracy of standard complexity estimates of using filters, including previous complexity estimates of differential meet-in-the-middle attacks.
We provide a new interpretation of the arithmetic on Hessian Kummer lines using level-3 theta structures. This allows us to break the record for tripling on elliptic curves and their Kummer lines, requiring only 4 multiplications and 4 squarings per tripling for well-chosen curve parameters.
