Stanislaw P. Radziszowski

The existence of simple 6-(14,7,4) designs

Abstract A cyclic 5-(13, 6, 4) design is constructed and is extended to a simple 6-(14, 7, 4) design via a theorem of Alltop. This design is the smallest possible nontrivial simple 6-design that can exist. Both have full automorphism group cyclic of order 13.

Subgraph Counting Identities and Ramsey Numbers

For each vertexvof a graphG, we consider the numbers of subgraphs of each isomorphism class which lie in the neighbourhood or complementary neighbourhood ofv. These numbers, summed overv, satisfy a series of identities that generalise some previous results of Goodman and ourselves. As sample applications, we improve the previous upper bounds on two Ramsey numbers. Specifically, we show thatR(5, 5)?49 andR(4, 6)?41. We also give some experimental evidence in support of our conjecture thatR(5, 5)=43.

Computation of the Folkman number F e (3, 3; 5)

The problem is considered under which conditions a 4-connected planar or projective planar graph has a Hamiltonian cycle containing certain prescribed edges and missing certain forbidden edges. The results are applied to obtain novel lower bounds on the number of distinct Hamiltonian cycles that must be present in a 5-connected graph that is embedded into the plane or into the projective plane with face-width at least five. Especially, we show that every 5-connected plane or projective plane triangulation on n vertices with no non-contractible cyles of length less than five contains at least

An overview of cryptanalysis research for the advanced encryption standard

2^{{\cal O}(n^{1/4})}

Trustworthy Data Collection From Implantable Medical Devices Via High-Speed Security Implementation Based on IEEE 1363

distinct Hamiltonian cycles.

On the covering of t -sets with ( t +1)-sets: C(9,5,4) and C(10,6,5)

Since its release in November 2001, the Advanced Encryption Standard (NIST FIPS-197) has been the subject of extensive cryptanalysis research. The importance of this research has intensified since AES was named, in 2003, by NSA as a Type-1 Suite B Encryption Algorithm (CNSSP-15). As such, AES is now authorized to protect classified and unclassified national security systems and information. This paper provides an overview of current cryptanalysis research on the AES cryptographic algorithm. Discussion is provided on the impact by each technique to the strength of the algorithm in national security applications. The paper is concluded with an attempt at a forecast of the usable life of AES in these applications.

Wheel and star-critical Ramsey numbers for quadrilateral

Implantable medical devices (IMDs) have played an important role in many medical fields. Any failure in IMDs operations could cause serious consequences and it is important to protect the IMDs access from unauthenticated access. This study investigates secure IMD data collection within a telehealthcare [mobile health (m-health)] network. We use medical sensors carried by patients to securely access IMD data and perform secure sensor-to-sensor communications between patients to relay the IMD data to a remote doctors server. To meet the requirements on low computational complexity, we choose N-th degree truncated polynomial ring (NTRU)-based encryption/decryption to secure IMD-sensor and sensor-sensor communications. An extended matryoshkas model is developed to estimate direct/indirect trust relationship among sensors. An NTRU hardware implementation in very large integrated circuit hardware description language is studied based on industry Standard IEEE 1363 to increase the speed of key generation. The performance analysis results demonstrate the security robustness of the proposed IMD data access trust model.

Linear programming in some Ramsey problems

Abstract A (υ, k , t ) covering system is a pair ( X , B ) where X is a υ-set of points and B is a family of k -subsets, called blocks, of X such that every t -subset of X is contained in at least one block. The minimum possible number of blocks in a (υ, k , t ) covering system is denoted by C (υ, k , t ). It is proven that there are exactly three non-isomorphic systems giving C (9, 5, 4) = 30, and a unique system giving C (10, 6, 5) = 50.

NTRU-based sensor network security: a low-power hardware implementation perspective

The star-critical Ramsey number r ? ( H 1 , H 2 ) is the smallest integer k such that every red/blue coloring of the edges of K n - K 1 , n - k - 1 contains either a red copy of H 1 or a blue copy of H 2 , where n is the graph Ramsey number R ( H 1 , H 2 ) . We study the cases of r ? ( C 4 , C n ) and R ( C 4 , W n ) . In particular, we prove that r ? ( C 4 , C n ) = 5 for all n ? 4 , obtain a general characterization of Ramsey-critical ( C 4 , C n ) -graphs, and establish the exact values of R ( C 4 , W n ) for 9 cases of n between 18 and 44 .

Cybersecurity Education: Bridging the Gap Between Hardware and Software Domains

We derive new upper bounds for the classical two-color Ramsey numbers R(4, 5) ≤ 27, R(5, 5) ≤ 52, and R(4, 6) ≤ 43; the previous best upper bounds known for these numbers were 28, 53, and 44, respectively. The new bounds are obtained by solving large integer linear programs and with the help of other computer algorithms.