Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Article Citation - WoS: 2Citation - Scopus: 3Integral Characteristics by Keyspace Partitioning(Springer, 2022) Demirbaş, Fatih; Kara, OrhunIn this work, we introduce a new method we call integral by keyspace partitioning to construct integral characteristics for some block ciphers by introducing new integral properties. We introduce the concepts of active with constant difference and identically active integral properties. Then, we divide the key space into equivalence classes and construct integral characteristics for each equivalence class individually by using these integral properties. We exploit the binary diffusion layer and key schedule algorithm of a block cipher to propagate these integral properties through rounds. We apply the new method to the Byte-oriented Substitution-Permutation Network (BSPN) cipher and Midori64 to show its effectiveness. We construct the first iterative integral characteristic for a block cipher to the best of our knowledge. We extend this iterative characteristic for the (M, n)-(BSPN) block cipher where each block of BSPN contains M number of n× n S-Boxes with the block and key sizes M· n. Using at most (M-12)+1 (only 106 when M= 16) chosen plaintexts, we mount key recovery attacks for the first time on BSPN and recover the key for the full round. The time complexity of the key recovery is almost independent of the number of rounds. We also use our method to construct an integral characteristic for Midori64, which can be utilized for a key recovery attack on 11-round Midori64. Our results impose a new security criteria for the design of the key schedule algorithm for some block ciphers.Conference Object Citation - WoS: 25Citation - Scopus: 26Quantum Key Distribution in the Classical Authenticated Key Exchange Framework(Springer, 2013) Mosca, Michele; Stebila, Douglas; Ustaoğlu, BerkantKey establishment is a crucial primitive for building secure channels in a multi-party setting. Without quantum mechanics, key establishment can only be done under the assumption that some computational problem is hard. Since digital communication can be easily eavesdropped and recorded, it is important to consider the secrecy of information anticipating future algorithmic and computational discoveries which could break the secrecy of past keys, violating the secrecy of the confidential channel. Quantum key distribution (QKD) can be used generate secret keys that are secure against any future algorithmic or computational improvements. QKD protocols still require authentication of classical communication, although existing security proofs of QKD typically assume idealized authentication. It is generally considered folklore that QKD when used with computationally secure authentication is still secure against an unbounded adversary, provided the adversary did not break the authentication during the run of the protocol. We describe a security model for quantum key distribution extending classical authenticated key exchange (AKE) security models. Using our model, we characterize the long-term security of the BB84 QKD protocol with computationally secure authentication against an eventually unbounded adversary. By basing our model on traditional AKE models, we can more readily compare the relative merits of various forms of QKD and existing classical AKE protocols. This comparison illustrates in which types of adversarial environments different quantum and classical key agreement protocols can be secure. © 2013 Springer-Verlag.Conference Object Citation - WoS: 2Citation - Scopus: 4Symbolic Computation of Petri Nets(Springer, 2007) Iglesias, Andres; Kapçak, SinanPetri nets are receiving increasing attention from the scientific community during the last few years. They provide the users with a powerful formalism for describing and analyzing a variety of information processing systems such as finite-state machines, concurrent systems, multiprocessors and parallel computation, formal languages, communication protocols, etc. Although the mathematical theory of Petri nets has been intensively analyzed from several points of view, the symbolic computation of these nets is still a challenge, particularly for general-purpose computer algebra systems (CAS). In this paper, a new Mathematica package for dealing with some Petri nets is introduced.