In this paper, we show structural cryptanalyses against two popular networks, i.e., the Feistel Network and the Substitute-Permutation Network (SPN). Our cryptanalyses are distinguishing attacks by an improved integral distinguisher. The integral distinguisher is one of the most powerful attacks against block ciphers, and it is usually constructed by evaluating the propagation characteristic of integral properties, e.g., the ALL or BALANCE property. However, the integral property does not derive useful distinguishers against block ciphers with non-bijective functions and bit-oriented structures. Moreover, since the integral property does not clearly exploit the algebraic degree of block ciphers, it tends not to construct useful distinguishers against block ciphers with low-degree functions. In this paper, we propose a new property called the division property, which is the generalization of the integral property. It can effectively construct the integral distinguisher even if the block cipher has non-bijective functions, bit-oriented structures, and low-degree functions. From viewpoints of the attackable number of rounds or chosen plaintexts, the division property can construct better distinguishers than previous methods. Although our attack is a generic attack, it can improve several integral distinguishers against specific cryptographic primitives. For instance, it can reduce the required number of chosen plaintexts for the 10-round distinguisher on Keccakf from 2 1025 to 2 515 . For the Feistel cipher, it theoretically proves that

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In this article, we revisit the design strategy of PRESENT, leveraging all the advances provided by the research community in construction and cryptanalysis since its publication, to push the design up to its limits. We obtain an improved version, named GIFT, that provides a much increased efficiency in all domains (smaller and faster), while correcting the well-known weakness of PRESENT with regards to linear hulls.GIFT is a very simple and clean design that outperforms even SIMON or SKINNY for round-based implementations, making it one of the most energy efficient ciphers as of today. It reaches a point where almost the entire implementation area is taken by the storage and the Sboxes, where any cheaper choice of Sbox would lead to a very weak proposal. In essence, GIFT is composed of only Sbox and bit-wiring, but its natural bitslice data flow ensures excellent performances in all scenarios, from area-optimised hardware implementations to very fast software implementation on highend platforms. We conducted a thorough analysis of our design with regards to stateof-the-art cryptanalysis, and we provide strong bounds with regards to differential/linear attacks.