On the Division Property of SIMON48 and SIMON64

{\sc Simon} is a family of lightweight block ciphers published by the U.S. National Security Agency (NSA) in 2013. Due to its novel and bit-based design, integral cryptanalysis on {\sc Simon} seems a tough job. At EUROCRYPT 2015 Todo proposed division property which is a generalized integral property, and he applied this technique to searching integral distinguishers of {\sc Simon} block ciphers by considering the left and right halves of {\sc Simon} independently. As a result, he found 11-round integral distinguishers for both {\sc Simon}48 and {\sc Simon}64. Recently, at FSE 2016 Todo \emph{et al.} proposed bit-based division property that considered each bit independently. This technique can find more accurate distinguishers, however, as pointed out by Todo \emph{et al.} the time and memory complexity is bounded by $2^n$ for an $n$-bit block cipher. Thus, bit-based division property is only applicable to {\sc Simon}32. In this paper we propose a new technique that achieves a trade-off between considering each bit independently and considering left and right halves as a whole, which is actually a trade-off between time-memory and the accuracy of the distinguishers. We proceed by splitting the state of {\sc Simon} into small pieces and study the division property propagations of circular shift and bitwise AND operations under the state partition. Moreover, we propose two different state partitions and study the influences of different partitions on the propagation of division property. We find that different partitions greatly impact the division property propagation of circular shift which will finally result in a big difference on the length of integral distinguishers. By using a tailored search algorithm for {\sc Simon}, we find 12-round integral distinguishers for {\sc Simon}48 and {\sc Simon}64 respectively, which improve Todo\u27s results by one round for both variants

The Maiorana-McFarland structure based cryptanalysis of Simon

In this paper we propose the linear hull construction for block ciphers with quadratic Maiorana-McFarland structure round functions. The search for linear trails with high squared correlations from our Maiorana-McFarland structure based constructive linear cryptanalysis is linear algebraic. Hence from this linear algebraic essence, the space of all linear trails has the structure such that good linear hulls can be constructed. Then for the Simon2n and its variants, we prove the lower bound $\frac{1}{2^n}$ on the potential of the linear hull with the fixed input and output masks at arbitrary long rounds, under independent assumptions. We argue that for Simon2n the potential of the realistic linear hull of the Simon2n with the linear key-schedule should be bigger than $\frac{1}{2^{2n}}$.\\ On the other hand we prove that the expected differential probability (EDP) is at least $\frac{1}{2^n}$ under the independence assumptions. It is argued that the lower bound of EDP of Simon2n of realistic differential trails is bigger than $\frac{1}{2^{2n}}$. It seems that at least theoretically the Simon2n is insecure for the key-recovery attack based on our new constructed linear hulls and key-recovery attack based on our constructed differential trails.\

A Review of Existing 4-bit Crypto S-box cryptanalysis Techniques and Two New Techniques with 4-bit Boolean Functions for Cryptanalysis of 4-bit Crypto S-boxes.

4-bit Linear Relations play an important role in Cryptanalysis of 4-bit Bijective Crypto S-boxes. 4-bit finite differences also a major part of cryptanalysis of 4-bit substitution boxes. Count of existence of all 4-bit linear relations, for all of 16 input and 16 output 4-bit bit patterns of 4-bit bijective crypto S-boxes said as S-boxes has been reported in Linear Cryptanalysis of 4-bit S-boxes. Count of existing finite differences from each element of output S-boxes to distant output S-boxes have been noted in Differential Cryptanalysis of S-boxes. In this paper a brief review of these cryptanalytic methods for 4-bit S-boxes has been introduced in a very lucid and conceptual manner. Two new Analysis Techniques, one to search for the existing Linear Approximations among the input Boolean Functions (BFs) and output BFs of a particular 4-bit S-Box has also been introduced in this paper. The search is limited to find the existing linear relations or approximations in the contrary to count the number existent linear relations among all 16 4-bit input and output bit patterns within all possible linear approximations. Another is to find number of balanced 4-bit BFs in difference output S-boxes. Better the number of Balanced BFs, Better the security

Cryptanalysis of Reduced round SKINNY Block Cipher

SKINNY is a family of lightweight tweakable block ciphers designed to have the smallest hardware footprint. In this paper, we present zero-correlation linear approximations and the related-tweakey impossible differential characteristics for different versions of SKINNY .We utilize Mixed Integer Linear Programming (MILP) to search all zero-correlation linear distinguishers for all variants of SKINNY, where the longest distinguisher found reaches 10 rounds. Using a 9-round characteristic, we present 14 and 18-round zero correlation attacks on SKINNY-64-64 and SKINNY- 64-128, respectively. Also, for SKINNY-n-n and SKINNY-n-2n, we construct 13 and 15-round related-tweakey impossible differential characteristics, respectively. Utilizing these characteristics, we propose 23-round related-tweakey impossible differential cryptanalysis by applying the key recovery attack for SKINNY-n-2n and 19-round attack for SKINNY-n-n. To the best of our knowledge, the presented zero-correlation characteristics in this paper are the first attempt to investigate the security of SKINNY against this attack and the results on the related-tweakey impossible differential attack are the best reported ones

A review of cryptographic properties of S-boxes with Generation and Analysis of crypto secure S-boxes.

In modern as well as ancient ciphers of public key cryptography, substitution boxes find a permanent seat. Generation and cryptanalysis of 4-bit as well as 8-bit crypto S-boxes is of utmost importance in modern cryptography. In this paper, a detailed review of cryptographic properties of S-boxes has been illustrated. The generation of crypto S-boxes with 4-bit as well as 8-bit Boolean functions (BFs) and Polynomials over Galois field GF(p^q) has also been of keen interest of this paper. The detailed analysis and comparison of generated 4-bit and 8-bit S-boxes with 4-bit as well as 8-bit S-boxes of Data Encryption Standard (DES) and Advance Encryption Standard (AES) respectively, has incorporated with example. Detailed analysis of generated S-boxes claims a better result than DES and AES in view of security of crypto S-boxes

Security of Ubiquitous Computing Systems

The chapters in this open access book arise out of the EU Cost Action project Cryptacus, the objective of which was to improve and adapt existent cryptanalysis methodologies and tools to the ubiquitous computing framework. The cryptanalysis implemented lies along four axes: cryptographic models, cryptanalysis of building blocks, hardware and software security engineering, and security assessment of real-world systems. The authors are top-class researchers in security and cryptography, and the contributions are of value to researchers and practitioners in these domains. This book is open access under a CC BY license

Security of Ubiquitous Computing Systems

The chapters in this open access book arise out of the EU Cost Action project Cryptacus, the objective of which was to improve and adapt existent cryptanalysis methodologies and tools to the ubiquitous computing framework. The cryptanalysis implemented lies along four axes: cryptographic models, cryptanalysis of building blocks, hardware and software security engineering, and security assessment of real-world systems. The authors are top-class researchers in security and cryptography, and the contributions are of value to researchers and practitioners in these domains. This book is open access under a CC BY license