The complexity of Boolean functions
The complexity of Boolean functions
The structured design of cryptographically good s-boxes
Journal of Cryptology
Differential cryptanalysis of the data encryption standard
Differential cryptanalysis of the data encryption standard
The Data Encryption Standard (DES) and its strength against attacks
IBM Journal of Research and Development
Linear cryptanalysis method for DES cipher
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Differential Cryptanalysis of DES-like Cryptosystems
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Linear Cryptanalysis Using Multiple Approximations
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Constructions of Freebly-One-Way Families of Permutations
ASIACRYPT '92 Proceedings of the Workshop on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Cryptanalysis of Block Ciphers with Overdefined Systems of Equations
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
A Fast New DES Implementation in Software
FSE '97 Proceedings of the 4th International Workshop on Fast Software Encryption
On the Classification of 4 Bit S-Boxes
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
PRESENT: An Ultra-Lightweight Block Cipher
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
Cube Attacks on Tweakable Black Box Polynomials
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
A Feebly Secure Trapdoor Function
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
A toolbox for cryptanalysis: linear and affine equivalence algorithms
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Hummingbird: ultra-lightweight cryptography for resource-constrained devices
FC'10 Proceedings of the 14th international conference on Financial cryptograpy and data security
Multiple differential cryptanalysis: theory and practice
FSE'11 Proceedings of the 18th international conference on Fast software encryption
Dependent linear approximations: the algorithm of biryukov and others revisited
CT-RSA'10 Proceedings of the 2010 international conference on Topics in Cryptology
The hummingbird-2 lightweight authenticated encryption algorithm
RFIDSec'11 Proceedings of the 7th international conference on RFID Security and Privacy
The hummingbird-2 lightweight authenticated encryption algorithm
RFIDSec'11 Proceedings of the 7th international conference on RFID Security and Privacy
Threshold implementations of all 3×3 and 4×4 s-boxes
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
Influence of S-Boxes to the resistance of GOST algorithm against linear cryptanalysis
Proceedings of the 6th International Conference on Security of Information and Networks
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We present cryptanalytic results of an exhaustive search of all 16! bijective 4-bit S-Boxes. Previously affine equivalence classes have been exhaustively analyzed in 2007 work by Leander and Poschmann. We extend on this work by giving further properties of the optimal S-Box linear equivalence classes. In our main analysis we consider two S-Boxes to be cryptanalytically equivalent if they are isomorphic up to the permutation of input and output bits and a XOR of a constant in the input and output. We have enumerated all such equivalence classes with respect to their differential and linear properties. These equivalence classes are equivalent not only in their differential and linear bounds but also have equivalent algebraic properties, branch number and circuit complexity. We describe a "golden" set of S-boxes that have ideal cryptographic properties. We also present a comparison table of S-Boxes from a dozen published cryptographic algorithms.