Nonlinarity of Boolean functions and hyperelliptic curves

We study the nonlinearity of functions defined on a finite field with 2^m elements which are the trace of a polynomial of degree 7 or more general polynomials. We show that for m odd such functions have rather good nonlinearity properties. We use for that recent results of Maisner and Nart about zeta functions of supersingular curves of genus 2. We give some criterion for a vectorial function not to be almost perfect nonlinear

C-DIFFERENTIALS AND GENERALIZED CRYPTOGRAPHIC PROPERTIES OF VECTORIAL BOOLEAN AND P-ARY FUNCTIONS

This dissertation investigates a newly defined cryptographic differential, called a c-differential, and its relevance to the nonlinear substitution boxes of modern symmetric block ciphers. We generalize the notions of perfect nonlinearity, bentness, and avalanche characteristics of vectorial Boolean and p-ary functions using the c-derivative and a new autocorrelation function, while capturing the original definitions as special cases (i.e., when c=1). We investigate the c-differential uniformity property of the inverse function over finite fields under several extended affine transformations. We demonstrate that c-differential properties do not hold in general across equivalence classes typically used in Boolean function analysis, and in some cases change significantly under slight perturbations. Thus, choosing certain affine equivalent functions that are easy to implement in hardware or software without checking their c-differential properties could potentially expose an encryption scheme to risk if a c-differential attack method is ever realized. We also extend the c-derivative and c-differential uniformity into higher order, investigate some of their properties, and analyze the behavior of the inverse function's second order c-differential uniformity. Finally, we analyze the substitution boxes of some recognizable ciphers along with certain extended affine equivalent variations and document their performance under c-differential uniformity.Commander, United States NavyApproved for public release. Distribution is unlimited

Implementing Symmetric Cryptography Using Sequence of Semi-Bent Functions

Symmetric cryptography is a cornerstone of everyday digital security, where two parties must share a common key to communicate. The most common primitives in symmetric cryptography are stream ciphers and block ciphers that guarantee confidentiality of communications and hash functions for integrity. Thus, for securing our everyday life communication, it is necessary to be convinced by the security level provided by all the symmetric-key cryptographic primitives. The most important part of a stream cipher is the key stream generator, which provides the overall security for stream ciphers. Nonlinear Boolean functions were preferred for a long time to construct the key stream generator. In order to resist several known attacks, many requirements have been proposed on the Boolean functions. Attacks against the cryptosystems have forced deep research on Boolean function to allow us a more secure encryption. In this work we describe all main requirements for constructing of cryptographically significant Boolean functions. Moreover, we provide a construction of Boolean functions (semi-bent Boolean functions) which can be used in the construction of orthogonal variable spreading factor codes used in code division multiple access (CDMA) systems as well as in certain cryptographic applications

Current implementation of advance encryption standard (AES) S-Box

Although the attack on cryptosystem is still not severe, the development of the scheme is stillongoing especially for the design of S-Box. Two main approach has beenused, which areheuristic method and algebraic method. Algebraic method as in current AES implementationhas been proven to be the most secure S-Box design to date. This review paper willconcentrate on two kinds of method of constructing AES S-Box, which are algebraic approachand heuristic approach. The objective is to review a method of constructing S-Box, which arecomparable or close to the original construction of AES S-Box especially for the heuristicapproach. Finally, all the listed S-Boxes from these two methods will be compared in terms oftheir security performance which is nonlinearity and differential uniformity of the S-Box. Thefinding may offer the potential approach to develop a new S-Box that is better than theoriginal one.Keywords: block cipher; AES; S-Bo

Machine Learning Attacks on Optical Physical Unclonable Functions

Traditional security algorithms for authentication and encryption rely heavily on the digital storage of secret information (e.g. cryptographic key), which is vulnerable to copying and destruction. An attractive alternative to digital storage is the storage of this secret information in the intrinsic, unpredictable, and non-reproducible features of a physical object. Such devices are termed physical unclonable functions (PUFs), and recent research proves that PUFs can resolve the vulnerabilities associated with digital key storage while otherwise maintaining the same level of security as traditional methods. Modern cryptographic algorithms rest on the shoulders of this one-way principle in certain mathematical algorithms (e.g. RSA or Rabin functions). However, a key difference between PUFs and traditional one-way algorithms is that conventional algorithms can be duplicated. Here, we investigate a silicon photonic PUF a novel cryptographic device based on ultrafast and nonlinear optical interactions within an integrated silicon photonic cavity. This work reviews the important properties of this device including high complexity of light interaction with the material, unpredictability of the response and ultrafast generation of private information. We further explore the resistance of silicon photonic PUFs against numerical modeling attacks and demonstrate the influence of cavity’s inherent nonlinear optical properties on the success of such attacks. Finally, we demonstrate encrypted data storage and compare the results of decryption using a genuine silicon PUF device the “clone” generated by the numerical algorithm. Finally, we provide similar analysis of modeling attacks on another well-known type of optical PUF, called the optical scattering PUF (OSPUF). While not as compatible with integration as the silicon photonic PUF, the OSPUF system is known to be extremely strong and resistant to adversarial attacks. By attacking a simulated model of OSPUF, we attempt to present the underlying reasons behind the strong security of this given device and how this security scales with the OSPUFs physical parameters