The objective of this paper is to give a comprehensive introduction to applied cryptography with an engineer or computer scientist in mind. The emphasis is on the knowledge needed to create practical systems which supports integrity, confidentiality, or authenticity. Topics covered includes an introduction to the concepts in cryptography, attacks against cryptographic systems, key use and handling, random bit generation, encryption modes, and message authentication codes. Recommendations on algorithms and further reading is given in the end of the paper. This paper should make the reader able to build, understand and evaluate system descriptions and designs based on the cryptographic components described in the paper.

[서평]「Applied Cryptography」

Introduction A fundamental objective of cryptography is to enable two persons to communicate over an insecure channel (a public channel such as the internet) in such a way that any other person is unable to recover their message (called the plaintext ) from what is sent in its place over the channel (the ciphertext ). The transformation of the plaintext into the ciphertext is called encryption , or enciphering. Encryption-decryption is the most ancient cryptographic activity (ciphers already existed four centuries b.c.), but its nature has deeply changed with the invention of computers, because the cryptanalysis (the activity of the third person, the eavesdropper, who aims at recovering the message) can use their power. The encryption algorithm takes as input the plaintext and an encryption key K E , and it outputs the ciphertext. If the encryption key is secret, then we speak of conventional cryptography , of private key cryptography , or of symmetric cryptography . In practice, the principle of conventional cryptography relies on the sharing of a private key between the sender of a message (often called Alice in cryptography) and its receiver (often called Bob). If, on the contrary, the encryption key is public, then we speak of public key cryptography . Public key cryptography appeared in the literature in the late 1970s.

/pdf/boolean-models-and-methods-in-mathematics-computer-science-3vbrnbyptk.pdf

Boolean Models and Methods in Mathematics, Computer Science, and Engineering: Boolean Functions for Cryptography and Error-Correcting Codes

This paper describes new techniques for fast correlation attacks, based on Gallager iterative decoding algorithm using parity-check equations of weight greater than 3. These attacks can be applied to any key-stream generator based on LFSRs and it does not require that the involved feedback polynomial have a low weight. We give a theoretical analysis of all fast correlation attacks, which shows that our algorithm with parity-check equations of weight 4 or 5 is usually much more efficient than correlation attacks based on convolutional codes or on turbo codes. Simulation results confirm the validity of this comparison. In this context, we also point out the major role played by the nonlinearity of the Boolean function used in a combination generator.

/pdf/improved-fast-correlation-attacks-using-parity-check-17j3r98z5q.pdf

Improved fast correlation attacks using parity-check equations of weight 4 and 5

Recently, algebraic attacks have received a lot of attention in the cryptographic literature. It has been observed that a Boolean function f used as a cryptographic primitive, and interpreted as a multivariate polynomial over F/sub 2/, should not have low degree multiples obtained by multiplication with low degree nonzero functions. In this paper, we show that a Boolean function having low nonlinearity is (also) weak against algebraic attacks, and we extend this result to higher order nonlinearities. Next, we present enumeration results on linearly independent annihilators. We also study certain classes of highly nonlinear resilient Boolean functions for their algebraic immunity. We identify that functions having low-degree subfunctions are weak in terms of algebraic immunity, and we analyze some existing constructions from this viewpoint. Further, we present a construction method to generate Boolean functions on n variables with highest possible algebraic immunity /spl lceil/n/2/spl rceil/ (this construction, first presented at the 2005 Workshop on Fast Software Encryption (FSE 2005), has been the first one producing such functions). These functions are obtained through a doubly indexed recursive relation. We calculate their Hamming weights and deduce their nonlinearities; we show that they have very high algebraic degrees. We express them as the sums of two functions which can be obtained from simple symmetric functions by a transformation which can be implemented with an algorithm whose complexity is linear in the number of variables. We deduce a very fast way of computing the output to these functions, given their input.

Algebraic immunity for cryptographically significant Boolean functions: analysis and construction

In this paper we investigate the relationship between the nonlinearity and the order of resiliency of a Boolean function. We first prove a sharper version of McEliece theorem for Reed-Muller codes as applied to resilient functions, which also generalizes the well known Xiao-Massey characterization. As a consequence, a nontrivial upper bound on the nonlinearity of resilient functions is obtained. This result coupled with Siegenthaler's inequality leads to the notion of best possible trade-off among the parameters: number of variables, order of resiliency, nonlinearity and algebraic degree. We further show that functions achieving the best possible trade-off can be constructed by the Maiorana-McFarland like technique. Also we provide constructions of some previously unknown functions.

/pdf/nonlinearity-bounds-and-constructions-of-resilient-boolean-58c5jgedav.pdf

Nonlinearity Bounds and Constructions of Resilient Boolean Functions

We study a corpus of particular Boolean functions: the idempotents. They enable us to construct functions which achieve the best possible tradeoffs between the cryptographic fundamental properties: balancedness, correlation-immunity, a high degree and a high nonlinearity (that is a high distance from the affine functions). They all represent extremely secure cryptographic primitives to be implemented in stream ciphers.

/pdf/highly-nonlinear-balanced-boolean-functions-with-a-good-1361nwnu8u.pdf

Highly nonlinear balanced Boolean functions with a good correlation-immunity

Assuming we only have the coded sequence produced by a convolutional encoder at one's disposal, is it possible to recover all the parameters defining this encoder ? The implementation of such complete reconstruction for convolutional codes of any rate is presented in this paper, for both noiseless and noisy communications. Each time, several different solutions, i.e. alleged reconstructed encoders, are obtained, contrary to the awaited unicity. Their study yields a new characterization of convolutional codes along with some properties.

Reconstruction of Convolutional Encoders over GF(q)

When designing secret key ciphers, one approach which has not been very often considered so far, is the construction of block ciphers out of stream ciphers. It nevertheless would combine the advantage of both sides without their respective drawbacks. Only few attempts have been presented yet, and we propose here a completely new approach to block cipher design. By using strong Boolean functions and non-linear feedback shift register (NLFSR), we build a family of block ciphers called crossing over system (COS) ciphers, with arbitrary block size, and a key size of 128, 256 or 192 bits. It is based on a new design called crossing-over, using the internal state of NLFSRs as the constituent of the ciphering output blocks. Two versions have been developed: one considers any kind of plaintext, and the other one is devoted to plaintext without redundancy (e.g. compressed).

http://ieeexplore.ieee.org/iel5/7447/20241/00936001.pdf

Eric Filiol

Papers

Highly nonlinear balanced Boolean functions with a good correlation-immunity

Reconstruction of Convolutional Encoders over GF(q)

A new, fast block cipher design: COS ciphers