Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

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.

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

We present a new block cipher LED. While dedicated to compact hardware implementation, and offering the smallest silicon footprint among comparable block ciphers, the cipher has been designed to simultaneously tackle three additional goals. First, we explore the role of an ultra-light (in fact non-existent) key schedule. Second, we consider the resistance of ciphers, and LED in particular, to related-key attacks: we are able to derive simple yet interesting AES-like security proofs for LED regarding related- or single-key attacks. And third, while we provide a block cipher that is very compact in hardware, we aim to maintain a reasonable performance profile for software implementation.

The LED block cipher

RFID security is currently one of the major challenges cryptography has to face, often solved by protocols assuming that an ontag hash function is available. In this article we present the PHOTON lightweight hash-function family, available in many different flavors and suitable for extremely constrained devices such as passive RFID tags. Our proposal uses a sponge-like construction as domain extension algorithm and an AES-like primitive as internal unkeyed permutation. This allows us to obtain the most compact hash function known so far (about 1120 GE for 64-bit collision resistance security), reaching areas very close to the theoretical optimum (derived from the minimal internal state memory size). Moreover, the speed achieved by PHOTON also compares quite favorably to its competitors. This is mostly due to the fact that unlike for previously proposed schemes, our proposal is very simple to analyze and one can derive tight AES-like bounds on the number of active Sboxes. This kind of AES-like primitive is usually not well suited for ultra constrained environments, but we describe in this paper a new method for generating the column mixing layer in a serial way, lowering drastically the area required. Finally, we slightly extend the sponge framework in order to offer interesting trade-offs between speed and preimage security for small messages, the classical use-case in hardware.

/pdf/the-photon-family-of-lightweight-hash-functions-3uam81b18v.pdf

The PHOTON family of lightweight Hash functions

An Introduction to Probability Theory and its Applications, Vol. II.

In this paper, we propose a 128-bit block cipher ARIA which is an involution substitution and permutation encryption network(SPN). We use the same S-boxes as Rijndael to eliminate defects which are caused by a totally involution structure. In the diffusion layer of ARIA, a 16 x 16 binary matrix of the maximum branch number 8 is used to avoid some attacks well applied to the reduced round of Rijndael. ARIA uses only basic operations, S-box substitutions and XOR's together with an involution structure so that it can be efficiently implemented on various platforms.

New block cipher: ARIA

We present a new method for upper bounding the maximum differential probability and the maximum linear hull probability for 2 rounds of SPN structures. Our upper bound can be computed for any value of the branch number of the linear transformation and by incorporating the distribution of differential probability values and linear probability values for S-box. On application to AES, we obtain that the maximum differential probability and the maximum linear hull probability for 4 rounds of AES are bounded by 1.144 × 2− 111 and 1.075 × 2− 106, respectively.

/pdf/improving-the-upper-bound-on-the-maximum-differential-and-10h0ttbn5a.pdf

Improving the upper bound on the maximum differential and the maximum linear hull probability for SPN structures and AES

In this paper, we propose a 128-bit block cipher ARIA which is an involution substitution and permutation encryption network(SPN). We use the same S-boxes as Rijndael to eliminate defects which are caused by a totally involution structure. In the diffusion layer of ARIA, a 16× 16 binary matrix of the maximum branch number 8 is used to avoid some attacks well applied to the reduced round of Rijndael. ARIA uses only basic operations, S-box substitutions and XOR’s together with an involution structure so that it can be efficiently implemented on various platforms.

New Block Cipher: ARIA

Let be random variables and a triangular array of constants. In this paper we find the various conditions on {ani } and {Xn } under which converges to zero almost surely. It is shown that for the identically distributed random variables the conditions a.s. A generalization of Marcinkiewicz's law of large numbers is given. It is shown that for the i.i.d. case the conditions and EX = 0 imply that a.s

Soo Hak Sung

Papers

New block cipher: ARIA

Improving the upper bound on the maximum differential and the maximum linear hull probability for SPN structures and AES

New Block Cipher: ARIA

Almost sure convergence theorems of weighted sums of random variables

More on complete convergence for arrays