A Family of Almost Difference Family on Galois Ring GR(22, 22s)

2021 ◽  
Vol 10 (02) ◽  
pp. 544-547
Author(s):  
丽彦 李
2020 ◽  
Vol 22 (2) ◽  
pp. 175-187
Author(s):  
Herman Westerink ◽  
Philippe Van Haute

Although Freud's ‘Family Romances’ from 1909 is hardly ever discussed at length in secondary literature, this article highlights this short essay as an important and informative text about Freud's changing perspectives on sexuality in the period in which the text was written. Given the fact that Freud, in his 1905 Three Essays, develops a radical theory of infantile sexuality as polymorphously perverse and as autoerotic pleasure, we argue that ‘Family Romances’, together with the closely related essay on infantile sexual theories (1908), paves the way for new theories of sexuality defined in terms of object relations informed by knowledge of sexual difference. ‘Family Romances’, in other words, preludes the introduction of the Oedipus complex, but also – interestingly – gives room for a Jungian view of sexuality and sexual phantasy. ‘Family Romances’ is thus a good illustration of the complex way in which Freud's theories of sexuality developed through time.


2021 ◽  
Vol 11 (8) ◽  
pp. 3330
Author(s):  
Pietro Nannipieri ◽  
Stefano Di Matteo ◽  
Luca Baldanzi ◽  
Luca Crocetti ◽  
Jacopo Belli ◽  
...  

Random numbers are widely employed in cryptography and security applications. If the generation process is weak, the whole chain of security can be compromised: these weaknesses could be exploited by an attacker to retrieve the information, breaking even the most robust implementation of a cipher. Due to their intrinsic close relationship with analogue parameters of the circuit, True Random Number Generators are usually tailored on specific silicon technology and are not easily scalable on programmable hardware, without affecting their entropy. On the other hand, programmable hardware and programmable System on Chip are gaining large adoption rate, also in security critical application, where high quality random number generation is mandatory. The work presented herein describes the design and the validation of a digital True Random Number Generator for cryptographically secure applications on Field Programmable Gate Array. After a preliminary study of literature and standards specifying requirements for random number generation, the design flow is illustrated, from specifications definition to the synthesis phase. Several solutions have been studied to assess their performances on a Field Programmable Gate Array device, with the aim to select the highest performance architecture. The proposed designs have been tested and validated, employing official test suites released by NIST standardization body, assessing the independence from the place and route and the randomness degree of the generated output. An architecture derived from the Fibonacci-Galois Ring Oscillator has been selected and synthesized on Intel Stratix IV, supporting throughput up to 400 Mbps. The achieved entropy in the best configuration is greater than 0.995.


Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 702
Author(s):  
Aixian Zhang ◽  
Keqin Feng

Normal bases are widely used in applications of Galois fields and Galois rings in areas such as coding, encryption symmetric algorithms (block cipher), signal processing, and so on. In this paper, we study the normal bases for Galois ring extension R / Z p r , where R = GR ( p r , n ) . We present a criterion on the normal basis for R / Z p r and reduce this problem to one of finite field extension R ¯ / Z ¯ p r = F q / F p ( q = p n ) by Theorem 1. We determine all optimal normal bases for Galois ring extension.


2021 ◽  
Vol 28 (04) ◽  
pp. 581-600
Author(s):  
Hai Q. Dinh ◽  
Hualu Liu ◽  
Roengchai Tansuchat ◽  
Thang M. Vo

Negacyclic codes of length [Formula: see text] over the Galois ring [Formula: see text] are linearly ordered under set-theoretic inclusion, i.e., they are the ideals [Formula: see text], [Formula: see text], of the chain ring [Formula: see text]. This structure is used to obtain the symbol-pair distances of all such negacyclic codes. Among others, for the special case when the alphabet is the finite field [Formula: see text] (i.e., [Formula: see text]), the symbol-pair distance distribution of constacyclic codes over [Formula: see text] verifies the Singleton bound for such symbol-pair codes, and provides all maximum distance separable symbol-pair constacyclic codes of length [Formula: see text] over [Formula: see text].


2019 ◽  
Vol 29 (09) ◽  
pp. 1950122 ◽  
Author(s):  
Jie Liu ◽  
Xiaojun Tong ◽  
Zhu Wang ◽  
Jing Ma ◽  
Longteng Yi

A Rao–Nam cryptosystem based on error correction code is proposed to provide both security and reliability. Since its security is drastically constrained by the limited error syndromes, in this paper, an improved Rao–Nam cryptosystem based on fractional order hyperchaotic system and Extended Difference Family–Quasi-Cyclic–Low-Density Parity-Check (EDF–QC–LDPC) codes is proposed to improve the security. A four-dimensional fractional order hyperchaotic system is constructed and is used to generate an excellent pseudorandom sequence. By replacing error syndromes with the pseudorandom sequence and permuting the coded message dynamically, the security of the Rao–Nam cryptosystem is enhanced greatly. The ability of the improved Rao–Nam cryptosystem against known attacks is analyzed and the error correction performance with different parameters is simulated. The results show that the proposed cryptosystem has a significant advantage of resisting the chosen-plaintext attack. Moreover, the proposed cryptosystem retains high capacity of error correction.


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