Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPublic key cryptography based on some extensions of group
97
0
0.0
(
0
)
Added by
Ali Abdallah
Publication date
2016
fields
Informatics Engineering
and research's language is
English
Authors
Ali Abdallah
Ask ChatGPT about the research
No Arabic abstract
Bogopolski, Martino and Ventura in [BMV10] introduced a general criteria to construct groups extensions with unsolvable conjugacy problem using short exact sequences. We prove that such extensions have always solvable word problem. This makes the proposed construction a systematic way to obtain finitely presented groups with solvable word problem and unsolvable conjugacy problem. It is believed that such groups are important in cryptography. For this, and as an example, we provide an explicit construction of an extension of Thompson group F and we propose it as a base for a public key cryptography protocol.
rate research
Read More
We study the mutual coupling of chaotic lasers and observe both experimentally and in numeric simulations, that there exists a regime of parameters for which two mutually coupled chaotic lasers establish isochronal synchronization, while a third laser coupled unidirectionally to one of the pair, does not synchronize. We then propose a cryptographic scheme, based on the advantage of mutual-coupling over unidirectional coupling, where all the parameters of the system are public knowledge. We numerically demonstrate that in such a scheme the two communicating lasers can add a message signal (compressed binary message) to the transmitted coupling signal, and recover the message in both directions with high fidelity by using a mutual chaos pass filter procedure. An attacker however, fails to recover an errorless message even if he amplifies the coupling signal.
Recent results of Kaplan et al., building on previous work by Kuwakado and Morii, have shown that a wide variety of classically-secure symmetric-key cryptosystems can be completely broken by quantum chosen-plaintext attacks (qCPA). In such an attack, the quantum adversary has the ability to query the cryptographic functionality in superposition. The vulnerable cryptosystems include the Even-Mansour block cipher, the three-round Feistel network, the Encrypted-CBC-MAC, and many others. In this work, we study simple algebraic adaptations of such schemes that replace $(mathbb Z/2)^n$ addition with operations over alternate finite groups--such as $mathbb Z/{2^n}$--and provide evidence that these adaptations are qCPA-secure. These adaptations furthermore retain the classical security properties (and basic structural features) enjoyed by the original schemes. We establish security by treating the (quantum) hardness of the well-studied Hidden Shift problem as a basic cryptographic assumption. We observe that this problem has a number of attractive features in this cryptographic context, including random self-reducibility, hardness amplification, and--in many cases of interest--a reduction from the search version to the decisional version. We then establish, under this assumption, the qCPA-security of several such Hidden Shift adaptations of symmetric-key constructions. We show that a Hidden Shift version of the Even-Mansour block cipher yields a quantum-secure pseudorandom function, and that a Hidden Shift version of the Encrypted CBC-MAC yields a collision-resistant hash function. Finally, we observe that such adaptations frustrate the direct Simons algorithm-based attacks in more general circumstances, e.g., Feistel networks and slide attacks.
In this note, we compute the {Sigma}^1(G) invariant when 1 {to} H {to} G {to} K {to} 1 is a short exact sequence of finitely generated groups with K finite. As an application, we construct a group F semidirect Z_2 where F is the R. Thompsons group F and show that F semidirect Z_2 has the R-infinity property while F is not characteristic. Furthermore, we construct a finite extension G with finitely generated commutator subgroup G but has a finite index normal subgroup H with infinitely generated H.
We compute the {Omega}^1(G) invariant when 1 {to} H {to} G {to} K {to} 1 is a split short exact sequence. We use this result to compute the invariant for pure and full braid groups on compact surfaces. Applications to twisted conjugacy classes and to finite generation of commutator subgroups are also discussed.
In this paper, we compute the {Sigma}^n(G) and {Omega}^n(G) invariants when 1 rightarrow H rightarrow G rightarrow K rightarrow 1 is a short exact sequence of finitely generated groups with K finite. We also give sufficient conditions for G to have the R_{infty} property in terms of {Omega}^n(H) and {Omega}^n(K) when either K is finite or the sequence splits. As an application, we construct a group F rtimes? Z_2 where F is the R. Thompsons group F and show that F rtimes Z_2 has the R_{infty} property while F is not characteristic.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
