Partial Orders, Lattices, Well-Founded Orderings, Unique Prime Factorization in ℤ and GCDs, Equivalence Relations, Fibonacci and Lucas Numbers, Public Key Cryptography and RSA, Distributive Lattices, Boolean Algebras, Heyting Algebras

2011 ◽  
pp. 257-363
Author(s):  
Jean Gallier
Keyword(s):  
Public Key Cryptography ◽  
Partial Orders ◽  
Boolean Algebras ◽  
Public Key ◽  
Equivalence Relations ◽  
Distributive Lattices ◽  
Heyting Algebras ◽  
Lucas Numbers ◽  
Prime Factorization ◽  
Fibonacci And Lucas Numbers

scholarly journals Bitopological duality for distributive lattices and Heyting algebras

2010 ◽  
Vol 20 (3) ◽  
pp. 359-393 ◽  
Author(s):  
GURAM BEZHANISHVILI ◽  
NICK BEZHANISHVILI ◽  
DAVID GABELAIA ◽  
ALEXANDER KURZ
Keyword(s):  
Boolean Algebras ◽  
Distributive Lattices ◽  
Heyting Algebras ◽  
Priestley Spaces ◽  
Spectral Spaces ◽  
Algebraic Concepts ◽  
Stone Spaces

We introduce pairwise Stone spaces as a bitopological generalisation of Stone spaces – the duals of Boolean algebras – and show that they are exactly the bitopological duals of bounded distributive lattices. The category PStone of pairwise Stone spaces is isomorphic to the category Spec of spectral spaces and to the category Pries of Priestley spaces. In fact, the isomorphism of Spec and Pries is most naturally seen through PStone by first establishing that Pries is isomorphic to PStone, and then showing that PStone is isomorphic to Spec. We provide the bitopological and spectral descriptions of many algebraic concepts important in the study of distributive lattices. We also give new bitopological and spectral dualities for Heyting algebras, thereby providing two new alternatives to Esakia's duality.

scholarly journals Linear Time Solution to Prime Factorization by Tissue P Systems with Cell Division

2011 ◽  
Vol 2 (3) ◽  
pp. 49-60 ◽  
Author(s):  
Xingyi Zhang ◽  
Yunyun Niu ◽  
Linqiang Pan ◽  
Mario J. Pérez-Jiménez
Keyword(s):  
Cell Division ◽  
Quantum Computer ◽  
Linear Time ◽  
Public Key Cryptography ◽  
Polynomial Time Algorithm ◽  
P Systems ◽  
Public Key ◽  
Prime Factorization ◽  
Factorization Problem ◽  
Time Solution

Prime factorization is useful and crucial for public-key cryptography, and its application in public-key cryptography is possible only because prime factorization has been presumed to be difficult. A polynomial-time algorithm for prime factorization on a quantum computer was given by P. W. Shor in 1997. In this work, it is considered as a function problem, and in the framework of tissue P systems with cell division, a linear-time solution to prime factorization problem is given on biochemical computational devices – tissue P systems with cell division, instead of computational devices based on the laws of quantum physical.

scholarly journals Linear Time Solution to Prime Factorization by Tissue P Systems with Cell Division

2014 ◽  
pp. 207-220
Author(s):  
Xingyi Zhang ◽  
Yunyun Niu ◽  
Linqiang Pan ◽  
Mario J. Pérez-Jiménez
Keyword(s):  
Cell Division ◽  
Quantum Computer ◽  
Linear Time ◽  
Public Key Cryptography ◽  
Polynomial Time Algorithm ◽  
P Systems ◽  
Public Key ◽  
Prime Factorization ◽  
Factorization Problem ◽  
Time Solution

Prime factorization is useful and crucial for public-key cryptography, and its application in public-key cryptography is possible only because prime factorization has been presumed to be difficult. A polynomial-time algorithm for prime factorization on a quantum computer was given by P. W. Shor in 1997. In this work, it is considered as a function problem, and in the framework of tissue P systems with cell division, a linear-time solution to prime factorization problem is given on biochemical computational devices – tissue P systems with cell division, instead of computational devices based on the laws of quantum physical.

Profinite Heyting Algebras and Profinite Completions of Heyting Algebras

2009 ◽  
Vol 16 (1) ◽  
pp. 29-47
Author(s):  
Guram Bezhanishvili ◽  
Patrick J. Morandi
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattice ◽  
Heyting Algebra ◽  
Boolean Algebras ◽  
Distributive Lattices ◽  
Heyting Algebras ◽  
Profinite Completion ◽  
Bounded Distributive Lattice ◽  
Recent Developments ◽  
Profinite Completions

Abstract This paper surveys recent developments in the theory of profinite Heyting algebras (resp. bounded distributive lattices, Boolean algebras) and profinite completions of Heyting algebras (resp. bounded distributive lattices, Boolean algebras). The new contributions include a necessary and sufficient condition for a profinite Heyting algebra (resp. bounded distributive lattice) to be isomorphic to the profinite completion of a Heyting algebra (resp. bounded distributive lattice). This results in simple examples of profinite bounded distributive lattices that are not isomorphic to the profinite completion of any bounded distributive lattice. We also show that each profinite Boolean algebra is isomorphic to the profinite completion of some Boolean algebra. It is still an open question whether each profinite Heyting algebra is isomorphic to the profinite completion of some Heyting algebra.

Analisis dan Implementasi Protokol Otentikasi FIDO U2F

2017 ◽  
Vol 9 (1) ◽  
pp. 30-35
Author(s):  
Sunderi Pranata ◽  
Hargyo Tri Nugroho ◽  
Hirofumi Yamaki
Keyword(s):  
Public Key Cryptography ◽  
Authentication Protocol ◽  
Public Key ◽  
Next Generation ◽  
Index Terms ◽  
Mitm Attack

It is known that password itself is not enough for formidable authentication method since it has a lot of vulnerabilities. Multi factor authentication (MFA) is introduced for the next generation for good authentication to address that issue. MFA combines two or more of three principles of good security, “something you know”, “something you have”, and “something you are”. Most MFA mechanisms work as one time passwords (OTP). However, they can still be vulnerable to phishing and MiTM attack. On top of that, OTP can be hard to use as it requires user to input another password given by the device (SMS, token, authenticator). Implemented in small USB U2F device, FIDO U2F delivers easier yet stronger security on authentication process which implements public key cryptography, challenge-response protocol, and phishing and MitM protection.  Index Terms— Authentication protocol, FIDO U2F, Multi factor authentication, OTP

Certificateless Mult-i receiver Signcryption Scheme Based on Multivariate Public Key Cryptography

2012 ◽  
Vol 35 (9) ◽  
pp. 1881 ◽  
Author(s):  
Hui-Xian LI ◽  
Xu-Bao CHEN ◽  
Liao-Jun PANG ◽  
Yu-Min WANG
Keyword(s):  
Public Key Cryptography ◽  
Public Key ◽  
Multivariate Public Key ◽  
Signcryption Scheme

IMPLEMENTASI ALGORITMA SCHMIDT-SAMOA PADA ENKRIPSI DEKRIPSI EMAIL BERBASIS ANDROID

2013 ◽  
Vol 9 (1) ◽  
Author(s):  
Willy Ristanto ◽  
Willy Sudiarto Raharjo ◽  
Antonius Rachmat Chrismanto
Keyword(s):  
Public Key Cryptography ◽  
Text Messages ◽  
Public Key ◽  
Client Application ◽  
Performance Measurements ◽  
Encryption And Decryption ◽  
Number Variation

Cryptography is a technique for sending secret messages. This research builds an Android-based email client application which implement cryptography with Schmidt-Samoa algorithm, which is classified as a public key cryptography. The algorithm performs encryption and decryption based on exponential and modulus operation on text messages. The application use 512 and 1024 bit keys. Performance measurements is done using text messages with character number variation of 5 – 10.000 characters to obtain the time used for encryption and decryption process. As a result of this research, 99,074% data show that decryption process is faster than encryption process. In 512 bit keys, the system can perform encryption process in 520 - 18.256 miliseconds, and decryption process in 487 - 5.688 miliseconds. In 1024 bit keys, system can perform encryption process in 5626 – 52,142 miliseconds (7.388 times slower than 512 bit keys) and decryption process with time 5463 – 15,808 miliseconds or 8.290 times slower than 512 bit keys.

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