Abstract: This paper presents a method for determining all of the co-prime right angle triangles in the Euclidean field by looking at the intersection of the Pythagorean and Platonic right angle triangles and the corresponding lattice that this produces. The co-prime properties of each lattice point representing a unique right angle triangle are then considered. This paper proposes a conjunction between these two ancient disparaging theorists. This work has wide applications in information security where cryptography involves improved ways of finding tuples of prime numbers for secure communication systems. In particular, this paper has direct impact in enhancing the encryption and decryption algorithms in cryptography.
Abstract: In this paper the development of a software to
encrypt messages with asymmetric cryptography is presented. In
particular, is used the RSA (Rivest, Shamir and Adleman) algorithm
to encrypt alphanumeric information. The software allows to
generate different public keys from two prime numbers provided by
the user, the user must then select a public-key to generate the
corresponding private-key. To encrypt the information, the user must
provide the public-key of the recipient as well as the message to be
encrypted. The generated ciphertext can be sent through an insecure
channel, so that would be very difficult to be interpreted by an
intruder or attacker. At the end of the communication, the recipient
can decrypt the original message if provide his/her public-key and
his/her corresponding private-key.
Abstract: In this article we explore the application of a formal
proof system to verification problems in cryptography. Cryptographic
properties concerning correctness or security of some cryptographic
algorithms are of great interest. Beside some basic lemmata, we
explore an implementation of a complex function that is used in
cryptography. More precisely, we describe formal properties of this
implementation that we computer prove. We describe formalized
probability distributions (σ-algebras, probability spaces and conditional
probabilities). These are given in the formal language of the
formal proof system Isabelle/HOL. Moreover, we computer prove
Bayes- Formula. Besides, we describe an application of the presented
formalized probability distributions to cryptography. Furthermore,
this article shows that computer proofs of complex cryptographic
functions are possible by presenting an implementation of the Miller-
Rabin primality test that admits formal verification. Our achievements
are a step towards computer verification of cryptographic primitives.
They describe a basis for computer verification in cryptography.
Computer verification can be applied to further problems in cryptographic
research, if the corresponding basic mathematical knowledge
is available in a database.
Abstract: In this paper we explore the application of a formal proof system to verification problems in cryptography. Cryptographic properties concerning correctness or security of some cryptographic algorithms are of great interest. Beside some basic lemmata, we explore an implementation of a complex function that is used in cryptography. More precisely, we describe formal properties of this implementation that we computer prove. We describe formalized probability distributions (o--algebras, probability spaces and condi¬tional probabilities). These are given in the formal language of the formal proof system Isabelle/HOL. Moreover, we computer prove Bayes' Formula. Besides we describe an application of the presented formalized probability distributions to cryptography. Furthermore, this paper shows that computer proofs of complex cryptographic functions are possible by presenting an implementation of the Miller- Rabin primality test that admits formal verification. Our achievements are a step towards computer verification of cryptographic primitives. They describe a basis for computer verification in cryptography. Computer verification can be applied to further problems in crypto-graphic research, if the corresponding basic mathematical knowledge is available in a database.