Basics of associative algebras
... Simple and semisimple algebras The above discussion suggests that you can have a wide variety of algebras even in quite small dimension. Not all of them are of equal interest however. Often it suffices to consider certain nice classes of algebras, such as simple algebras. The definition of a simple al ...
... Simple and semisimple algebras The above discussion suggests that you can have a wide variety of algebras even in quite small dimension. Not all of them are of equal interest however. Often it suffices to consider certain nice classes of algebras, such as simple algebras. The definition of a simple al ...
CLASS NUMBER DIVISIBILITY OF QUADRATIC FUNCTION
... function fields F whose ideal class numbers are divisible by a given positive integer g. In [3], using the Friesen’s result, Chakraborty and Mukhopadhyay ...
... function fields F whose ideal class numbers are divisible by a given positive integer g. In [3], using the Friesen’s result, Chakraborty and Mukhopadhyay ...
rsa
... It is possible to perform arithmetic with equivalence classes mod n. – [a] + [b] = [a+b] – [a] * [b] = [a*b] In order for this to make sense, you must get the same answer (equivalence) class independent of the choice of a and b. In other words, if you replace a and b by numbers equivalent to a or b ...
... It is possible to perform arithmetic with equivalence classes mod n. – [a] + [b] = [a+b] – [a] * [b] = [a*b] In order for this to make sense, you must get the same answer (equivalence) class independent of the choice of a and b. In other words, if you replace a and b by numbers equivalent to a or b ...
Splittings of Bicommutative Hopf algebras - Mathematics
... ring K(n)∗ ' Fp [vn±1 ] where p is a prime and the degree of vn is 2(pn − 1). The first two authors were led by their study [KL02] to an interest in the fibration K(Z, 3) → BOh8i → BSpin. The Morava K-theory for p = 2 of this was analyzed in [KLW]. In particular, for n = 2, although the first map do ...
... ring K(n)∗ ' Fp [vn±1 ] where p is a prime and the degree of vn is 2(pn − 1). The first two authors were led by their study [KL02] to an interest in the fibration K(Z, 3) → BOh8i → BSpin. The Morava K-theory for p = 2 of this was analyzed in [KLW]. In particular, for n = 2, although the first map do ...
Classical Cryptography
... Two identical segments of plaintext are encrypted to the same ciphertext if they are δ position apart, where δ = 0 (mod m) Kasiski Test: find all identical segments of length > 3 and record the distance between them: δ1, δ2, ... m divides gcd(δ1), gcd(δ2), ... ...
... Two identical segments of plaintext are encrypted to the same ciphertext if they are δ position apart, where δ = 0 (mod m) Kasiski Test: find all identical segments of length > 3 and record the distance between them: δ1, δ2, ... m divides gcd(δ1), gcd(δ2), ... ...
Contents 1. Recollections 1 2. Integers 1 3. Modular Arithmetic 3 4
... clearly write rk = am + bn for some a, b ∈ Z. That is, rk is a common divisor and at least as large as the gcd(m, n); therefore, rk = gcd(m, n), as claimed. Theorem 2.6 has a number of consequences. We need a couple more definitions: Definition 2.7. A pair m, n of integers is called relatively prime ...
... clearly write rk = am + bn for some a, b ∈ Z. That is, rk is a common divisor and at least as large as the gcd(m, n); therefore, rk = gcd(m, n), as claimed. Theorem 2.6 has a number of consequences. We need a couple more definitions: Definition 2.7. A pair m, n of integers is called relatively prime ...
Deterministic Approximation Algorithms for the Nearest Codeword
... approximation ratio. Finally, our third algorithm has the same approximation ratio as the randomized algorithm of [3] and a slightly super-polynomial running time. All our algorithms (as well as other known algorithms for the NCP in the literature) can be easily generalized to fields other than F2 . ...
... approximation ratio. Finally, our third algorithm has the same approximation ratio as the randomized algorithm of [3] and a slightly super-polynomial running time. All our algorithms (as well as other known algorithms for the NCP in the literature) can be easily generalized to fields other than F2 . ...
Algebraic Proof Complexity: Progress, Frontiers and Challenges
... research was recently covered in SigLog; see Nordström [Nordström, 2015]). For resolution and its weak extensions, strong lower bounds are known since Haken [Haken, 1985]. But the major open questions in proof complexity, those originating from boolean circuit complexity and complexity class separ ...
... research was recently covered in SigLog; see Nordström [Nordström, 2015]). For resolution and its weak extensions, strong lower bounds are known since Haken [Haken, 1985]. But the major open questions in proof complexity, those originating from boolean circuit complexity and complexity class separ ...