M04/01
... As mentioned above, ways of axiomatizing a group based on the right division operation have appeared in several works, the first apparently being [23]. In Section 2 we list some of these sets of axioms and give concise proofs that several of the various identities which have appeared are in fact equ ...
... As mentioned above, ways of axiomatizing a group based on the right division operation have appeared in several works, the first apparently being [23]. In Section 2 we list some of these sets of axioms and give concise proofs that several of the various identities which have appeared are in fact equ ...
Section2.2
... Cryptanalysis of Affine Ciphers • For an affine cipher y (ax b) MOD 26, an enemy must know the multiplicative parameter a and additive parameter b in order to decipher and break a message. Once a and b are known, x a 1 ( y b) MOD 26 can be computed and the message broken. Two methods of ...
... Cryptanalysis of Affine Ciphers • For an affine cipher y (ax b) MOD 26, an enemy must know the multiplicative parameter a and additive parameter b in order to decipher and break a message. Once a and b are known, x a 1 ( y b) MOD 26 can be computed and the message broken. Two methods of ...
Exponential sums with multiplicative coefficients
... (ii) If q < N ~ and (a,q)= 1, then there is an f e o ~ for which [S(a/q)[>>Nq -~. (iii) If N(log N)- 3 < Q < N, then there are a, q, f s u c h that Q - 3 N Q- 1 < q < Q, (a, q)= 1,fe ~- and [S(a/q)l >>(Nq) ~. In fact, in each of the above the f we construct is totally multiplicative and satisfies If ...
... (ii) If q < N ~ and (a,q)= 1, then there is an f e o ~ for which [S(a/q)[>>Nq -~. (iii) If N(log N)- 3 < Q < N, then there are a, q, f s u c h that Q - 3 N Q- 1 < q < Q, (a, q)= 1,fe ~- and [S(a/q)l >>(Nq) ~. In fact, in each of the above the f we construct is totally multiplicative and satisfies If ...
