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Fermat theorem, Euler's function

Prove an interesting theorem before proving these theorems.For 0 mod m,n mod m, 2n mod m, 3n mod m, 4n mod m ... (m-1) n mod mThe corresponding solution set sequence must have M/D part 0 D 2d 3d. M-d. (not necessarily in order) su

The nature of the same remainder operation

The remainder of 100 divided by 7 is 2, meaning that 100 items seven seven are divided into one group and the last 2 are left. The remainder has a strict definition: if dividend is a and the divisor is B (assuming they are all positive integers), then we can always find a natural number less than B r and an integer m, making the a=bm+r. This r is the remainder of a divided by B, and M is called quotient. We often use MoD to represent the remainder, a

Poj 1061 frog appointment, poj1061 frog

sides of the equation by d to get a/d * x + B/d * y = c/d. Obviously, a is the division of d, and B is the division of d, x and y are Integer Solutions, So c/d is also an integer. If c does not divide d, of course it is Impossible. Otherwise, if we can find the solutions x0 and y0 for ax0 + by0 = d, multiply the two sides by c/d, that is, a (c/d * x0) + B (c/d * y0) = c, you can get the solution of the original equation x = (c/d * x0), y = (c/d * y0. Theorem involved: ax+by=c(1)There is a group

Instructions for Mmix

, $ Z(Store OCTA): S (M8 [a]) ⟵ S ($ X ). A2Stbu $ X, $ y, $ Z(Store byte unsigned): U (m1 [a]) ⟵ U ($ X) mod 28. A6Stwu $ X, $ y, $ Z(Store wyde unsigned): U (m2 [a]) ⟵ U ($ X) mod 216. AASTTU $ X, $ y, $ Z(Store Tetra unsigned): U (M4 [a]) ⟵ U ($ X) mod 232. AESTOU $ X, $ y, $ Z(Store Octa unsigned): U (M8 [a]) ⟵ U ($ X ). B2Stht $ X, $ y, $ Z(Store high t

More details on understanding RSA algorithm

, secret key generation and encryption and decryption process1. Secret key generationEach user will generate their own public and private keys, with the following process:1) Select two large primes $p$ and $q$.2) Calculate the product $n=p \times q$ of $p$ and $q$.3) Randomly select a number coprime with $\phi (n) = (p-1) \times (q-1) $ $e$, which is $GCD (d, (p-1) \times (1-1)) =1$, which is usually selected in the application.4) Calculate $e$ modulo $\phi (n) $ for the modulo inverse element $

ZOJ 3903 Ant (math, push-to-publish + multiply inverse)

modulus, division to seek the inverse of the yuan, where the expansion of Euclid easy to find.1#include 2#include 3#include 4#include 5#include 6 #defineLL Long Long7 #defineMoD 10000000078 #defineIn Freopen ("In.txt", "R", stdin);9 using namespacestd;Ten One LL x,y,gcd; A voidEX_GCD (LL a,ll b) - { - if(!B) {x=1; y=0; gcd=A;} the Else{EX_GCD (b,a%b); LL temp=x;x=y;y=temp-a/b*y;} - } - - intMainintargcChar Const*argv[]) + { - //in ; + A LL two,six; atEX_GCD (2,

Diffie-hellman Key Negotiation algorithm

, algorithm flow and principleIn accordance with the Convention, Alice and Bob, the two cryptography in the role of the network, described the DH algorithm flow.Suppose Alice needs to negotiate a secret key with Bob (The secret key is essentially a bit sequence, which is a large number from a computational point of view).1) First Alice and Bob share a prime $p$ and the primitive root of the prime $p$ $g$ (Geneator), of course there are $2\leqslant g\leqslant p-1$. These two numbers can be sent u

Linux Kernel source code scenario analysis-insmod

+ module image (which contains init_module and Cleanup_ Module) + other parameters (such as Deps) of the collection body .3. Then, the system calls Create_module to create a module data structure in the kernel and "subscribe" to the required system (kernel) space.4, finally, through the system call Init_module, the user space to complete the one-way connection module image into the kernel space, and then call the module named init_module function (in the Linux character device driver article is

RSA encryption algorithm and SSH remote connection server

Server side and client's key system is not the same, called Asymmetric Key system RSA algorithm is based on modulo operation x mod n, in fact: [(a mod n) + (b mod n)] mod n = (a+b) mod n[(a mod n)-(b

"Template" segment tree 2

,128mData size:For 30% data: nFor 70% data: nFor 100% data: n(data has been strengthened ^_^)Sample Description:Therefore the output should be 17, 2 (mod 38=2)Ideas:The main problem is not to break the first ride or add, I can be a stack of the same doctrine, the stack of line tree ... Forgive me for incompetence.The general solution is to turn multiplication into addition.(S+flag) *lazy=s*lazy+flag*lazy.Attention:Data size, not only to open a long lo

Asymmetric encryption (2) Asymmetric encryption algorithm

Q are available. Step 3 determines the decryption key D:D * e = 1 mod (p-1) * (q-1) can easily compute d based on E, p, and Q. Step 4 exposes integers r and E, but does not expose D. Step 5 encrypts the plaintext P (p is an integer less than R) to ciphertext C, calculated as C = p^e mod R. Step 6 decrypts ciphertext C to plaintext p, and the method is: p = c^d modulo R. However only according to R and

Introduction to the principle of ECC encryption algorithms

definitions, see the number of modern algebra. Simply put, the elements in a field have their own addition, multiplication, division, Unit Element (1), zero element (0), and meet the exchange rate and allocation rate, just like rational numbers.☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆Below, we provide a finite field FP, which has only limited elements.In FP, only P (P is a prime number) elements 0, 1, 2 ...... P-2, P-1;The addition (A + B) of FP is a + B ≡ C (

BZOJ4591[SHOI2015] super-energy particle cannon • change

(ch>='0'ch'9') x=x*Ten+ch-'0', ch=GetChar (); - returnf*x; the } -ll N,K,C[MAXN][MAXN],SM[MAXN][MAXN];intT; - voidCalc () { -c[0][0]=sm[0][0]=1; Inc (I,1, MoD) sm[0][i]=1; +Inc (I,1, MoD) { -d[n][0]=sm[i][0]=1; +Inc (J,1, i) c[i][j]= (c[i-1][j-1]+c[i-1][J])%MoD; AInc (J,1, MoD) sm[i][j]= (sm[i][j-1]+C[I][J])%

51_1228 Sequence Summation (Bernoulli number)

of the method, see the next chapter of the blog.1228 Sequence summationSource: Hackerrank Base time limit: 3 seconds Space limit: 131072 KB score: 160 Difficulty: 6-level algorithm problem collection attention T (n) = N^k,s (n) = t (1) + t (2) + ... T (n). Given N and K, ask for S (n). For example k = 2,n = 5,s (n) = 1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 55. As a result, output s (n) Mod 1000000007 results. InputLine 1th: A number t that represents the numbe

1732 Fibonacci Series 2

1732 Fibonacci Series 2time limit: 1 sspace limit: 128000 KBtitle level: Diamonds Diamond SolvingTitle DescriptionDescriptionIn the "1250 Fibonacci series", we find the value of the nth Fibonacci series. But in 1250, nEnter a descriptionInput DescriptionEnter multiple sets of data, one row for each group of data, and an integer n (1 Output descriptionOutput DescriptionOutputs several rows. Output per line (corresponding input) n Fibonacci number (considering the number will be very large,

Introduction to the principle of ECC encryption algorithm

the Fp is a+b≡c (mod p); that is, the remainder of (a+c) ÷p is the same as the remainder of C÷p.The rule of the Fp multiplication (AXB) is axb≡c (mod p);The Fp Division (a÷b) rule is a/b≡c (mod p), which is axb-1≡c (mod p); (B-1 is also an integer between 0 and p-1, but satisfies the bxb-1≡1 (

A probe into the modular drag technology of Flash website

", "latest article" These contents, all when he is MC1,MC2,MC3, the experiment begins with the simplification first! Open Flash, do a similar figure in the MC,MC has a dynamic text box, variable name: Mctext, at the same time to the MC plus the corresponding link identification ======================flash Source Code ======================//Set margin First, 10px var border:number = new number (10); var xmodel = border; var mod:array = new Array (); This.attachmovie ("MC", "MC", This.getnexthig

UbuntuLinux: Apache installation settings

UbuntuLinux: Apache installation settings-Linux Enterprise Application-Linux server application information. For details, refer to the following section. Install Apache2 Sudo apt-get install apache2 Edit the/etc/apache2/apache2.conf file. before modifying the file, back up the configuration file. In this way, you can recover an error. AddDefaultCharset ISO-8859-1 => AddDefaultCharset GB2312 In this way, we won't go through the garbled code every time we open the web page! Add the security M

Medusa crack ssh Password

From accidentally climbing the blog It hurts. as you write your hand, medusa is still quick to crack. First, let's take a look at the help. Root @ perl-exploit:/pentest/exploits/framework3 # medusaMedusa v1.5 [http://www.foofus.net] (C) JoMo-Kun/Foofus Networks ALERT: Host information must be supplied. Syntax: medusa [-h host |-H file] [-u username |-U file] [-p password |-P file] [-C file]-M module [OPT]-H [TEXT]: Target hostname or IP address-H [FILE]: File containing target hostnames or IP a

2 The pattern of the positive power end number

2 positive Powers-2, 4, 8, 16, 32, 64, 128, 256, ...-at the end of the numbers follow an obvious rule: 2, 4, 8, 6, 2, 4, 8, 6, .... These 4 numbers are always going to loop. In addition to the last number there is a loop-actually the final m bit-a power of 2 starting at 2m. For example, there is a loop of length 20 for the last two digits starting at 04, and a loop of length 100 for the last 3 digits starting from 008.In this article, I will show you why there are these loops, how long they are,

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