RSA Decryption from Public Key Values - algorithm

I'm a little stuck trying to figure out how to decrypt some messages and could use some hints as to what I may be doing wrong.
I was given a series of integer values that make up my cipher text. Here are just a few of them:
6584 15650 16198 11003
I was given the following public key
b = 3001
n = 18209
So to encrypt a message M, you would use the formula:
C = M^3001 mod 18209
I understand to encrypt, I need to find a 'd' value that satisfies:
bd = 1 mod 18209
3001d = 1 mod 18209
Any hints on a technique or algorithm to help me find a suitable value for 'd'?
EDIT: I figured it out! I'll come back and post the answer in a week or two as I'm sure my professor wouldn't be too pleased if I posted it here on public domain while my peers continue to work on it.

Related

Having trouble with a coding problem, can someone help me out?

I am very new here and to coding in general so apologies in advance for any mistakes in my questions and code.
I am currently working on this problem:
Primary U.S. interstate highways are numbered 1-99. Odd numbers (like the 5 or 95) go north/south, and evens (like the 10 or 90) go east/west. Auxiliary highways are numbered 100-999, and service the primary highway indicated by the rightmost two digits. Thus, I-405 services I-5, and I-290 services I-90. Note: 200 is not a valid auxiliary highway because 00 is not a valid primary highway number. Given a highway number, indicate whether it is a primary or auxiliary highway. If auxiliary, indicate what primary highway it serves. Also indicate if the (primary) highway runs north/south or east/west.
EX: if the input is:
290
the output is:
I-290 is auxiliary, serving I-90, going east/west.
My code is currently as shown:
#include iostream
using namespace std;
int main()
{
int A; // A is the value for the Auxiliary highway
// This message will display when the code is run//
cout << "Please enter the three digit Auxiliary highway number" << endl;
cin >> A; // User inputs the Auxiliary highway number
do A-= 100;
while (A>100);
I am not sure what I am doing but I have no clue how to go about this so I am first starting with the second part(trying to make the code understand that if I am at the auxiliary number of I-290 then I would be servicing I-90). I tried this by trying to subtract 100 when the value for A was over 100 which would in theory leave me with a 2-digit number that would be the interstate highway number. I know that an error will happen when a number that ends in two zeros is entered so I planned to just use an if-else statement at the beginning of the code that would essentially just prevent this but, again, no clue how to do it but I think it may work
The first thing you want to do with a problem like this is think through it step by step. How do you solve this problem as a human with a pen and paper if you are given a highway number?
First you need a piece of code to tell you if the number is primary, so the code needs to tell you if the number is less than or equal to 99, if yes, then it is primary, if no, then it is auxillary.
In the case that is is not primary, you need a piece of code to tell you what the last 2 digits are of the number. The easiest way to do this is to convert the number to a string and remove the first character, and then convert back into an integer.
Lastly, you need a piece of code that tells you whether the primary road runs north/south, or east/west. So you need to check whether the number is even or odd. The easiest way to do this is to use the modulo function (x%2==y). If y is equal to zero, then you know the road runs east/west, otherwise it runs north south.
Hopefully you can see that the problem is a series of little problems that you can solve 1 by 1 to get the full solution. Problems become a lot less scary then.
I'm afraid I don't know C++ that well to give you a coded solution, but hopefully you can figure it out from here. It will be good practice for you to work through it because a lot of programming is about banging your head against a wall until you figure out the solution.
There are many ways to solve this problem. Here is one:
first, fix your header
#include <iostream>
accept user "highwayNumber"
cin >> highwayNumber;
write an if loop to determine highway properties:
if(highwayNumber > 0 && highwayNumber < 100){
highwayType = "primary";
//determine if highwayNumber is even or odd
if(highwayNumber % 2 == 0){
primaryType = “east-west”;
} else {
primaryType = “north-south”;
}
} else if (highwayNumber >= 100 && highwayNumber <= 999){
highwayType = “auxiliary”;
//determine what primaryHighway the auxiliaryHighway services
auxiliaryServiced = highwayNumber % 100;
} else {
cout << "invalid highway number” << end;
}
print output to user

Is there a way to use range with Z3ints in z3py?

I'm relatively new to Z3 and experimenting with it in python. I've coded a program which returns the order in which different actions is performed, represented with a number. Z3 returns an integer representing the second the action starts.
Now I want to look at the model and see if there is an instance of time where nothing happens. To do this I made a list with only 0's and I want to change the index at the times where each action is being executed, to 1. For instance, if an action start at the 5th second and takes 8 seconds to be executed, the index 5 to 12 would be set to 1. Doing this with all the actions and then look for 0's in the list would hopefully give me the instances where nothing happens.
The problem is: I would like to write something like this for coding the problem
list_for_check = [0]*total_time
m = s.model()
for action in actions:
for index in range(m.evaluate(action.number) , m.evaluate(action.number) + action.time_it_takes):
list_for_check[index] = 1
But I get the error:
'IntNumRef' object cannot be interpreted as an integer
I've understood that Z3 isn't returning normal ints or bools in their models, but writing
if m.evaluate(action.boolean):
works, so I'm assuming the if is overwritten in a way, but this doesn't seem to be the case with range. So my question is: Is there a way to use range with Z3 ints? Or is there another way to do this?
The problem might also be that action.time_it_takes is an integer and adding a Z3int with a "normal" int doesn't work. (Done in the second part of the range).
I've also tried using int(m.evaluate(action.number)), but it doesn't work.
Thanks in advance :)
When you call evaluate it returns an IntNumRef, which is an internal z3 representation of an integer number inside z3. You need to call as_long() method of it to convert it to a Python number. Here's an example:
from z3 import *
s = Solver()
a = Int('a')
s.add(a > 4);
s.add(a < 7);
if s.check() == sat:
m = s.model()
print("a is %s" % m.evaluate(a))
print("Iterating from a to a+5:")
av = m.evaluate(a).as_long()
for index in range(av, av + 5):
print(index)
When I run this, I get:
a is 5
Iterating from a to a+5:
5
6
7
8
9
which is exactly what you're trying to achieve.
The method as_long() is defined here. Note that there are similar conversion functions from bit-vectors and rationals as well. You can search the z3py api using the interface at: https://z3prover.github.io/api/html/namespacez3py.html

Problems calculating LRC

I'm trying to calculate the LRC value (Longitudinal Redundancy Check) in order to send a message to a pinpad.
All I know about LRC is: "It is calculated by performing an XOR of all the characters in the message, excluding the STX in the calculation."
I'm using this function to generate the LRC:
Public Shared Function calculateLRC(bytes As Byte()) As Byte
Dim LRC As Byte = 0
For i As Integer = 0 To bytes.Length - 1
LRC = LRC Xor bytes(i)
Next
Return CByte(LRC)
End Function
But I can't make that the pinpad answers me.
Now, I know that I have to send the message in HEX but I can't make that the pinpad answers me and I can't figure out if I have a problem calculating the LRC or i am making something else wrong.
The format is asked this way: < STX > < type of msg> < param>< ETX>< LRC>.
I already tried to calculate the LRC first and then convert everything to hex AND convert everything to hexa and then calculate the LRC but nohing works.
Any help is appreciated.
Edit: Ok, the LRC is ok. The issue is with the way i'm sending the data (mostly because I have so little documentation and I'm just trying everthing I can think of)
I'm gonna try to think how to explain the issues here cause, like I say, I have a very poor documentation and it is in spanish.

Electronic signature

I was asked to code electronic signature for the form. But I can't understand a thing from the description. Is it my qualification or something is missing?
Here is description:
MAC008(x1, x2, …, xn) := RSA(SHA-1(p(x1)||x1||p(x2)||x2||…||p(xn)||xn),d,n)
where:
|| - symbol lines connecting
x1, x2, …, xn inquiry parameters;
p function that returns the parameter length. The result is provided as a three-segment number (e.g. 007)
d – RSA secret exponent
n- RSA module
Let's say that p1 is defined as returning "Hello \x1, how are you" so
p1(chris) = "Hello chris, how are you".
What this is asking you to do is turn
MAC008(chris) = RSA(SHA-1(Hello chris, how are youchris),SOMESECRET,someRSAmodule)
Into the modules "signature". Sha-1 is a hashing algorithm that turns a set of data into a pre determined length string, or hash. RSA is a signature algorithm that uses a public/private key encryption scheme. You freely make available the public key, and encrypt the hash with your private key. This provides no data security, but an individual with your public key can be positive that the data is from you, because this is the only way their public key would work on your data set.

Generating nice looking BETA keys

I built a web application that is going to launch a beta test soon. I would really like to hand out beta invites and keys that look nice.
i.e. A3E6-7C24-9876-235B
This is around 16 character, hexadecimal digits.
It looks like the typical beta key you might see.
My question is what is a standard way to generate something like this and make sure that it is unique and that it will not be easy for someone to guess a beta key and generate their own.
I have some ideas that would probably work for beta keys:
MD5 is secure enough for this, but it is long and ugly looking and could cause confusion between 0 and O, or 1 and l.
I could start off with a large hexadecimal number that is 16 digits in length. To prevent people from guessing what the next beta key might be increment the value by a random number each time. The range of numbers between 1111-1111-1111-1111 and eeee-eeee-eeee-eeee will have plenty of room to spare even if I am skipping large quantities of numbers.
I guess I am just wondering if there is a standard way for doing this that I am not finding with google. Is there a better way?
The canonical "unique identifying number" is a uuid. There are various forms - you can generate one from random numbers (version 4) or from a hash of some value (user's email + salt?) (versions 3 and 5), for example.
Libraries for java, python and a bunch more exist.
PS I have to add that when I read your question title I thought you were looking for something cool and different. You might consider using an "interesting" word list and combining words with hyphens to encode a number (based on hash of email + salt). That would be much more attractive imho: "your beta code is secret-wombat-cookie-ninja" (I'm sure I read an article describing an example, but I can't find it now).
One way (C# but the code is simple enough to port to other languages):
private static readonly Random random = new Random(Guid.NewGuid().GetHashCode());
static void Main(string[] args)
{
string x = GenerateBetaString();
}
public static string GenerateBetaString()
{
const string alphabet = "ABCDEF0123456789";
string x = GenerateRandomString(16, alphabet);
return x.Substring(0, 4) + "-" + x.Substring(4, 4) + "-"
+ x.Substring(8, 4) + "-" + x.Substring(12, 4);
}
public static string GenerateRandomString(int length, string alphabet)
{
int maxlen = alphabet.Length;
StringBuilder randomChars = new StringBuilder(length);
for (int i = 0; i < length; i++)
{
randomChars.Append(alphabet[random.Next(0, maxlen)]);
}
return randomChars.ToString();
}
Output:
97A8-55E5-C6B8-959E
8C60-6597-B71D-5CAF
8E1B-B625-68ED-107B
A6B5-1D2E-8D77-EB99
5595-E8DC-3A47-0605
Doing this way gives you precise control of the characters in the alphabet. If you need crypto strength randomness (unlikely) use the cryto random class to generate random bytes (possibly mod the alphabet length).
Computing power is cheap, take your idea of the MD5 and run an "aesthetic" of your own devising over the set. The code below generates 2000 unique keys almost instantaneously that do not have a 0,1,L,O character in them. Modify aesthetic to fit any additional criteria:
import random, hashlib
def potential_key():
x = random.random()
m = hashlib.md5()
m.update(str(x))
s = m.hexdigest().upper()[:16]
return "%s-%s-%s-%s" % (s[:4],s[4:8],s[8:12],s[12:])
def aesthetic(s):
bad_chars = ["0","1","L","O"]
for b in bad_chars:
if b in s: return False
return True
key_set = set()
while len(key_set) < 2000:
k = potential_key()
if aesthetic(k):
key_set.add(k)
print key_set
Example keys:
'4297-CAC6-9DA8-625A', '43DD-2ED4-E4F8-3E8D', '4A8D-D5EF-C7A3-E4D5',
'A68D-9986-4489-B66C', '9B23-6259-9832-9639', '2C36-FE65-EDDB-2CF7',
'BFB6-7769-4993-CD86', 'B4F4-E278-D672-3D2C', 'EEC4-3357-2EAB-96F5',
'6B69-C6DA-99C3-7B67', '9ED7-FED5-3CC6-D4C6', 'D3AA-AF48-6379-92EF', ...

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