Consider two computers A and B. A has uses G and B uses G' where G' != G and of different degrees. Computer A wants to send a data D and it uses CRC for that cause.
The claim says that there couldn't be a scenario where A sends a CRC-message corresponding to data D and computer B will accept it as a valid message. Why is that?
We know that computer A sends D*2^r XOR R (r is the degree of G) and computer B divides by G'. So in other words, why can't G', accidentally, divide D*2^r XOR R?
Obviously it has something to do with the fact that deg(G) != deg(G') but I didn't figure it out.
Thanks!
Related
Reading the book of Aziz & Prakash 2021 I am a bit stuck on problem 3.7 and the associated solution for which I am trying to implement.
The problem says :
You have n users with unique hashes h1 through hn and
m servers, numbered 1 to m. User i has Bi bytes to store. You need to
find numbers K1 through Km such that all users with hashes between
Kj and Kj+1 get assigned to server j. Design an algorithm to find the
numbers K 1 through Km that minimizes the load on the most heavily
loaded server.
The solution says:
Let L(a,b) be the maximum load on a server when
users with hash h1 through ha are assigned to servers S1 through Sb in
an optimal way so that the max load is minimised. We observe the
following recurrence:
In other words, we find the right value of x such that if we pack the
first x users in b - 1 servers and the remaining in the last servers the max
load on a given server is minimized.
Using this relationship, we can tabulate the values of L till we get
L(n,m). While computing L(a,b) when the values of L is tabulated
for all lower values of a and b we need to find the right value of x to
minimize the load. As we increase x, L(x,b-1) in the above expression increases the the sum term decreases. We can do binary search for x to find x that minimises their max.
I know that we can probably use some sort of dynamic programming, but how could we possibly implement this idea into a code?
The dynamic programming algorithm is defined fairly well given that formula: Implementing a top-down DP algorithm just needs you to loop from x = 1 to a and record which one minimizes that max(L(x,b-1), sum(B_i)) expression.
There is, however, a simpler (and faster) greedy/binary search algorithm for this problem that you should consider, which goes like this:
Compute prefix sums for B
Find the minimum value of L such that we can partition B into m contiguous subarrays whose maximum sum is equal to L.
We know 1 <= L <= sum(B). So, perform a binary search to find L, with a helper function canSplit(v) that tests whether we can split B into such subarrays of sum <= v.
canSplit(v) works greedily: Remove as many elements from the start of B as possible so that our sum does not exceed v. Repeat this a total of m times; return True if we've used all of B.
You can use the prefix sums to run canSplit in O(m log n) time, with an additional inner binary search.
Given L, use the same strategy as the canSplit function to determine the m-1 partition points; find the m partition boundaries from there.
I need to decrypt c and I was given only n, e and c and computing p and q or phi(n) would be close to impossible so what other alternatives do I have? I tried calculating p and q but I made very little progress with the search in the last 24 hours of continuous running the program.
These are the values I was given:
n: 58900433780152059829684181006276669633073820320761216330291745734792546625247
e: 65537
c: 56191946659070299323432594589209132754159316947267240359739328886944131258862
Also, in another challenge only c and n were given and the values were a lot bigger. Do you have any suggestions for that too?
Well, it seems that this question is CTF related, because the patterns of n, e, and c are weak numbers.
You can solve it with RsaCtfTool:
python RsaCtfTool -n 58900433780152059829684181006276669633073820320761216330291745734792546625247 -e 65537 --uncipher 56191946659070299323432594589209132754159316947267240359739328886944131258862
timctf{CENSORED}
https://www.dcode.fr/rsa-cipher
Try this one but it need p and q. So I use the hand calculator to find p and q.
Using Fact(n), ex: Fact(91)= 7x13, so p=7, q=13
I'm creating an encryptor/decryptor for ascii strings where I take the ascii value of a char, add 1 to it, then mod it by the highest ascii value so that I get a valid ascii char out.
The problem is the decryption.
Let's say that (a + b) % c = d
I know b, c, and d's values.
How do I get the a variables value out from that?
This is exactly the ROT1 substitution cipher. Subtract 1, and if less than lowest value (0 I assume, given how you're describing it), then add the highest value.
Using terms like "mod," while accurate, make this seem more complicated than it is. It's just addition on a ring. When you go past the last letter, you come back to the first letter and vice-versa. Once you put your head around how the math works, the equations should pop out. Basically, you just add or subtract as normal (add to encrypt, subtract to decrypt in this case), and at the end, mod "normalizes" you back onto the ring of legal values.
Use the inverse formula
a = (b - d) mod c
or in practice
a = (b - d + c) % c.
The term + c needs to be added as a safeguard because the % operator does not implement a true modulo in the negatives.
Let's assume that c is 2, d is 0 and b is 4.
Now we know that a must be 2... Or 4 actually.. or 6... Or any other even number.
You can't solve this problem, there are infinite solutions.
I am fairly new to the Z80 and machine code, so please don't assume I know anything.
Basically, what I want to know is this: If you load register H with a value (I'll call it y), will HL then be 0xy0? e.g. if H was loaded with 0xAF would HL be 0xAF00?
And would the same be true for loading L with y?
Thanks in advance.
The H and L 8-bit registers can be treated independently. Loading a value in H, will not affect the value in L, and vice versa. The two registers H and L can also be treated as a 16-bit register pair. The following source FIRST STEPS IN MACHINE CODE describes this.
two single register transfers, e.g.
LD H, B
LD L, C
to copy BC into
HL.
and
You can, if you wish, load a register pair directly with a single
instruction, rather than use two instructions. From last time, you
will recall that the H and L, B and C, and D and E registers can be
paired such that they effectively can hold any number between 0 and
65535 (00 to FFFF hex). C, E, and L form the low byte of the pair,
while B, D, and H are the high bytes.
As a background, I'm a computer programmer and I'm working on a software library that allows a computer to quickly search through all dates to find a set of dates that satisfies a criteria. For example:
I want a list of every possible time that has ever occurred that has occurred on a friday or a saturday that is in April or May during the first week of the month.
My library uses numerical sets to efficiently represent ranges of dates that satisfy a criteria.
I've been thinking about ways to improve the performance of some parts of the app and I think that by combining sets and some geometry, I can really improve my results. However, my geometry is a bit rusty and I was hoping you might could help.
Here's my thought:
Certain elements of time can be represented as a circular dial. For example, Minutes can be positioned on a clock with values between 0...59. We could store valid ranges as a list of arcs. For example, If we wanted all times that ended with 05..10, we could store [5,10]. If we wanted all times that end with :45-59 or :00-15, we could store [45, 15]. Notice how this last arc "loops around" the dial. Here's a mockup showing different ranges intersecting on a dial
My question is this:
Given a set of whole numbers between N...M arranged into a circle.
Given Arc1 which is representing by [A, B] and Arc2 which is represented by [C, D] where A, B, C, and D are all within in range N...M
How do I determine:
A. Whether the arcs intersect.
B. If they do, what their intersection is.
C. If they do, what their union is.
Thank you so much for your help. If you're not able to help, if you can point me in the right direction, that would be great.
Thanks!
A simple and safe approach is to split the intervals that straddle 0. Then you perform pairwise interval intersection/union (for instance if A < D and C < B then [max(A,C), min(B,D)] for the intersection), and merge them if they meet at 0.
It seems the primitive operation to implement would be something like 'is the number X contained in the arch [A,B]'. Once you have that, you could implement an [A,B]/[C,D] arch-intersection predicate by something like -
Arch intersection means exactly that at least one of the following conditions is met:
C is contained in [A,B]
D is contained in [A,B]
A is contained in [C,D]
B is contained in [C,D]
One way to implement this contained-in-arch test without any branches is with some trigonometry and vector cross product. Not sure it would be faster (the math/branches performance tradeoff is entirely empiric), but it might be worth a try.
Denote Xa = sin(X/N * 2PI), Ya = cos(X/N * 2PI) and similarly for Xb,Yb etc.
C is contained in [A,B] is equivalent to:
Xa * Yc - Ya * Xc > 0
AND
Xc * Yb - Yc * Xb > 0
You can complete the other 3 conditions in an identical manner.
Hope this turns out useful.