[Math][Python] Project Euler #99 and logarithmic representation

From their website: Comparing two numbers written in index form like \( 2^{11} \) and \( 3^7 \) is not difficult, as any calculator would confirm that \( 2^{11} = 2048 519432^{525806} \) would be much more difficult, as both numbers contain over three million digits. Using base_exp.txt (right click and 'Save Link/Target As...'), a 22K text...

2w

[Math] Modulo inverse and the solution to the reverse engineering challenge #87

The following reverse engineering challenge was published by me in summer 2017, as the hardest among those challenges. What does it do? Here is it rewritten to pure C: uint32_t modinv32 (uint32_t x) { uint32_t rslt=1; for (int i=0; i<31; i++) { rslt = (rslt * x); x = (x * x); ...

3w

[Math] Factlets about integer factorization

There is a toyish *NIX utility factor available, which can factorize small numbers. GCD is simply common factors. Here is 3*3: % factor 9999999999 9999999999: 3 3 11 41 271 9091 87654321 87654321: 3 3 1997 4877 Let's check: % python3 Python 3.8.10 (default, Jun 22 2022, 20:18:18) [GCC 9.4.0] on linux Type "help", "copyright",...

3w

[SAT] Deducing CNF for multi-input XOR function

From Wikipedia I knew a CNF formula for 2-input XOR: \( (\overline{A} \vee \overline{B} \vee C) \wedge (A \vee B \vee C) \wedge (A \vee \overline{B} \vee \overline{C}) \wedge (\overline{A} \vee B \vee \overline{C}) \) I wanted to generalize it to multi-input XOR. Let's first try to use Wolfram Mathematica's CNF generator. What it will say...

3w

[Math] Exponentiation and binary logarithm for network administrators

Well-known Google free DNS IPv4 address: % whois 8.8.8.8 ... NetRange: 8.0.0.0 - 8.127.255.255 CIDR: 8.0.0.0/9 ... How many hosts in this network? (Python) >>> 2**(32-9) 8388608 Majority of networks has the prefix x.y.z.t/24 >>> 2**(32-24) 256 Yes, 256 hosts in...

3w

[RevEng][Math] Data compression and entropy

This is yet another blog post about entropy. This time we will measure a weight of effective information in some data. Or payload (not in exploit sense). # generate RSA key openssl genrsa -out keypair.pem 4096 # extract public key out of it openssl rsa -in keypair.pem -pubout -out pubkey.pub # dump secret key: openssl rsa -noout -text...

4w

Using tabs

Yes, any text editor can be tuned so that it will use spaces instead of tabs, always. But sometimes, tabs are useful: #!/usr/bin/env python3 # instead of: for i in range(10): print ("%5d %5d %5d" % (i, i**2, i**3)) print ("") # we write this: for i in range(10): print ("%d\t%d\t%d" % (i, i**2, i**3)) 0 0 ...

4w

[Math][Python] Mixed radix, role-playing dices and PRNG

I'm not into RPG. But I always wondered, how to get some big number by throwing all these dices? When you have a coin, and you want to get a 16-bit number (16 bits of entropy), just throw it 16 times. When you have a D4 or D8 dice it's also easy -- the first can generate 2 bits at each throw, the second -- 3 bits. Having a D10 is good for generating...

Jul 2022

[Russian] Как писать технические тексты

Disclaimer: всё это только о технических текстах. Художественная литераура, поэзия -- это совершенно другое, и с технической/научной литературой имеет мало чего общего. Наверное мне еще рановато раздавать такие советы. Это эквивалентно публичному признанию, что ты уже исписался, а может и не умел-то ничего. Ну да ладно, всё равно напишу. ...

Jul 2022

[Crypto] Safe backups (or ransomware) using RSA/PGP/GnuPG/OpenSSL

As you may know, RSA itself isn't used for encryption/decryption, because it's too slow for that. (However, this is possible.) But rather RSA is used to generate a small key that is used with AES (or another symmetric cryptoalgo). Here is a typical scheme. Alice wants to encrypt a message to Bob. She generates a random session key....

Jun 2022