It is like trying to break RSA by using low numbers, and thinking that if you can factorize a small number like 323 into two primes, 17 and 19, then you can do the same on bigger numbers. You cannot, because you need a better algorithm, and your simplified solution will not give you any hints.
Even worse, some inefficient algorithms will give you some answers in a reasonable time, so you won't improve them if you stay on lower numbers. For example, if you will use some fake EC y^2=x^3+7, with p=67 and n=79, then to find an inverse of a number, you don't even need to use Extended Euclidean algorithm, because for such low numbers, bruteforcing every combination will work. So, you won't encounter some problems on smaller numbers, that you will encounter on bigger ones.
Another example is trying to use less bits in a hash function. If you have SHA-1, you have IV equal to "0x67452301,0xefcdab89,0x98badcfe,0x10325476,0xc3d2e1f0", and you have k-values equal to "0x5a827999,0x6ed9eba1,0x8f1bbcdc,0xca62c1d6". There are three types of left rotations, equal to "1,5,30". You can switch from 32-bit values into 8-bit values, and produce 40-bit hashes, instead of 160-bit hashes. You can use IV equal to "0x67,0xef,0x98,0x10,0xc3", k-values equal to "0x5a,0x6e,0x8f,0xca", and left rotations, equal to "1,5,6". Then, you can produce a message, where w-values will be also 8-bit. After that, you can find some 128-bit chunk with many leading zeroes:
00 2e 35 3c
f9 80 00 00
00 00 00 00
00 00 00 28