Thanks, now this is starting to make sense.
A question though: presumably, since both w0 and w1 are known, we have both s1 xor w1 and s1 xor w0 already known. Meaning s0 xor (s0 >> 1) is left to be determined.
A cyclic shift of A by n bits, can be represented as (Ai - 1) % n, according to Wikipedia. The paper says that a unique s0 can't be found if n is odd. Presumably it's because even n make the same modulus for the circular shift above and so an s0 can be found for it (example: w0 = 1100 and w1 = 1111, s1 = 0000, would give us 1100 and 1111 respectively for the xor. s0 could be set to 1000 which satisfies the equation) . But wouldn't w0 and w1 with odd, non-prime different number of bits also have some s0 that can be found for it, or am I going off on something completely unrelated?
I think you misunderstood what i wrote in my paper.
W0 and w1 have an odd number of different bits, which means that they are compared bit by bit, and there are odd numbers of different bits. Or it can be understood that w0 xor w1 has an odd bits of 1.
In addition, I have put the paper on
https://www.researchgate.net/publication/348992129_Eagle_A_new_symmetric_encryption_algorithm_against_any_linear_attacks_and_differential_attacks_The_existence_of_one-way_function_means_PNPWelcome to discuss.