Can you identify these cryptographic algorithmic symbols?

I am mostly self taught and have limited knowledge of the symbology in the image below. It is a diagram of a sub block the RIPEMD-160 algorithm: Are such symbols standardized? Is there a good dictionary or atlas someone is aware of that could link such symbols to their definitions?

Here is the source: https://en.wikipedia.org/wiki/RIPEMD

It is RIPEMD-160 and the paper describes them as;

• $$f$$ represents nonlinear functions at bit level: $$exor, mux, -, mux, -$$ and varies with rounds;

• $$f(j, x, y, z) = x ⊕ y ⊕ z \quad \quad \quad \quad \quad (0 ≤ j ≤ 15)$$
• $$f(j, x, y, z) = (x ∧ y) ∨ (¬x ∧ z) \quad (16 ≤ j ≤ 31)$$
• $$f(j, x, y, z) = (x ∨ ¬y) ⊕ z \quad \quad \quad (32 ≤ j ≤ 47)$$
• $$f(j, x, y, z) = (x ∧ z) ∨ (y ∧ ¬z) \quad (48 ≤ j ≤ 63)$$
• $$f(j, x, y, z) = x ⊕ (y ∨ ¬z) \quad \quad \quad (64 ≤ j ≤ 79)$$
• $$\boxplus$$ denotes addition modulo $$2^{32}$$

• $$rol_s$$ denotes cyclic left shift (rotate) over $$s$$ positions. in the figure there is one fixed 10 and one variable with $$s[i]$$

I don't know of a glossary for symbols on these diagrams, however in this case:

• $$f$$ is some sbox, that is, some lookup table (and whose details must be given somewhere else in the document where this image is found)

• $$\boxplus$$ is either modular addition (modulo $$2^w$$, where $$w$$ is the number of bits in each line) or bit-wise exclusive-or. Most typically, it is modular addition; however that usage is commonly used in conjunction with $$\oplus$$; hence the alterative meaning is possible.

• $$<<$$ is left-wise rotate, where each bit is moved a number of locations to the left and if a bit goes past the top of the word, it wraps around to the bottom; the number of locations each bit moves is either $$s[i]$$ or the fixed value 10 (as shown in the diagram). Now, $$<<$$ more commonly refers to a left-wise shift, where bits going past the top of the word are discarded, and we insert zeros on the right; however that would not make sense in this context.

The document this diagram came from should give more details...

• Common, RIPEMD Dec 4 '21 at 15:17
• I'd say $f$ is some function, using an sbox to make it fast is an implementation detail. Dec 5 '21 at 17:42