cryptography - How can we use hash values >= 160 bits (e.g SHA-1) in security if most computers can address only values no more than 64 bits? -

so here confusion: in cryptography use huge values our hashes >= 160 bits. how can operate on values if computers can address 64 or 32 bits?

your post 174 bytes large, i.e., 1392 bits. computers did sorts of things can read writing comfort of chair. isn't puzzling, it?

you mention arithmetic overflow. leads me assumption think arithmetic circuits in our cpus somehow special. aren't. give me loops, memory, , basic logic operations (and, or, not) , can implement sorts of arithmetic on numbers large memory can hold. may not efficient optimized hardware, works. (and numbers few times larger hardware can work on, few times slower.)

furthermore, operations used in hashes , block ciphers of bitwise nature (bit shifts, rotations, xor, etc.) , don't need of above. in fact, if @ sha-1 code you'll find performs operations on individual 32 bit chunks of state.