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section .data
 ; the string
 string: db "this is the string we are searching in"
 stringlength: equ $-stringlength
 ; the substring
 substring: db "string we are searching"
 substringlength: equ $-substring 
 
 mov rsi, string ; pointer to string in RSI
 mov rdx, stringlength ; length of string in RDX
 ; Subtract substring length to prevent looking beyond the string length,
 ; We can also check here if the substring fits in the string.
 ; If not we never can find the substring in the string
 sub rdx, substringlength
 cmp rdx, 0
 jl .@@notfound
 ; enter the compare loop
.@@repeat: 
 mov rdi, substring ; pointer to substring in RDI
 mov rcx, substringlength ; length substring in RCX (loop counter)
 cld
 repe cmpsb ; compare string at rdi with length rcx with string in rsi
 jz .@@found ; if zero flag then substring is found within string, exit loop
 ; substring is not found yet, put substring pointer at begin of substring
 dec rdx ; decrement length of string
 and rdx, rdx ; check remaining length to search in
 jnz .@@repeat ; remaining length non-zero, repeat
.@@notfound:
 ; else, substring wasn't found, exit loop
 ; substring not found actions
 
.@@found:
 ; substring found actions
 ; rsi has address to start of substring+the length of the substring
 ; subtracting the start of the string we can calculate the offset (or index) in the string where substring starts
 sub rsi, substringlength

section .data
 ; the string
 string: db "this is the string we are searching in"
 stringlength: equ $-string
 ; the substring
 substring: db "string we are searching"
 substringlength: equ $-substring 
 
 mov rsi, string ; pointer to string in RSI
 mov rdx, stringlength ; length of string in RDX
 ; Subtract substring length to prevent looking beyond the string length,
 ; We can also check here if the substring fits in the string.
 ; If not we never can find the substring in the string
 sub rdx, substringlength
 cmp rdx, 0
 jl .@@notfound
 ; enter the compare loop
.@@repeat: 
 mov rdi, substring ; pointer to substring in RDI
 mov rcx, substringlength ; length substring in RCX (loop counter)
 cld
 repe cmpsb ; compare string at rdi with length rcx with string in rsi
 jz .@@found ; if zero flag then substring is found within string, exit loop
 ; substring is not found yet, put substring pointer at begin of substring
 dec rdx ; decrement length of string
 and rdx, rdx ; check remaining length to search in
 jnz .@@repeat ; remaining length non-zero, repeat
.@@notfound:
 ; else, substring wasn't found, exit loop
 ; substring not found actions
 
.@@found:
 ; substring found actions
 ; rsi has address to start of substring+the length of the substring
 ; subtracting the start of the string we can calculate the offset (or index) in the string where substring starts
 sub rsi, substringlength

Maybe next code snippet can be useful? (perhaps I am a bit to late but anyway) we are looking if a substring appears in a string. This algorithm/code snippet is written for x86_64 intel on linux with nasm. It's quit shorter but because of the repe cmpsb certainly not the fastest.

I hope this will be helpful

We are determining if a substring appears in a string. This algorithm/code snippet is written for x86_64 Intel on Linux with NASM. It's quite shorter but because of the repe cmpsb, it's certainly not the fastest.

section .data
 ; the string
 string: db "this is the string we are searching in"
 stringlength: equ $-stringlength
 ; the substring
 substring: db "string we are searching"
 substringlength: equ $-substring 
 
 mov rsi, string ; pointer to string in RSI
 mov rdx, stringlength ; length of string in RDX
 ; Subtract substring length to prevent looking beyond the string length,
 ; We can also check here if the substring fits in the string.
 ; If not we never can find the substring in the string
 sub rdx, substringlength
 cmp rdx, 0
 jl .@@notfound
 ; enter the compare loop
.@@repeat: 
 mov rdi, substring ; pointer to substring in RDI
 mov rcx, substringlength ; length substring in RCX (loop counter)
 cld
 repe cmpsb ; compare string at rdi with length rcx with string in rsi
 jz .@@found ; if zero flag then substring is found within string, exit loop
 ; substring is not found yet, move to next character in the string

 inc rsi ; next character address
 dec rdx ; decrement length of string
 and rdx, rdx ; check remaining length to search in
 jnz .@@repeat ; remaining length non-zero, repeat
.@@notfound:
 ; else, substring wasn't found, exit loop
 ; substring not found actions
 
.@@found:
 ; substring found actions
 ; rsi has address to start of substring+the length of the substring
 ; subtracting the start of the string we can calculate the offset (or index) in the string where substring starts
 sub rsi, substringlength

section .data
 ; the string
 string: db "this is the string we are searching in"
 stringlength: equ $-stringlength
 ; the substring
 substring: db "string we are searching"
 substringlength: equ $-substring 
 
 mov rsi, string ; pointer to string in RSI
 mov rdx, stringlength ; length of string in RDX
 ; Subtract substring length to prevent looking beyond the string length,
 ; We can also check here if the substring fits in the string.
 ; If not we never can find the substring in the string
 sub rdx, substringlength
 cmp rdx, 0
 jl .@@notfound
 ; enter the compare loop
.@@repeat: 
 mov rdi, substring ; pointer to substring in RDI
 mov rcx, substringlength ; length substring in RCX (loop counter)
 cld
 repe cmpsb ; compare string at rdi with length rcx with string in rsi
 jz .@@found ; if zero flag then substring is found within string, exit loop
 ; substring is not found yet, put substring pointer at begin of substring
 dec rdx ; decrement length of string
 and rdx, rdx ; check remaining length to search in
 jnz .@@repeat ; remaining length non-zero, repeat
.@@notfound:
 ; else, substring wasn't found, exit loop
 ; substring not found actions
 
.@@found:
 ; substring found actions
 ; rsi has address to start of substring+the length of the substring
 ; subtracting the start of the string we can calculate the offset (or index) in the string where substring starts
 sub rsi, substringlength