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c - How to find the offset of the section header string table of an elf file?

I have to write a C program that prints an ELF file. I'm having trouble figuring out where the section header string table is.

Let's say I have a file that gave me the following output with:

readelf -h

ELF Header:
  Magic:   7f 45 4c 46 01 01 01 00 00 00 00 00 00 00 00 00 
  Class:                             ELF32
  Data:                              2's complement, little endian
  Version:                           1 (current)
  OS/ABI:                            UNIX - System V
  ABI Version:                       0
  Type:                              REL (Relocatable file)  
  Machine:                           Intel 80386
  Version:                           0x1
  Entry point address:               0x0
  Start of program headers:          0 (bytes into file)
  Start of section headers:          17636 (bytes into file)
  Flags:                             0x0
  Size of this header:               52 (bytes)
  Size of program headers:           0 (bytes)
  Number of program headers:         0
  Size of section headers:           40 (bytes)
  Number of section headers:         23
  Section header string table index: 20

and with:

readelf -S:

There are 23 section headers, starting at offset 0x44e4:
Section Headers:
  [Nr] Name              Type            Addr     Off    Size   ES Flg Lk Inf Al
  [ 0]                   NULL            00000000 000000 000000 00      0   0  0
  [ 1] .text             PROGBITS        00000000 000034 000028 00  AX  0   0  4
  [ 2] .rel.text         REL             00000000 0049d0 000018 08     21   1  4
  [ 3] .data             PROGBITS        00000000 00005c 000000 00  WA  0   0  4
  [ 4] .bss              NOBITS          00000000 00005c 000000 00  WA  0   0  4
  [ 5] .rodata           PROGBITS        00000000 00005c 00000a 00   A  0   0  1
  [ 6] .debug_info       PROGBITS        00000000 000066 00008f 00      0   0  1
  [ 7] .rel.debug_info   REL             00000000 0049e8 0000b0 08     21   6  4
  [ 8] .debug_abbrev     PROGBITS        00000000 0000f5 000041 00      0   0  1
  [ 9] .debug_loc        PROGBITS        00000000 000136 000038 00      0   0  1
  [10] .debug_aranges    PROGBITS        00000000 00016e 000020 00      0   0  1
  [11] .rel.debug_arange REL             00000000 004a98 000010 08     21  10  4
  [12] .debug_line       PROGBITS        00000000 00018e 0001b3 00      0   0  1
  [13] .rel.debug_line   REL             00000000 004aa8 000008 08     21  12  4
  [14] .debug_macinfo    PROGBITS        00000000 000341 003fb9 00      0   0  1
  [15] .debug_str        PROGBITS        00000000 0042fa 0000bf 01  MS  0   0  1
  [16] .comment          PROGBITS        00000000 0043b9 00002b 01  MS  0   0  1
  [17] .note.GNU-stack   PROGBITS        00000000 0043e4 000000 00      0   0  1
  [18] .eh_frame         PROGBITS        00000000 0043e4 000038 00   A  0   0  4
  [19] .rel.eh_frame     REL             00000000 004ab0 000008 08     21  18  4
  [20] .shstrtab         STRTAB          00000000 00441c 0000c5 00      0   0  1
  [21] .symtab           SYMTAB          00000000 00487c 000130 10     22  16  4
  [22] .strtab           STRTAB          00000000 0049ac 000021 00      0   0  1
Key to Flags:
  W (write), A (alloc), X (execute), M (merge), S (strings)
  I (info), L (link order), G (group), T (TLS), E (exclude), x (unknown)
  O (extra OS processing required) o (OS specific), p (processor specific)

How would I be able to calculate the location of the section header string table?

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This is what I do:

#pragma pack(push,1)

typedef struct
{
  uint8  e_ident[16];
  uint16 e_type;
  uint16 e_machine;
  uint32 e_version;
  uint32 e_entry;
  uint32 e_phoff;
  uint32 e_shoff;
  uint32 e_flags;
  uint16 e_ehsize;
  uint16 e_phentsize;
  uint16 e_phnum;
  uint16 e_shentsize;
  uint16 e_shnum;
  uint16 e_shstrndx;
} Elf32Hdr;

typedef struct
{
  uint32 sh_name;
  uint32 sh_type;
  uint32 sh_flags;
  uint32 sh_addr;
  uint32 sh_offset;
  uint32 sh_size;
  uint32 sh_link;
  uint32 sh_info;
  uint32 sh_addralign;
  uint32 sh_entsize;
} Elf32SectHdr;

#pragma pack(pop)

{
  FILE* ElfFile = NULL;
  char* SectNames = NULL;
  Elf32Hdr elfHdr;
  Elf32SectHdr sectHdr;
  uint idx;

  // ...

  // read ELF header
  fread(&elfHdr, 1, sizeof elfHdr, ElfFile);

  // read section name string table
  // first, read its header
  fseek(ElfFile, elfHdr.e_shoff + elfHdr.e_shstrndx * sizeof sectHdr, SEEK_SET);
  fread(&sectHdr, 1, sizeof sectHdr, ElfFile);

  // next, read the section, string data
  SectNames = malloc(sectHdr.sh_size);
  fseek(ElfFile, sectHdr.sh_offset, SEEK_SET);
  fread(SectNames, 1, sectHdr.sh_size, ElfFile);

  // read all section headers
  for (idx = 0; idx < elfHdr.e_shnum; idx++)
  {
    const char* name = "";

    fseek(ElfFile, elfHdr.e_shoff + idx * sizeof sectHdr, SEEK_SET);
    fread(&sectHdr, 1, sizeof sectHdr, ElfFile);

    // print section name
    if (sectHdr.sh_name);
      name = SectNames + sectHdr.sh_name;
    printf("%2u %s
", idx, name);
  }

  // ...
}

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