Primeiro de tudo, esta não é a sua incapacidade de instalar o arch, se a sua iso for de um par de meses atrás, você provavelmente tem um banco de dados GPG ruim, e por causa disso você tem esse problema.
O caminho mais rápido é baixar o ISO mais recente, já que o problema já está resolvido.
Por outro lado, você pode tentar isso
sudo pacman -S archlinux-keyring
A saída deve ser algo como:
resolving dependencies...
looking for conflicting packages...
Packages (1) archlinux-keyring-20170104-1
Total Installed Size: 0.81 MiB
Net Upgrade Size: 0.04 MiB
>
:: Proceed with installation? [Y/n] y
(1/1) checking keys in keyring [######################] 100%
(1/1) checking package integrity [######################] 100%
(1/1) loading package files [######################] 100%
(1/1) checking for file conflicts [######################] 100%
(1/1) checking available disk space [######################] 100%
:: Processing package changes...
(1/1) upgrading archlinux-keyring [######################] 100%
==> Appending keys from archlinux.gpg...
gpg: marginals needed: 3 completes needed: 1 trust model: PGP
gpg: depth: 0 valid: 1 signed: 6 trust: 0-, 0q, 0n, 0m, 0f, 1u
gpg: depth: 1 valid: 6 signed: 69 trust: 0-, 0q, 0n, 6m, 0f, 0u
gpg: depth: 2 valid: 69 signed: 7 trust: 69-, 0q, 0n, 0m, 0f, 0u
gpg: next trustdb check due at 2017-09-07
==> Locally signing trusted keys in keyring...
-> Locally signing key 0E8B644079F599DFC1DDC3973348882F6AC6A4C2...
-> Locally signing key 684148BB25B49E986A4944C55184252D824B18E8...
-> Locally signing key 91FFE0700E80619CEB73235CA88E23E377514E00...
-> Locally signing key 44D4A033AC140143927397D47EFD567D4C7EA887...
-> Locally signing key 27FFC4769E19F096D41D9265A04F9397CDFD6BB0...
-> Locally signing key AB19265E5D7D20687D303246BA1DFB64FFF979E7...
==> Importing owner trust values...
==> Disabling revoked keys in keyring...
-> Disabling key F5A361A3A13554B85E57DDDAAF7EF7873CFD4BB6...
-> Disabling key 7FA647CD89891DEDC060287BB9113D1ED21E1A55...
-> Disabling key D4DE5ABDE2A7287644EAC7E36D1A9E70E19DAA50...
-> Disabling key BC1FBE4D2826A0B51E47ED62E2539214C6C11350...
-> Disabling key 9515D8A8EAB88E49BB65EDBCE6B456CAF15447D5...
-> Disabling key 4A8B17E20B88ACA61860009B5CED81B7C2E5C0D2...
-> Disabling key 63F395DE2D6398BBE458F281F2DBB4931985A992...
-> Disabling key 0B20CA1931F5DA3A70D0F8D2EA6836E1AB441196...
-> Disabling key 8F76BEEA0289F9E1D3E229C05F946DED983D4366...
-> Disabling key 66BD74A036D522F51DD70A3C7F2A16726521E06D...
-> Disabling key 81D7F8241DB38BC759C80FCE3A726C6170E80477...
-> Disabling key E7210A59715F6940CF9A4E36A001876699AD6E84...
==> Updating trust database...
gpg: next trustdb check due at 2017-09-07
Depois disso, corra mais uma vez:
sudo pacman -Syy
depois disso, você pode executar novamente o
pacstrap /mnt base
espero que ajude