The spec, https://tools.ietf.org/html/rfc3394, section 2, states that we need at least two 64 bit blocks for wrapping and, accordingly, three 64 bit blocks for unwrapping. That is: we need at least 16 bytes for wrapping and 24 bytes for unwrapping.
This also matches the lower bounds that OpenSSL have in their CRYPTO_128_{un,}wrap() functions. In fact, if we pass an input with 'inlen < 8' to AES_unwrap_key(), this results in a segfault since then inlen -= 8 underflows. Found while playing with the Wycheproof keywrap test vectors. Index: aes/aes_wrap.c =================================================================== RCS file: /var/cvs/src/lib/libcrypto/aes/aes_wrap.c,v retrieving revision 1.10 diff -u -p -r1.10 aes_wrap.c --- aes/aes_wrap.c 10 Sep 2015 15:56:24 -0000 1.10 +++ aes/aes_wrap.c 17 Oct 2018 23:12:19 -0000 @@ -66,7 +66,8 @@ AES_wrap_key(AES_KEY *key, const unsigne { unsigned char *A, B[16], *R; unsigned int i, j, t; - if ((inlen & 0x7) || (inlen < 8)) + + if ((inlen & 0x7) || (inlen < 16)) return -1; A = B; t = 1; @@ -100,11 +101,10 @@ AES_unwrap_key(AES_KEY *key, const unsig { unsigned char *A, B[16], *R; unsigned int i, j, t; - inlen -= 8; - if (inlen & 0x7) - return -1; - if (inlen < 8) + + if ((inlen & 0x7) || (inlen < 24)) return -1; + inlen -= 8; A = B; t = 6 * (inlen >> 3); memcpy(A, in, 8);