Well, I finally was able to build a subset of OpenSSL with only RSA
encryption (no communications, just an encryption library). In adition
to Bignumbers and Random, I had to throw a few things in, e.g. MD5 for
random number generation and lotsa things from ASN1 (What's ASN1?). The
complete lists of .c's I had to include in the build is as follows:

a_bitstr.c
a_bytes.c
a_enum.c
a_gentm.c
a_int.c
a_object.c
a_octet.c
a_print.c
a_set.c
a_type.c
a_utctm.c
a_utf8.c
a_vis.c
asn1_lib.c
bio_lib.c
bn_add.c
bn_asm.c
bn_blind.c
bn_comba.c
bn_div.c
bn_err.c
bn_exp.c
bn_exp2.c
bn_gcd.c
bn_lib.c
bn_mont.c
bn_mpi.c
bn_mul.c
bn_prime.c
bn_print.c
bn_rand.c
bn_recp.c
bn_shift.c
bn_sqr.c
bn_word.c
bss_file.c
buffer.c
cryptlib.c
err.c
ex_data.c
lhash.c
md5_dgst.c
md5_one.c
md_rand.c
mem.c
obj_dat.c
obj_lib.c
rand_lib.c
rsa_eay.c
rsa_err.c
rsa_gen.c
rsa_lib.c
rsa_none.c
rsa_pk1.c
rsa_sign.c
rsa_ssl.c
stack.c
x_algor.c
x_sig.c

Is there something else I could get rid of? I was able to exclude the
SHA modules by defining NO_SHA and NO_SHA1.
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