How to upgrade openssl version and link it to python 3.6.5

Question

I have several versions of python my Ubuntu machine. The default is 2.7. However, I could manage to run python 3.6 by going to a specific path which is:

/usr/local/bin/code/tls-client

I need to use openSSL library in my python code. I want to run specific version: 1.1.0 . I tried to use pip install openssl then check if the version got updated, but it is not.

python3
Python 3.6.5 (default, May  3 2018, 10:08:28) 
[GCC 5.4.0 20160609] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import ssl
>>> ssl.OPENSSL_VERSION
'OpenSSL 1.0.2g  1 Mar 2016'

How can I link python 3.6.5 to a specific version of openSSL (say OpenSSL 1.1.0)? or even 1.1.1 (if possible)?

EDIT: After compiling it from the source as the answer suggests, I checked the verison and this is what I get:

/usr/local/bin/openssl-1.1.0h$ openssl version -a
OpenSSL 1.0.2g  1 Mar 2016
built on: reproducible build, date unspecified
platform: debian-amd64
options:  bn(64,64) rc4(16x,int) des(idx,cisc,16,int) blowfish(idx) 
compiler: cc -I. -I.. -I../include  -fPIC -DOPENSSL_PIC -DOPENSSL_THREADS -D_REENTRANT -DDSO_DLFCN -DHAVE_DLFCN_H -m64 -DL_ENDIAN -g -O2 -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -Wl,-Bsymbolic-functions -Wl,-z,relro -Wa,--noexecstack -Wall -DMD32_REG_T=int -DOPENSSL_IA32_SSE2 -DOPENSSL_BN_ASM_MONT -DOPENSSL_BN_ASM_MONT5 -DOPENSSL_BN_ASM_GF2m -DSHA1_ASM -DSHA256_ASM -DSHA512_ASM -DMD5_ASM -DAES_ASM -DVPAES_ASM -DBSAES_ASM -DWHIRLPOOL_ASM -DGHASH_ASM -DECP_NISTZ256_ASM
OPENSSLDIR: "/usr/lib/ssl"

Answer 1

Assuming you haven't updated to the most recent stable version of OpenSSL (from bash console):

$ sudo apt update && sudo apt upgrade openssl

If that doesn't install the version you expect (check by doing openssl version -a ), then try compiling it and installing manually:

wget https://www.openssl.org/source/openssl-1.1.0h.tar.gz
tar xzvf openssl-1.1.0h.tar.gz
cd openssl-1.1.0h
./config -Wl,--enable-new-dtags,-rpath,'$(LIBRPATH)'
make
make install

openssl version -a

should update OpenSSL to version 1.1.0h — linking should be handled automatically.