AES-GCM GHASH calculation; I'm trying to make an GHASH() function and need some clarification. 
Implementation is based on gcm-spec. Page 8 describes polynomial mult and page 27 has a "Test Case 2" which I use to verify result.

From my understanding X1 is a first round of GHASH function and effectively a result of multiplication of 16B of ciphertext and 'H'. From test case

X1&lt;-C * H
X1&lt;= '0388dace60b6a392f328c2b971b2fe78' * '66e94bd4ef8a2c3b884cfa59ca342b2e'


My implementation gives a different result. I also have tried some online tools which gave a totally different numbers as well :(

So the question is do I got it right that X1 is a result of multH(C,H)? 

Thanks
Yes, you a right; also after running the GF(128)/GCM multiplication test I confirm that the product of the test values is

0x0388DACE60B6A392F328C2B971B2FE78 $\times$ 0x66E94BD4EF8A2C3B884CFA59CA342B2E = 0x5E2EC746917062882C85B0685353DEB7