## Schedule

Read: Chapter 3: Mechanics of Bitcoin, from Arvind Narayanan, Joseph Bonneau, Edward Felten, Andrew Miller, Steven Goldfeder. Bitcoin and Cryptocurrency Technologies. Sections 3.2 and 3.3 are about bitcoin scripts, and should be read carefully. (You should read the whole chapter, but those sections are most relevant to today’s class.)

Friday, October 9: Problem Set 2 (8:29pm).

Monday, October 19: Midterm Exam

# Hash Collisions!

Private Key: pick a random number, k.
Public Key: compute (Ux, Uy) = Gk

(elliptic curve multiplication, G is specified generator point)
Ux and Uy are 32 bytes each.

The bitcoin address is (|| is bitstring concatenation):

raw = 1 || RIPEMD160(SHA256(Ux || Uy))
RIPEMD output is 160 bits (20 bytes) + one byte for 1
checksum = first 4 bytes of SHA256(SHA256(raw))
Compute a checksum using SHA256 double hash
convert to printable, unambiguous characters

How important is pre-image resistance for the security of bitcoin addresses?

How important is collision resistance for the security of bitcoin addresses?

How important is pre-image resistance for the integrity of bitcoin’s proof-of-work?

How important is collision resistance for the integrity of bitcoin’s proof-of-work?

Xiaoyun Wang and Hongbo Yu, How to Break MD5 and Other Hash Functions, EuroCrypt 2005.

# Bitcoin Script

Transaction outputs in bitcoin are protected by locking scripts, and must be unlocked by unlocking scripts. The scripts are written in a simple (compared to, say, the Java Virtual Machine language, but quite complex and poorly specified for what one might expect would be needed for bitcoin transactions) stack-based language. A transaction output is not unlocked unless an unlocking script is provided such that the result of executing the unlocking script, followed by executing the locking script, is a stack with value True on top (and no invalid transaction results during the execution).

Some script instructions:

 Opcode Input Output Description OP_1 - 1 Pushes a 1 (True) on the stack OP_DUP a a a Duplicates the top element of the stack OP_ADD a b (a+b) Pushes the sum of the top two elements. OP_EQUAL a b 0 or 1 Pushes 1 if the top two elements are exactly equal, otherwise 0. OP_VERIFY a - If a is not True (1), terminates as Invalid. OP_RETURN - - Terminates as Invalid. OP_EQUALVERIFY a b - If a and b are not equal, terminates as Invalid. OP_HASH160 a H(a) Pushes bitcoin address, RIPEMD160(SHA256(a)).

Is the bitcoin scripting language Turing-complete?

If you are not clear on what Turing-complete means (and why real machines are not ideal), see Dori-Mic and the Universal Machine!