Bitcoin Under Broken Crypto Primitives

Bitcoin’s security relies solely on cryptographic primitives, namely on digital signatures, hash functions and Merkle trees. This chapter discusses the security of the Bitcoin system if some primitives become weaker due to advances in cryptanalysis, an increasing computing power of the adversaries or improper software implementations. The chapter starts with a general overview of the primitives in use, explaining possible attack strategies against each of them, which is followed by combined attack strategies. The chapter closes by showing the consequences of Grover’s and Shor’s quantum algorithms for Bitcoin’s security.

Analysis of the Cryptographic Tools for Blockchain and Bitcoin

Blockchain is one of the most interesting emerging technologies nowadays, with applications ranging from cryptocurrencies to smart contracts. This paper presents a review of the cryptographic tools necessary to understand the fundamentals of this technology and the foundations of its security. Among other elements, hash functions, digital signatures, elliptic curves, and Merkle trees are reviewed in the scope of their usage as building blocks of this technology.

Sound Hashing Modes of Arbitrary Functions, Permutations, and Block Ciphers

Cryptographic hashing modes come in many flavors, including Merkle-Damgård with various types of strengthening, Merkle trees, and sponge functions. As underlying primitives, these functions use arbitrary functions, permutations, or block ciphers. In this work we provide three simple proofs, one per primitive type, that cover all modes where the input to the primitive consists of message bits, chaining value bits, and bits that only depend on the mode and message length. Our approach generalizes and simplifies over earlier attempts of Dodis et al. (FSE 2009) and Bertoni et al. (Int. J. Inf. Sec. 2014). We prove tight indifferentiability bounds for modes using each of these three primitive types provided that the mode satisfies some easy to verify conditions.