In this paper we present effective small scale formulations of the Secure Hash Standard; we focus on the SHA-2 family of algo- rithms, introducing new compact instances baptized SHA-16, SHA-32, and SHA-64. These may be useful for computing hashes and Message Authentication Codes (MACs) on small platforms where only 8-bit pro- cessors are available, such as in the case of Radio Frequency Identifi- cation (RFID) devices and embedded systems. To prove the soundness of our scaling approach, we analyze the cryptographic properties of the proposed constructions in terms of adherence to the Strict Avalanche Criterion (SAC) and of robustness to birthday attacks, by also compar- ing the results with the expected values from random functions. As an additional contribution, we complete the theoretical results for the bal- ance property of random functions, thereby also calculating the expected robustness of the original SHA-2 family versus birthday attacks. Keywords: hash functions, balance, SAC, small scale, RFID.
ECRYPT workshop on RFID and lightweight cryptography