The Kolmogorov birthday paradox

The bosonic birthday paradox

We motivate and prove a version of the birthday paradox for k identical bosons in n possible modes. If the bosons are in the uniform mixed state, also called the maximally mixed quantum state, then we need k p n bosons to expect two in the same state, which is smaller by a factor of p 2 than in the case of distinguishable objects (boltzmannons). While the core result is elementary, we generaliz...

Breaking H2-MAC Using Birthday Paradox

We propose an efficient method to break H-MAC, by using a generalized birthday attack to recover the equivalent key, under the assumption that the underlying hash function is secure (collision resistance).

Breaking H-MAC Using Birthday Paradox

H-MAC was proposed to increase efficiency over HMAC by omitting its outer key, and keep the advantage and security of HMAC at the same time. However, as pointed out by the designer, the security of H-MAC also depends on the secrecy of the intermediate value (the equivalent key) of the inner hashing. In this paper, we propose an efficient method to break H-MAC, by using a generalized birthday at...

Beating the Birthday Paradox in Dining Cryptographer Networks

Kolmogorov Complexity, String Information, Panspermia and the Fermi Paradox

Bit strings rather than byte files can be a mode of transmission both for intelligent signals and for travels of extraterrestrial life. Kolmogorov complexity, i.e. the minimal length of a binary coded string completely defining a system, can then, due to its universality, become a key concept in the strategy of the search of extraterrestrials. Evaluating, for illustration, the Kolmogorov comple...