By Jonathan Katz (auth.)
Digital Signatures is the 1st complete account of the theoretical rules and methods utilized in the layout of provably safe signature schemes. as well as offering the reader with a greater knowing of the protection promises supplied by means of electronic signatures, the booklet additionally comprises complete descriptions and specified proofs for basically all recognized safe signature schemes within the cryptographic literature. A precious reference for college kids, professors, and researchers, electronic Signature Schemes can be utilized for self-study, as a complement to a path on theoretical cryptography, or as a textbook in a graduate-level seminar.
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Extra resources for Digital Signatures
Integer k¯ such that p(k) Observe that any PPT algorithm A inverting f can be used to forge signatures in Π as follows: given pk, run A to obtain a string r. If f (r) = pk, then this means that ¯ running Gen(1k ; r) yields a pair (pk, sk ). It is then trivial to output a forgery on any message m by computing the signature σ ← Signsk (m). , there may be multiple valid secret keys associated with the single public key pk. 2 Trapdoor Permutations A stronger notion than that of one-way functions is obtained by introducing an “asymmetry” of sorts whereby one party can efficiently accomplish some task that is infeasible for anyone else.
Signature verification: Algorithm Vrfy∗pk (m, σ ) is defined as follows: • Let L < 2k/4 be the length of m, and parse m into blocks m1 , . . , m , each of length k/4 (padding with 0s if necessary, though again not counting this padding when determining the length). • Parse σ as (r, σ1 , . . , σ ). • Output 1 if and only if = and Vrfy pk (r L i mi , σi ) = 1 for 1 ≤ i ≤ . exercise. We deal with the case of existential unforgeability, but the case of strong unforgeability is essentially the same.
4: From “short” messages to arbitrary length messages Let Π = (Gen, Sign, Vrfy) be a signature scheme for k-bit messages. Construct signature scheme Π ∗ = (Gen∗ , Sign∗ , Vrfy∗ ) for messages of length less than 2k/4 as follows: Key generation: Gen∗ (1k ) simply runs Gen(1k ) to generate keys (pk, sk). These are the public and secret keys, respectively. Signature generation: Algorithm Sign∗sk (m) is defined as follows: • Let L < 2k/4 be the length of m, and parse m into blocks m1 , . . , m , each of length k/4.