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Digital Signatures

A cryptographic technique using asymmetric key cryptography to verify the authenticity and integrity of digital documents or messages.
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The statement of the theorem

Let (PKA,SKA)(PK_A, SK_A) be the public/secret key pair for signer AA, and H:M→HH: \mathcal{M} \to \mathcal{H} be a collision-resistant hash function mapping messages M\mathcal{M} to hash values H\mathcal{H}. To sign a message MM: \n1. Compute the hash digest: h=H(M)h = H(M). \n2. Generate the signature σ\sigma: σ=SignSKA(h)\sigma = \text{Sign}_{SK_A}(h). \nVerification by recipient BB: \n1. Compute the expected hash: h′=H(M)h' = H(M). \n2. Verify the signature using AA's public key: VerifyPKA(h′,σ)=True\text{Verify}_{PK_A}(h', \sigma) = \text{True}. \nThe security relies on the computational difficulty of solving the underlying hard problem (e.g., factoring or discrete logarithm) to forge σ\sigma without SKASK_A.
Source: Wikipedia