In Libgcrypt before 1.7.7, an attacker who learns the EdDSA session key (from side-channel observation during the signing process) can easily recover the long-term secret key. 1.7.7 makes a cipher/ecc-eddsa.c change to store this session key in secure memory, to ensure that constant-time point operations are used in the MPI library.
The mixing functions in the random number generator in Libgcrypt before 1.5.6, 1.6.x before 1.6.6, and 1.7.x before 1.7.3 and GnuPG before 1.4.21 make it easier for attackers to obtain the values of 160 bits by leveraging knowledge of the previous 4640 bits.
Libgcrypt before 1.6.5 does not properly perform elliptic-point curve multiplication during decryption, which makes it easier for physically proximate attackers to extract ECDH keys by measuring electromagnetic emanations.
Libgcrypt before 1.5.4, as used in GnuPG and other products, does not properly perform ciphertext normalization and ciphertext randomization, which makes it easier for physically proximate attackers to conduct key-extraction attacks by leveraging the ability to collect voltage data from exposed metal, a different vector than CVE-2013-4576.
GnuPG before 1.4.14, and Libgcrypt before 1.5.3 as used in GnuPG 2.0.x and possibly other products, allows local users to obtain private RSA keys via a cache side-channel attack involving the L3 cache, aka Flush+Reload.