# Aggregate and Verifiably Encrypted Signatures from Bilinear Maps

**Authors:**

*D. Boneh, C. Gentry, H. Shacham, and B. Lynn*

** Abstract: **

An aggregate signature scheme is a digital signature that supports
aggregation: Given *n* signatures on *n* distinct messages
from *n* distinct users, it is possible to aggregate all these
signatures into a single short signature. This single signature (and
the *n* original messages) will convince the verifier that the
*n* users did indeed sign the *n* original messages (i.e.,
user *i* signed message *M _{i}* for

*i*=1,...,

*n*). In this paper we introduce the concept of an aggregate signature scheme, present security models for such signatures, and give several applications for aggregate signatures. We construct an efficient aggregate signature from a recent short signature scheme based on bilinear maps due to Boneh, Lynn, and Shacham. Aggregate signatures are useful for reducing the size of certificate chains (by aggregating all signatures in the chain) and for reducing message size in secure routing protocols such as SBGP. We also show that aggregate signatures give rise to verifiably encrypted signatures. Such signatures enable the verifier to test that a given ciphertext

*C*is the encryption of a signature on a given message

*M*. Verifiably encrypted signatures are used in contract-signing protocols. Finally, we show that similar ideas can be used to extend the short signature scheme to give simple ring signatures.

** Reference:**

In proceedings of Eurocrypt 2003, LNCS 2656, pp. 416-432, 2003

**Full paper:**
pdf
[first posted
5/2003 ]