Small Public Keys and Fast Verification for <img src="/fulltext-image.asp?format=htmlnonpaginated&src=Q787280033544114_html\978-3-642-23951-9_31_Chapter_TeX2GIF_IEq1.gif" border="0" alt="$\mathcal{M}$" />ultivariate <img src="/fulltext-image.asp?format=htmlnonpaginated&src=Q787280033544114_html\978-3-642-23951-9_31_Chapter_TeX2GIF_IEq2.gif" border="0" alt="$\mathcal{Q}$" />uadratic Public Key Systems