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Introduction to Modern Cryptography
Interactive Learning Session Week 7: Digital Signatures Thursday, 17 March 2016, 15:00-17:00
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Plain RSA signatures Give a no-message attack, i.e. a forgery without querying the signature oracle Remember how to forge a signature on an arbitrary message by requesting signatures on two other messages
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Encoded RSA Signatures
See homework!
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RSA Full-Domain-Hash Signature
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Schnorr Identification Scheme
𝑦 −1 =751 𝐼=3 21 =734 𝐼=3 1 =3 𝐼=3 𝑘 = … 𝑟=391 𝑟=665 𝑟=250 X=666 s = 391 * mod 1012 𝑠=343 𝑠=647 𝑠= ? 3 343 ⋅ =734 3 647 ⋅ =3 3 𝑠 ⋅ = 3 𝑘 Use your eavesdropped knowledge and try identify yourself!
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Schnorr Identification Scheme
𝑦 −1 =751 𝐼=3 21 =734 𝐼=3 1 =3 𝐼=3 776 =858 𝑟=391 𝑟=665 𝑟=250 … X=666 s = 391 * mod 1012 𝑠=343 𝑠=647 𝑠=296 3 343 ⋅ =734 3 647 ⋅ =3 3 296 ⋅ =858 Generate a valid (and properly distributed) transcripts yourself!
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Schnorr Identification Scheme
𝑦 −1 =751 𝐼=3 21 =734 𝐼=3 1 =3 𝐼=3 776 =858 𝑟=391 𝑟=665 𝑟=250 𝑠=343 𝑠=647 𝑠=296 124^(-1) mod 1012 = 482 3 343 ⋅ =734 3 647 ⋅ =3 3 296 ⋅ =858 𝐼=3 21 =734 𝑟=390 Extract the secret key! 𝑠=689 3 689 ⋅ =734
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Schnorr Identification Scheme
𝑦 −1 =751 𝐼=3 21 =734 𝐼=3 1 =3 𝐼=3 776 =858 𝑟=391 𝑟=665 𝑟=250 𝑠=343 𝑠=647 𝑠=296 124^(-1) mod 1012 = 482 3 343 ⋅ =734 3 647 ⋅ =3 3 296 ⋅ =858 𝐼=3 21 =734 𝑟=390 Extract the secret key! 343− −390 =666 𝑚𝑜𝑑 1012 𝑠=689 3 689 ⋅ =734
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