Jonathan Berger

Introduction to Cyber Security

TA 5: PKI – RSA

Based on slides of Benny Pinkas and Avishay Yanai

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Warmup exercise

Reminder - Plain/Textbook RSA

RSA - Exercise #1

Plain RSA – Exercise #2

Plain RSA – Exercise #3

Reminder - Plain/Textbook RSA Signature

Signatures vs. MACs

Signatures

MACs

Plain RSA signatures – Exercise #4

Plain RSA signatures – Exercise #4.1

RSA Signatures – Exercise #5

RSA Problems in the Real World

RSA Problems in the Real World (cont.)

RSA Problems in the Real World (cont.)

• The line in bold would cause an iteration to take more time, thus making this code suspectable to timing attacks allowing to leak the key

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• Furthermore, assume a smartcard that generates signatures
• It was found out that during multiplication the smartcard’s power consumption is higher. By measuring the length of this period it is possible to distinguish the number of multiplication – allowing an attacker to extract the key

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Lamport’s One-Time Signature Scheme

Lamport’s One-Time Signature Scheme - Example

Lamport’s One-Time Signature Scheme (cont.)

Yehuda’s One-Time Signature Scheme

• וַיֹּאמֶר מָה הָעֵרָבוֹן אֲשֶׁר אֶתֶּן לָּךְ וַתֹּאמֶר חֹתָמְךָ וּפְתִילֶךָ וּמַטְּךָ אֲשֶׁר בְּיָדֶךָ וַיִּתֶּן לָּהּ וַיָּבֹא אֵלֶיהָ וַתַּהַר לוֹ. (בראשית ל"ח:יח)

Exercise

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Questions?