It was a striking moment in the history of Russian dissidence. On December 27, 2013, three days after their release from remote penal colonies, Nadezhda  (known as Nadya) Tolokonnikova and Maria (known as Masha) Alyokhina were in a shiny Moscow TV studio, with Vladimir Bukovsky on the line from England. Bukovsky spent 12 years in Soviet prisons and psychiatric hospitals in the 1960s and 70s as punishment for repeated acts of public protest. Since his release in a prisoner swap in 1976, he has lived in Cambridge. In their TV press conference Tolokonnikova named Bukovsky as her hero: a true defender of human rights who never abandoned political activism. In her 21 months in prison, she had read and reread his autobiography, she said, leaving it as a precious gift to a fellow inmate on her release. In Tolokonnikova and Alyokhina Bukovsky recognised his own kind. The elderly dissident spoke with them naturally, as equals. He told them "from the heart" that he knew how hard it would be to adapt to life outside prison, that freedom would bring a mass of cares. He wished them luck. 

Tolokonnikova and Alyokhina have confronted the challenges of freedom with the same cool demeanour that they displayed during their trial and imprisonment. In their tour of Europe and the US in the days before the Sochi Winter Olympics, politicians, human rights activists and rock stars lined up to bask in their moral authority. The young women make a good double act but Tolokonnikova is the true performer. She combines beauty and charisma with a remarkable mind, and knows instinctively how to take the high ground. The Putin regime "did not just make Tolokonnikova a star, it turned her into a saint," the writer Dmitri Bykov said during her prison hunger strike. "She is now the best-known Russian after Putin himself."

To capture imaginations is to be caught up in other people's fantasies and vanities. On an Irish chat show, the hapless presenter told Tolokonnikova that Madonna had described Pussy Riot as "fellow freedom fighters". Incredulous for a moment, she threw back her head and laughed. Again, she explained (as she had done to the judge who sentenced her in July 2012 for "hooliganism motivated by religious hatred") that the "punk prayer", "Mother of God, Drive Away Putin", was not an attack on religion, but a political protest. Days later, at an Amnesty benefit in Brooklyn's vast Barclays Center, Madonna introduced Tolokonnikova and Alyokhina with a foul-mouthed speech about the dangers she herself had faced for the sake of freedom. In T-shirts decorated with the cross of the Teutonic knights, they thanked her graciously and proceeded to read aloud the court statements of Russia's May 6 prisoners, incarcerated for street protests since 2012.

Back home, Tolokonnikova and Alyokhina face a tougher crowd. Many believe they are in the pay of the West. More sympathetic members of the intelligentsia cannot reconcile the dazzling moral clarity and erudition of their court statements with the antics in the Cathedral of Christ the Saviour, never mind Tolokonnikova's participation (with her husband Petr Verzilov) in a notorious sex protest in the State Museum of Biology in 2008. Others wait for the magic to wear off. "Why is everyone so obsessed with those stupid girls?" the Moscow TV anchor and socialite Ksenia Sobchak reportedly complained.  

Other members of Pussy Riot have disowned Tolokonnikova and Alyokhina for succumbing to a cult of personality. Undeterred, the two showed up in Sochi in their Pussy Riot balaclavas. This is the kind of stubborn dissident persistence that Bukovsky taught. The local police obliged: they were first detained, then horsewhipped by Cossacks, creating another colourful spectacle for the assembled global media. They incorporated footage of it all into their song "Putin will teach you to love the Motherland".

In her excellent new book Words will Break Cement: The Passion of Pussy Riot (Granta Books, £9.99), Masha Gessen finds evidence enough of genius in the "punk prayer" itself, which she calls "a great work of art . . . a miracle". The dissident priest Gleb Yakunin regards the performance in the cathedral as a miracle in the full Christian sense of the word. Pussy Riot's words "black cassock, gold epaulettes" drove "to the very heart of Patriarch Kirill", he said. During their imprisonment, Yakunin composed a verse cycle in Pussy Riot's honour, The Pussiniad. He too did time in prisons and labour camps in the Soviet period. In 1993, five years after his amnesty, the Russian Orthodox Church excommunicated him for exposing its infiltration by the KGB. Yakunin had unmasked Kirill as a high-ranking agent codenamed Mikhailov.

"Passion, honesty and naivety are superior to hypocrisy, mendacity and false modesty that disguises crime," Tolokonnikova said in court. These are words for a dissident to live by. Yakunin considers Tolokonnikova a person graced with "exceptional gifts". He believes that once they have established their new human rights group, Justice Zone, she and Alyokhina will found a political party — a "genuine Christian democratic party" — that will drive out Putin and transform Russia. That really would be a miracle.